TS Inter 1st Year English Grammar Transformation of Sentences

Telangana TSBIE TS Inter 1st Year English Study Material Grammar Transformation of Sentences Exercise Questions and Answers.

TS Inter 1st Year English Grammar Transformation of Sentences

Q. No. 13 (4 × 1 = 4)

A. VOICE

The term ‘voice’ in grammar refers to one aspect of the verb. If the verb group in a sentence has ‘be + pp of the verb’, that sentence is said to be in the passive voice. If any of or both the elements (be + V3) are missing in the structure of the verb, the sentence is said to be in the active voice. (వాక్యంలోని verb groupలో ‘be + V3 ఉంటే ఆ వాక్యాన్ని passive voice అని, be + V3 లలో ఏ ఒక్కటి లేకున్నా active voice అని అంటారు.)

If the verb is in the passive form, the subject of that sentence is just the ‘sufferer’ of the action indicated by the verb, (verb passive లో ఉంటే ఆ వాక్యంలోని subject, verb సూచించిన పని ఫలితాన్ని అనుభవిస్తుంది. అందుకనే ఈ రూపానికి ‘passive’ ‘సోమరిగా’, ‘పనిచేయకుండా’ అని పేరు.)

If the verb group is in the active voice, the subject of that sentence is the ‘doer’ of the action shown by the verb. (Verb Active voice లో ఉన్నప్పుడు, ఆ వాక్యం యొక్క subject, verb సూచించిన పనిని చేస్తుంది. అందుకే ఈ రూపానికి ‘Active చురుకుగా పనిచేస్తున్న’ అని పేరు)

If the doer of an action is either unimportant or unknown, the passive structure is natural. (పనిచేసినవారు ప్రధానం కాకున్నా, తెలియకున్నా, passive నిర్మాణాలు సహజంగా ఉంటాయి. )

Someone admitted him to the hospital immediately. (AV)
He was admitted to the hospital immediately. (PV)
He was killed in the war.
Rice is grown in many parts of Telangana and Andhra Pradesh.
English is spoken all over the world.
The roads have been swept The syllabus was changed last year.
The shop has been closed.
The doubts have been cleared by my teacher Agent

TS Inter 1st Year English Grammar Transformation of Sentences

Transformation of sentences from one voice to the other involves five steps.

1. The object in the Active Voice sentence becomes the subject in the Passive Voice sentence.
Ex : They made (ten kites)Object (A.V)
(Ten kites) Subject were made by them. (P.V.)

If there are two objects in the A.V. sentence, either of them can be made the subject in the PV. sentence.
TS Inter 1st Year English Grammar Transformation of Sentences 1
An interesting book was given to her brother by her.

Active :

  1. I told them an interesting story.
  2.  I told an interesting story to them.

Passive:

  1. An interesting story was told to them.
  2. They were told an interesting story.

2. A suitable ‘be’ form is to be introduced. This is the most important step. Selection of the right be’ form is based on two factors : (a) the number and person of the subject in the passive voice and (b) the tense of the verb in the Active Voice.
The following table helps one select the right be form.

S. No. Subject in the Passive Voice Tense of the verb in Active Voice ‘Be form to be used in the Passive Voice
1 I Simple Present am
2 he, she, it singlar nouns Simple Present is
3 We, you, they plural nouns Simple Present are
4 I, he, she, it singular nouns Simple Past was
5 We, you, they plural nouns Simple Past were
6 I Present Continuous am being
7 he, she, it singular nouns Present Continuous is being
8 We, you, they plural subjects Present Continuous are being
9 1, he, she, it singular nouns Past Continuous was being
10 We, you, they plural subjects Past Continuous were being
11 ‘ he, she, it Singular nouns Present Perfect has been
12 I, we, you, they plural nouns Present Perfect have been
13 Any subject Past Perfect had been
14 Any subject will/shall/can/ may/would should/could/ might/ must, etc. will, etc. +be
15 Any subject will etc + have will, etc. + have been

TS Inter 1st Year English Grammar Transformation of Sentences 2

3. The main verb in the Active Voice sentence is to be changed into its past participle form. One must know the correct past participle forms of irregular verbs.
TS Inter 1st Year English Grammar Transformation of Sentences 3

TS Inter 1st Year English Grammar Transformation of Sentences

4. The preposition ‘by’ is used.

5. The subject in the Active voice sentence is made the object of the preposition ‘by’ in the passive voice sentence.
Ex : He broke the glass. (A.V.)
The glass was broken by him. (P.V.)
prep+object
If the subject in the A.V. sentence is either unimportant or a general one, ‘by + object’ may be dropped.
Ex : Someone removed the dead snake. (A.V.)
The dead snake was removed. (P-V.)
(by someone’ is dropped)
People call him ‘Babuji’. (A.V.)
He is called ‘Babuji’. (‘by people’ not necessary) (P.V.)

CHANGE IMPERATIVE SENTENCES INTO PASSIVE

We follow a slightly different method to change imperative sentences from the A.V. to the P.V. (Sentences with dropped subject and with V + object structure, conveying a request or an order are called imperative sentences.)
1. The passive voice sentence begins with ‘Let’.
Ex : Close the door. (A.V.) imperative
Let the door be closed. (P.V.)

2. The object in the A.V. sentence becomes the subject in the RV. sentence.
Answer this question. (A.V.)
Object
Let this question be answered. (P.V.)
Subject

3. The ‘be’ form ‘be’ is introduced.
(Whatever be the subject or the tense form, it is always ‘be’ in imperative sentences.)
Ex : Clean the room. (A.V.)
Let the room be cleaned. (P.V.)

TS Inter 1st Year English Grammar Transformation of Sentences

4. The M.V. is changed into its Past Participle form.
Ex : Paint this chair. (A.V.)
M.V.
Let this chair be painted. (P.V.)
As the subject is not explicit in the imperative sentences, the need to use ‘by’ and its object doesn’t arise, while changing imperative sentences into the passive voice.

CHANGING QUESTIONS INTO PASSIVE

Study carefully the transformation of the interrogative sentences into the passive voice.
Ex : Who brought this book ? (A.V.)
By whom was this book brought ? (P.V.)
All the steps followed here are exactly like those we follow in changing the declarative sentences. But the word order is different.
By whom + be + Subject + M.V in PP + etc ?
Nbw, notice the transformation of Questions with other ‘wh’ words.
Ex : Where did you put my pen ? (A.V.)
Where was my pen put ? (P.V.)
‘Wh’ word + be + subject + MV in PP ?
Observe how ‘yes / no’ Questions are rewritten in the passive voice.
Have you solved the problem ? (A.V.)
Has the problem been solved ? (P.V.)
Helping Verb + Subject + be + MV in pp + etc. ?

EXAMPLES
1. Advertise the post. (A.V.)
Let the post be advertised. (P.V.)

2. America imports Indian tea. (A.V.)
Indian tea is imported by America. (P.V.)

3. The auditors are checking the accounts. (A.V.)
The accounts are being checked by the auditors. (P.V.)

4. They have sent the information. (A.V.)
The information has been sent. (P.V.)

5. Hurry can gain nothing. (A.V.)
Nothing can be gained by hurry. (P.V.)

TS Inter 1st Year English Grammar Transformation of Sentences

6. Put the culprit in prison. (A.V)
Let the culprit be put in prison. (P.V.)

7. John teaches us English. (A.V.)
We are taught English by John. (P.V.)
English is taught to us by John. (P.V.)

8. The Manager sent a mail yesterday. (A.V)
A mail was sent by the manager yesterday. (P.V)

9. The conductor has issued tickets to all the passengers. (A.V.)
Tickets have been issued to all the passengers. (P.V.)
All the passengers have been issued tickets. (P.V.)

10. Narayana Murthy started Infosys. (A.V.)
Infosys was started by Narayana Murthy. (P.V.)
Look at the following sentence and observe the changes.
TS Inter 1st Year English Grammar Transformation of Sentences 4

Tense Active Voice Passive Voice
Simple present Floods cause a lot of damage. am/are/is+v3(past participle)
A lot of damage is caused by floods
Present continuous The gardener is watering the plants. am/are/is+being+v3
The plants are being watered by the gardner.
Present perfect We have organized a special programme for children. have/has+been+v3 A special programme has been organized for children (by us).
Simple past Raghavendar Rao directed the film ‘Annamayya’. was/were + v3
The film Annamayya’ was directed by Raghavendar Rao.
Past continuous When they were shifting the patient to the ICU, he died. Was / were + being v3
When the patient was being shifted to the ICU, he died.
Past perfect The driver had already alerted the passengers before the robbers entered the bus. had + been + v3
The passengers had already been alerted before the robbers entered the bus.
Simple future I will conduct a spelling – contest tomorrow. shall/will + be + v3
A spelling – contest will be conducted tomorrow.
Future perfect They will have decorated the hall by evening. shall / will + have + been + v3
The hall will have been decorated by evening.
The future of intention (be going to) Keeravani is going to compose music this song. is going to be + v3
Music is going to be composed by Keeravani for this song.
Modal veibs (should, must, ought to, can, etc.) I will type this letter tomorrow. should/would/must/tought/can + be + v3
ThisletowiBbetypedbyrnetorrKxrcw.
It is said (that) or subject+is said to be Villagers say that there is a ghost in the old building. It is said that there is a ghost in the old building.
Imperative Check the spelling. Let…. be + v3
Let the spelling be checked.

EXERCISES

I. Change the following sentences into the passive voice.

1. We practise yoga every day in the morning.
2. He will make all the arrangements.
3. The judge declared the verdict.
4. They had already announced the results before we entered the hall.
5. Many students sacrificed their precious lives for Telangana.
6. The students borrowed some books from the library.
7. Nobody can save him.
8. How much loan amount has the Bank sanctioned ?
9. One should wear a helmet while riding a two-wheeler.
10. Money alone cannot solve all problems.
11. Switch off the lights.
12. Please maintain silence in the prayer hall.
13. We have to undergo many formalities for getting a visa.
14. The workers called off the strike.
15. The teacher is explaining the lesson.
16. The postman will deliver the letters at noon.
Answers:
1. Yoga is practised by us every day in the morning.
2. All the arrangements will be made by him.
3. The verdict was declared by the judge.
4. The results had already been announced before we entered the hall.
5. Their precious lives were sacrificed by many students for Telangana.
6. Some books were borrowed by the students from the library.
7. He cannot be saved.
8. How much loan amount has been sanctioned by the Bank ?
9. Helmet should be worn while riding a two-wheeler.
10. All problems cannot be solved by money.
11. Let the lights be switched off.
12. Let silence be maintained in the prayer hall.
13. Many formalities have to be undergone for getting a visa.
14. The strike was called off by the workers.
15. The lesson is being explained by the teacher.
16. The letters will be delivered by the postman at noon.

TS Inter 1st Year English Grammar Transformation of Sentences

II. Change the following sentences into the active voice.

1. The parcels will be delivered at any time (by the courier agents)
2. Surya was invited to tea by Chandra.
3. Traffic rules should be followed.
4. Vegetables are washed before cooking.
5. Let the following sentences be changed into the passive voice.
6. How many times were you reminded of the medicine ?
7. Let the dustbin be kept away from the eatables.
8. Hpve all your friends been invited to your birthday ?
9. Every sentence can’t be changed into the passive voice.
10. If the ointment isn’t applied to the wound, it will not heal.
11. My brother has never been beaten at chess by anyone in his school.
12. It is believed that Sammakka and Saralamma are the saviors of their lives in times of crisis by the villagers.
Answers:
1. The courier agents will deliver the parcels at any time.
2. Chandra invited Surya to tea.
3. One (We) should follow traffic rules.
4. We wash vegetables before cocking.
5. Change the following sentences into the passive voice.
6. How many times did I (we) remind you of the medicine ?
7. Keep the dustbin away from the eatables, (food)
8. Have you invited all your friends to your birthday party ?
9. One (We) can’t change every sentence into the passive voice.
10. If you don’t apply the ointment to the wound, it will not heal.
11. No one in his school has ever beaten my brother in chess.
12. The villagers believe that Sammakka and Saralamma are the saviours of their lives in times of crisis.

TS Inter 1st Year English Grammar Transformation of Sentences

III. Change the following sentences into the passive voice.

1. Rainwater fills potholes on roads.
2. He is buying a TV set at the moment.
3. I have been growing plants since 1990.
4. They were reading the newspaper.
5. She had answered it already.
6. I will write an essay tonight.
7. You will have posted it by Monday.
8. Can she play the violin ?
9. They may not telecast it.
10. One must do one’s duty.
11. Gall in the doctor.
12. Close the door.
13. The Government has to do it.
14. Someone has already cast my vote.
15. Who could help him ?
Answers:
1. Potholes on roads are filled with (by) rainwater.
2. A TV set is being bought by him at the moment.
3. Plants have been being grown by me since 1990.
4. TKe newspaper was being read (రెడ్) by them.
5. It had already been answered by her.
6. An essay will be written by me tonight.
7. It will have been posted by you by Monday.
8. Can the violin be played by her ?
9. It may not be telecast, (by them)
10. One’s duty must be done, (by one)
11. Let the doctor be called in.
12. Let the door be closed.
13. It has to be done by the Government.
14. My vote has already been cast, (by someone)
15. By whom could he be helped ?

TS Inter 1st Year English Grammar Transformation of Sentences

IV. Change the following into Active Voice.

1. He was seen crossing the road.
2. You are advised to be careful.
3. Let the picture be seen by me.
4. Her purchases were paid for by me.
5. There are no shops to be let.
6. She has been selected their monitor (by the class)
7. It is said that the earth is round.
8. The road had been repaired.
9. I am surprised at this news.
10. It is hoped that I shall win.
Answers:
1. We saw him crossing the road.
2. We advise you to be careful.
3. Let me see the picture.
4. I paid for her purchases.
5. There are no shops to let (out).
6. The class has selected her their monitor.
7. People say that the earth is round.
8. They had repaired the road.
9. This news surprises me.
10. I hope that I shall win.

TS Inter 1st Year English Grammar Transformation of Sentences

V. Change the following sentences into the passive voice.

1. I have made a mistake.
2. Your students will respect you a great deal more for your frankness and honesty.
3. Call the attention of your near neighbour at the table to the excellence of the coffee.
4. Do you apply Pythagoras Theorem or Newton’s Law of Gravity ?
5. Rahul lost a quarter mark in English.
6. She planted trees; fenced, watered and guarded them.
7. Their hope and encouragement gave me greater strength.
8. Instantly remove that hatter.
Answers:
1. A mistake has been made by me.
2. You will be respected by your students a great deal more for your frankness and modesty.
3. Let the attention of your near neighbour at the table be called to the excellence of the coffee.
4. Is Pythagoras Theorem or Newtons Law of Gravity applied by you ?
5. A quarter mark in English was lost by Rahul.
6. Trees were planted, fenced, watered and guarded by her.
7. I was given greater strength by their hope and encouragement. (OR) Greater strength was given to me by their hope and encouragement.
8. Let that hatter be removed instantly.

TS Inter 1st Year English Grammar Transformation of Sentences

B. DIRECT SPEECH AND INDIRECT SPEECH/REPORTED SPEECH

Sometimes it becomes necessary to report a person’s words. It can be done in two different ways. One -way is to reproduce the actual words of the speaker. The speaker’s actual words are shown in quotation marks in writing. This kind of reporting is called the ‘Direct Speech’.

The other kind is to express the idea of the speaker in the reporter’s words. This type is referred to as the ‘Indirect Speech’.
(ఒక వ్యక్తి అన్న మాటలకు అన్నట్లుగా తిరిగి చెబితే Direct Speech. కేవలం భావం మాత్రమే తిరిగి చెబితే Indirect Speech.)

The sentence in the Direct Speech has two parts. They are (a) the part outside the quotation marks (called the reporting part and (b) the part within the quatation marks (called the reported part).
TS Inter 1st Year English Grammar Transformation of Sentences 5
The verb in the reporting part is called “the reporting verb.”
“Don’t make a noise,” said the teacher. (Reporting verb)
To change a sentence from the direct speech to the indirect speech, the following steps are to be followed.

1. The reporting part is to be written first. This is applicable only when the reporting part is either in the middle or at the end of the sentence.

Direct Speech :
“Ramu has solved all the problems.” said the teacher (Reporting part at the end)
Indirect Speech :
The teacher said that Ramu had solved all the problems. Reporting part begins the sentence.

TS Inter 1st Year English Grammar Transformation of Sentences

2. The order of the words in the reporting part is arranged as “Subject + Verb.” This is applicable only when this order is not followed in the direct speech sentence.
TS Inter 1st Year English Grammar Transformation of Sentences 6

3. The reporting verb is changed to words like ordered, requested, enquired, told, asked, ad-vised exclaimed, depending on the meaning of the reported part.
TS Inter 1st Year English Grammar Transformation of Sentences 7

4. The quotation marks and the comma between the reporting and reported parts are removed in the indirect speech.
Ex : The boy said,” This plant has grown very tall.” (D.S.)
The boy said that plant had grown very tall. (I.S.)

5. A suitable connecting word is used to connect the reporting and reported parts. The selection of the right connecting word needs careful observation.
The following table will help you to select the right word.

SI.No. Sentence in quotation marks Connecting word
1. Assertive or Exclamatory that
2. Imperative to
3. Yes/No type Question if or whether
4. ‘Wh’ type Question No connecting word

TS Inter 1st Year English Grammar Transformation of Sentences 8

TS Inter 1st Year English Grammar Transformation of Sentences

6. The pronouns in the reported part are to be changed suitably. This depends on the first speaker, the speaker’s listener, the reporter and the reporter’s listener. One has to ensure that the original speaker’s intention is correctly reported. (Indirect speech లోకి మార్చేటప్పుడు, ఎవరు ఎవరితో అన్న మాటలను తిరిగి ఎవరు ఎవరికి చెబుతున్నారు అనే దానిని బట్టి pronouns మారతాయి. మొదట మాట్లాడిన వ్యక్తి ఉద్దేశ్యం మారకుండా సరిగ్గా చెప్పడం అవసరం.)

Now notice the following examples carefully :
a) The teacher said to you, ‘You are late again.” (D.S.)
The teacher told you that you were late again. (I.S.) ‘you’ not changed.

b) The teacher said to me, “You have improved your performance.” (D.S.)
The teacher told me that I had improved my performance.
You → 1 & Your → my

c) The teacher said to Geetha, “You have to submit your assignments tomorrow.” (D.S.)
The teacher told Geetha that she had to submit her assignments the following day. (I.S.)
You → she and you → her

d) The teacher said to Prudhvi, “When will you finish your computer course” ? (D.S.)
The teacher asked Prudhvi when he would finish his computer course. (I.S.)
You → he and your → his

e) The teacher said to the students, “You must consult your parents.” (D.S.)
The teacher told the students that they should consult their parents. (I.S.)
You → they and Your → their
As the examples a, b, c, d and e show you, pronouns change in accordance with the speaker’s reference to a person/persons.

7. In changing sentences into the indirect speech, the tense form of the verbs in the reported part is to be changed. This is the most important part of the transformation. This is done in accor-dance with the concept popularly known as “the sequence of tenses.” (Reported part లోని verbs tenses మార్చడం అతి ప్రధాన భాగము దీనిని ‘Sequence of tenses’ అనే నియమానుసారంగా )
The following table clearly shows when and how to change the tense.
TS Inter 1st Year English Grammar Transformation of Sentences 9
TS Inter 1st Year English Grammar Transformation of Sentences 10
TS Inter 1st Year English Grammar Transformation of Sentences 11

TS Inter 1st Year English Grammar Transformation of Sentences

8. The next step in the transformation from the direct to the indirect is to change the adjectives or adverbs showing ‘nearness to those showing ‘distance as explained in the following table:

SI. Ajjective / Adverb Adjective or Adverb
No. in ‘direct speech’ in ‘indirect speech’
1. this that
2. these those
3. here there
4. now then
5. today/tonight that day/that night
6. yesterday the previous day/ the day before
7. tomorrow the next day/the following day
8. ago before

9. The transformation from the direct to the indirect involves a change in the word order. This principle is applicable to interrogative and exclamatory sentences only. This is exemplified in the table given below.

SI. No. Word order in Direct Speech with examples Word order in Indirect Speech with examples
1 … Helping verb+subject+ Main verb
… said … “are you coming”…
subject-1-Helping verb+Main
verb
asked … you were / coming
2 Helping verb 4- subject + Main verb
said … do you like …
subject +…… + Main verb

asked … he …. liked

3 ‘wh’ word+adj/adv+ subject + verb said “How beautiful + the toy is … subject + verb + intensifier adj/adv exclaimed – the toy was very n beautiful.

Note that the ‘wh’ word in exclamatory sentences doesn’t have the meaning of a question. It just emphasises the adjective or adverb. Hence this ‘wh’ word in the direct speech becomes the intensifier ‘very’ in the indirect speech.

TS Inter 1st Year English Grammar Transformation of Sentences

10. The last step in this kind of transformation is to change the ‘Question mark’ or the ‘exclamatory mark’ into a full stop in the indirect speech.

You must note that all the Ten steps detailed above are not necessary to follow in the case of all kinds of sentences. You carefully check which steps are necessary and which steps are not necessary to follow in changing a given sentence.

EXAMPLES

1. Direct speech:
Reporter : Are you a vegetarian or non-vegetarian?
Bernard Shaw : I don’t want to make my stomach a burial ground for dead animais.
Reporter : How wonderful your answer is!
Bernard Shaw : Thank you for your compliments.

Indirect speech :
A reporter asked the famous writer Bernard Shaw whether he was a vegetarian or a non-vegetarian. Bernard Shaw replied that he didn’t want to make his stomach a burial ground for dead animals. The reporter responded that it was a wonderful answer. Bernard Shaw thanked him for his compliments.

3. Gandhi said, “I respect all religions.” (D.S)
Gandhi said that he respected all religions. (I.S)

4. He said to me, “Who is your favourite politician ?” (D.S)
He asked me who my favourite politician was (I.S)

5. An American said, “How hard-working Indians are !” (D.S)
An American exclaimed that Indians were hard-working. (I.S)

6. A customer said to the manager, “Can you do me a favour ?” (D.S)
A customer requested the manager to do him/her a favour. (I.S)

7. Abdul Kalam said, “I have come from a poor background.” (D.S)
Abdul Kalam said that he had come from a poor background. (I.S)

8. The teacher said to a student, “Are you confident ?” . (D.S)
The teacher asked a student whether he / she was confident. (I.S)

TS Inter 1st Year English Grammar Transformation of Sentences

9. Amulya says, “I am learning music”. (D.S)
Amulya says that she is learning music. (I.S)

10. The teacher said,’The sun rises in the east.” (D.S)
The teacher said that the sun rises in the east. (I.S)

11. Dr. Rahul said, “1 will try my best to save the patient.” (D.S)
Dr. Rahul said that he would try his best to save the patient. (I.S)

12. Yasoda said to Krishna, “You are mischievous and trouble me a lot. (D.S)
Yasoda told Krishna that he was mischievous and troubled her a lot.” (I.S)

13. They said, “The Minister has at last unveiled the statue today. It has not been unveiled for so many months for reasons unknown.” (D.S)
They said that the Minister had at last unveiled the statue that day and added (that) it had not been unveiled for so many months for reasons unknown. (I.S)

14. A North Indian friend of mine said, “Unlike in Delhi, the climate in Hyderabad is moderate.” (D.S)
A North Indian friend of mine remarked that unlike in Delhi, the climate in Hyderabad was moderate. (I.S)

15. “How is your health ?” said Dr. Charan to a patient. (D.S)
Dr. Charan asked a patient how his/her health was. (I.S)

16. A stranger said to me, “Where is Golconda ?”. (D.S)
A stranger asked me where Golconda was. (I.S)

17. “Dheeraj said to his friend, “Are you interested in teaching ?” (D.S)
Dheeraj asked his friend if/whether he was interested in teaching. (I.S)

18. I said my daughter, “Do you want to do B.Tech. or B.Sc ?” (D.S)
I asked my daughter whether she wanted to do B.Tech or B.Sc. (I.S)

II. Study the following examples and observe how statements are changed into the indirect speech.

Direct Speech Indirect Speech
1. Simple present
He said, “I have many problems.”
1. Simple past
He said that he had many problems.
2. Present continuous
“I am reporting her words,” he said.
2. Past continuous
He said that he was reporting her words.
3. Present perfect
The cashier in the Bank said, “I have sent a report.”
3. Past perfect
The cashier in die Bank said that he had sent a report.
4. Present perfect continuous
A student said, “I have been trying to speak English for two years.”
4. Past perfect continuous
A student said that he had been trying to speak English for two years.
5. Simple past
‘I forgot my hall ticket,” a candidate said.
5. Simple pastíPast perfect
A candidate said that he / she had forgotten his hail ticket.
6. Past continuous
“I was watering the plants in the garden,” she said.
6. Past continuous / Past per.cont.
She said that she had been watering the plants in the garden.
7. Simple future
“We will move to Hyderabad next year, “Rajitha said.
7. Rajitha said that they would move to Hyderabad the following year.
8. The English teacher said to the class, “I will tell you the difference between the two sentences.” 8. The English teacher told the class that he would tell them the difference between the two sentences.

TS Inter 1st Year English Grammar Transformation of Sentences

III. Study the following examples and observe how questions are changed into indirect speech.

TS Inter 1st Year English Grammar Transformation of Sentences 18

IV. All the verbs are changed into infinitives [to + verb (v1)] while reporting imperative sentences.

Direct Speech Indirect Speech
1. Order/Command
The Site engineer said to his colleagues : “Don’t deviate from the plan.”
1. The Site engineer ordered his colleagues not to deviate from the plan.
2. Request
A student said to the teacher : “Can you, please, repeat the question, Madam ?”
2. A student requested the teacher to repeat the question.
3. Advice
Ahmad said to his son : “Don’t waste time and money.”
3. Ahmad advised his son not to waste time and money.
4. Instruction
The invigilator said to the candidates in the examination hall:”Write your hall ticket number on the question paper.”
4. The invigilator instructed the candidates in the examination hall to write their hall ticket number on the question paper.
5. Threat
A girl said to a boy : “I will complain to the police, if you tease me.”
5. A girl warned the boy that she would complain to the police if he teased her.
6. Offer
A volunteer said to me : “Can I help you ?”
6. A volunteer offered to help me.
7. Invitation
Praveena said to her friends : “Welcome to my home.”
7. Praveena invited her friends to her house.
8. Warning
Mother said to her son : “Don’t swim in the turbulent river.”
8. Mother warned her son not to swim in the turbulent river.
9. Promise
You said to your mother : Til be careful.”
9. You promised to your mother to be careful.
10. Apology
Raheem said to you :
“I am sorry I am unable to help you.”
10. Raheem apologized to you for not being able to help you.
Direct Speech Indirect Speech
1. Keerthi said to us, “Let us have some snacks.” 1. Keerthi suggested (invited) to us that we should have some snacks.
2. Dev said to us, “Shall we visit the Thousand-Pillar temple today ?” 2. Dev proposed that we should visit the Thousand- Pillar temple that day.

TS Inter 1st Year English Grammar Transformation of Sentences

Exclanations :

Direct Speech Indirect Speech
1. “Oh ! They have lost the match,” he said. 1. He expressed regret that they had lost the match.
2. “Hurrah ! We have won the match,” said the boys. 2. The boys exdamed with delight that they had won the match.
3. My brothers said to me, “Better luck next time.” 3. My brothers wished me better luck next time.

Some More Examples :
1. He said to me, ‘You are lucky.” (D.S)
He told me (that) I was lucky. (I.S)

2. He said, “My father went to Chennai.” (D.S)
He said (that) his father had gone to Chennai. (I.S)

3. He said, “The sun rises in the east”. (D.S)
He said that the sun rises in the east. (I.S)

4. He said, “Kutub Minar is in Delhi.” (D.S)
He said that Kutub Minar is in Delhi. (I.S)

5. He said, “1 always go to bed early.” (D.S)
He said he always goes to bed earlier (I.S)

6. He said to me, “Do you want coffee ?” (D.S)
He asked me if I wanted coffee. (I.S)

7. He said to me, “Where did you go ?” (D.S)
He asked me where I had gone. (I.S)

8. He said to his son, “Go out and play.” (D.S)
He told his son to go out and play. (I.S)

9. He said, “Don’t disturb me.” (D.S)
He instructed him not to disturb him. (I.S)

10. He said, “What a terrible storm it is !” (D.S)
He exclaimed that it was a terrible storm. (I.S)

TS Inter 1st Year English Grammar Transformation of Sentences

11. He said to her, “How foolish of you !” (D.S)
He exclaimed that she was very foolish. (I.S)

12. He said, “Alas ! What a tragedy.” (D.S)
He exclaimed with sorrow that it was a great tragedy. (I.S)

EXERCISES

I. Report the following statements.

1. Sunil said to his daughter, “I will take care of you.”
2. The M.L.A. said to villagers, ‘You have every right to question me.”
3. The Inspector said to the constable, “I am your boss.”
4. It is better for you to join M.PC.” said Bharath’s mother.
5. The principal said to the lecturers, You should maintain records.”
6. “I have been waiting here for you for one hour, “Vasundhara said to Vandana.
7. Kranthi said to the Inspector, “I met with an accident while taking a turn.”
8. He said, “I have lost my bag.”
9. The girl said, “I can change any given sentence into reported speech.”
10. “I am your fan,” said the boy to Allu Aijun.
Answers:
1. Sunil told his daughter that he would take care of her.
2. Tlje M.L.A told villagers that they had every right to question him.
3. The Inspector told the constable that he was his boss.
4. Bharath’s mother said that it would be better for him to join MPC.
5. The principal told the lecturers that they should maintain records.
6. Vasundhara told Vandana that she had been waiting there for her for an hour.
7. Kranthi informed the Inspector that he had met with an accident while taking a turn.
8. He said that he had lost his bag.
9. The girl said that she could change any given sentence into reported speech.
10. The boy told Allu Aijun that he was his fan.

TS Inter 1st Year English Grammar Transformation of Sentences

II. Match the reported clause of Set n A with each reported statement of the direct speech in Set n B and then change the sentence into the reported speech.
TS Inter 1st Year English Grammar Transformation of Sentences 12
Answers:
1. The palmist told a woman that she would become a good writer.
2. In a press meet, the Union Minister promised that the government would take all precautionary measures regarding cyclone.
3. Dr. Gopal told them that the operation was successful and the patient was out of danger.
4. The lawyer told the client that they could file an appeal in the High Court.
5. The boy came late to the class and told his teacher that his father had been ill for a few days.

III. Report the following questions in indirect speech.

1. A visitor said to me, “Are there any places worth seeing in Warangal ?”
2. The mother said to her son, “When will you have your breakfast ?”
3. The shopkeeper said to the customer, “Shall I show you the latest model ?”
4. I said to the shop assistant, “What is the price of this dress ?”
5. A classmate said to me, “Is your father a businessman ?”
6. Harika said to her friend, “Will you come to my home tomorrow ?”
7. The passenger said to the driver, “Does the bus stop at the crossroads ?”
8. A girl said to the principal, “Do I need to be a postgraduate to become an IAS officer ?”
9. The father said to his daughter, “Who teaches you English, Anitha ?”
10. The teacher said to Kavitha, “What does the word ‘corruption’ mean ?”
Answers:
1. A visitor asked me if there were any worth seeing places in Warangal.
2. The mother asked her son when he would have his breakfast.
3. The shopkeeper asked the customer if he could show him the latest model.
4. I asked the shop assistant what the price of that dress was.
5. A classmate asked me if my father was a businessman.
6. Harika asked her friend if she would come to her home the following day.
7. The passenger asked the driver if the bus would stop at the crossroads.
8. A girl asked the principal if she needed to be a postgraduate to become an IAS officer.
9. The father asked his daughter Anita who would teach them English.
10. The teacher asked Kavitha what the word corruption meant.

TS Inter 1st Year English Grammar Transformation of Sentences

IV. Change the following imperatives into the indirect speech.

1. Hima said, “Get out from here.”
2. Neha said, “Mom, please give me your mobile.”
3. Hardik said to Annu, “Go and study.”
4. Nani said to me, “Exercise daily.”
5. Father said to Swetha, “Switch off the fan.
Answers:
1. Hima ordered him/them to get out from there.
2. Neha requested her mother to give her mobile.
3. Hardik asked Annu to go and study.
4. Nani advised me to exercise daily.
5. Father asked Swetha to switch off the fan

V. Change the following exclamations into the indirect speech.

1. Nivya said to her sister, “How interesting the serial is !”
2. My friend said to me, “What a wonderful opportunity it is !”
3. “Oh ! he is dead,” the doctor said.
4. “Thank goodness ! I’ve passed my exams,” my son said.
5. “Hurray ! I’ve got first rank in the entrance examination !” my friend said.
6. “How awful! She has missed the chance,” Mahesh said.
7. A visitor said, “What sultry weather !”
8. “What a pity ! Many passengers died in the accident,” said an eye witness.
9. Akshay said to his partner, “Bad luck, never mind.”
10. “Oh ! What a beautiful place it is !” he said.
Answers:
1. Nivya exclaimed to her sister that the serial was very interesting.
2. My friend exclaimed to me that it was a wonderful opportunity.
3. The doctor declared sadly that he was dead.
4. My son happily said that he had passed his exams.
5. My friend cheerfully declared that he had got the first rank in the entrance examination.
6. Mahesh rather sadly exclaimed that she had missed the chance.
7. A visitor exclaimed that it was very sultry weather.
8. An eye witness exclaimed sadly that many passengers had died in the accident.
9. Akshay told his partner that it was their bad luck and said better not mind that.
10. He exclaimed that it was a very beautiful place.

TS Inter 1st Year English Grammar Transformation of Sentences

VI. Report the following sentences.

1. A father said to his son. “Ramu, concentrate on your studies now.”
2. “What a wonderful poem it is !” said the teacher.
3. The principal said to the student, “Vinay, can you spell this word ?”
4. “Is there any train to Mumbai now ?” I asked the enquiry clerk.
5. “How much time does a ray of the sun take to reach the earth ?” the quiz master asked the team.
6. “Alas ! India has lost a famous scientist,” said the Prime Minister on the death of Abdul Kalam.
7. “How would you help develop the company ?” the interview board member said to the can-didate.
8. “If I get a job, I will arrange a grand party,” said Spandana.
9. “Stand where you are,” the officer said to the cadets.
10. “Don’t make friends with bad boys,” said the mother to her son.
11. “Hearty welcome to our village !” Radha said to her friends.
12. “Hurrah ! We have defeated Pakistan in T 20 too,” said Kohli.
13. “Please be seated. My father is sleeping,” said the girl to the visitors.
14. “I am a pure vegetarian,” Gandhi said.
15. “How exciting it is to see Telangana as a separate state !” said a hundred-year old man.
16. “Remember, Man is mortal,” said the Swamiji.
17. He said, “We need not wait here for the bus.”
18. “While I was going to see Deepthi, it started raining,” Kiran said.
19. The doctor said, “Sorry, I cannot help it.”
20. “Nothing is in our hands,” said the priest.
Answers:
1. A father advised his son Ramu to concentrate on his studies then.
2. The teacher exclaimed that it was a very wonderful poem.
3. The principal asked Vinay if he could spell that word.
4. I asked the enquiry clerk if there was any train to Mumbai then.
5. The quiz master asked the team how much time a ray of the sun took to reach the earth.
6. The Prime Minister said on the death of Abdul Kalam that India had lost a famous scientist.
7. The interview board member asked the candidate how he would help the company develop.
8. Spandana said that if she got a job she would arrange a grand party.
9. The officer ordered the cadets to stand where they were.
10. The mother advised her son not to make friends with bad boys.
11. Radha extended hearty welcome to her friends to her village.
12. Kohli gladly said that they had defeated Pakistan in T20 too.
13. The girl requested the visitors to be seated and informed them that her father was sleeping.
14. Gandhi said that he was a pure vegetarian.
15. A hundred – year old man exclaimed that it was very exciting to see Telangana as a separate state.’
16. The Swamiji said emphatically that man is mortal.
17. He said that they needed not wait there for the bus.
18. Kiran said that while he was going to see Deepthi, it had started raining.
19. The doctor apologetically said that he couldnot help it.
20. The priest said that nothing was in their hands.

TS Inter 1st Year English Grammar Transformation of Sentences

VII. Change the following sentences into the indirect speech.

1. I said to her, “I had already applied for a job.”
2. You said to me, “She loves you.” * ‘
3. We said to him, “Can we use your phone ?”
4. The teacher said to her, ‘Why did you fail the exam ?”
5. She will say to me, “How do you solve the problem ?”
6. I said to them, “I don’t ever waste my time.”
7. You said to me, “I have not yet met them.”
8. The minister said, “The problem will surely be looked into.”
9. They said to rile, “Have you been working here since 2015 ?”
10. We said to them, ‘We were watching a movie.”
11. She said, “I went to the market yesterday.”
12. They said to us, “We will be waiting for you.”
13. John said to her, “1 will call a doctor for you.”
14. I said to her, “Alas, I am undone !”
15. She said to him, “Please complete the job.”
16. He shouted at them, “Shut up!”
17. The officer said to him, “Don’t repeat this mistake in the future.”
18. The teacher said, “Akbar died in 1605 AD.”
19. She said to her, “Knowledge is power.”
20. A soft voice said, “What a cold day !”
Answers:
1. I told her that I had already applied for a job.
2. You told me that she loved me.
3. We asked him if we could use his phone.
4. The teacher asked her why she had failed the exam.
5. She will ask me how I will solve the problem.
6. I told them that I never wasted my time. (OR) I told them that I never waste my time.
7. You told me that you had not yet met them.
8. The minister said that the problem would surely be looked into.
9. They asked me if I had been working there since 2015.
10. We told them that we had been watching a movie.
11. She said that she had gone to the market the previous day.
12. They told us that they would be waiting for us.
13. John told her that he would call a doctor for her.
14. I exclaimed with sorrow to her that I was undone.
15. She requested him politely to complete the job.
16. He ordered them loudly to shut up.
17. The officer warned him not to repeat that mistake in the future.
18. The teacher said that Akbar had died in 1605 AD.
19. She told her that knowledge is power.
20. A soft voice exclaimed that it was a very cold day.

TS Inter 1st Year English Grammar Transformation of Sentences

VIII. Change the following sentences into the other speech.

1. A good teacher will say frankly and clearly, “I don’t know, 1 cannot answer that question.”
2. I asked my Biology teacher what I should do to save it.
3. I asked my grandmother how she got to be so wise.
4. Thimmakka concludes, “Even one sapling each could make a better place for our children.”
5. Box : Stop ! Can you inform me who the individual is that I invariably encounter going downstairs when I’m coming up, and coming upstairs when I’m going down ?
Answers:
1. A good teacher will say frankly and clearly that he/she doesn’t know. He/She will add that he/ she cannot answer that question. (I.S)
2. I said to my Biology teacher, “What shuld I do to save it ?” (D.S)
3. I said to my grandmother, “How did you get to be so wise” ? (D.S)
4. Thimmakka concludes that even one sapling each could make a better place for our children. (I.S)
5. Box asked (her) to stop. He further asked her if she could inform him who that individual was that he invariably encountered going downstairs when he was coming up and coming upstairs when he was going down. (I.S)

TS Inter 1st Year English Grammar Transformation of Sentences

C. DEGREES OF COMPARISON

Man craves for variety. He knows that variety is the spice of life. Hence he tries to express the same idea in various different ways. The result is the tradition of describing the quality, quantity size etc., of some thing or person in three different ways. Most adjectives and some adverbs have three different forms. They are positive, comparative and superlative. They are known as the three degrees of comparision.

(ఒక వ్యక్తి యొక్క వస్తున్న యొక్క గుణ, పరిమాణాలను మూడు భిన్న రూపాలలో వ్యక్తీకరించడం ఆనవాయితీ. ఈ రూపాలనే Degrees of comparison అని పిలుస్తారు)

When the comparison is among a minimum of three persons/things, that can be ex-pressed in all the three degrees. If the compared persons are two only, the superlative degree is not possible. When we talk of the quality, quantity of a single item, only positive degree is possible.

Interchange of Degrees of comparison :
Transforming one sentence from the Superlative Degree to Comparative Degree involves the following steps.

1. First, remove ‘the’ that is used before the superlative adjective, while changing it into the comparative.
2. Write the comparative form of the adjective.
3. Then, add ‘than any other’ after the adjective.
Ex : Praveen is the youngest boy in the class. (S.D.)
Praveen is younger than any other? boy in the class.

To change that sentence into the positive :

1. Begin the sentence with ‘No other’.
2. Secondly, place the phrase after the superlative adjective after ‘No other’.
3. Use ‘so + adj in positive Degree + as’ after the verb.
4. Place the subject in the S.D after ‘as’ in RD.
Ex : He is the richest man in our town. (S.D.)
TS Inter 1st Year English Grammar Transformation of Sentences 13
Transforming one sentence from the superlative Degree to comparative or positive Degree involves the following steps.
TS Inter 1st Year English Grammar Transformation of Sentences 14
TS Inter 1st Year English Grammar Transformation of Sentences

Sentences with ‘one of phrase in the Superlative degree follow a slightly different wording. This is as explained here under.
TS Inter 1st Year English Grammar Transformation of Sentences 15
Some sentences show the comparison between only two things/persons. In such cases, the superlative is not possible. The interchange is made as shown here.
TS Inter 1st Year English Grammar Transformation of Sentences 16

EXAMPLES

Change the following sentences into other degrees.

Question 1.
Bengaluru is as cool as Ooty. (P.D)
Answer:
Ooty is not cooler than Bengaluru. (C.D)

Question 2.
Australia is the biggest island in the world. (S.D)
Answer:
Australia is bigger than any other island in the world. (C.D)
No other island in the world is so big as Australia. (PD)

Question 3.
The moon is brighter than the stars. (C.D)
Answer:
The stars are not so bright as the moon. (P.D)

Question 4.
There is no vice so bad as drink. (P.D)
Answer:
Drink is worse than any other vice. (C.D)

Question 5.
Kashmir is the most beautiful place in India. (S.D)
Answer:
No other place in India is so beautiful as Kashmir. (P.D)
Kashmir is more beautiful than any other place in India. (C.D)

TS Inter 1st Year English Grammar Transformation of Sentences

Question 6.
Silver is not so precious as gold. (P.D)
Answer:
Gold is more precious than silver. (C.D)

Question 7.
Kumble is one of the ablest bowlers. (S.D)
Answer:
Very few bowlers are so able as Kumble. (P.D)
Kumble is abler them most other bowlers. (C.D)

Question 8.
The lion is more ferocious than any other animal. (C.D)
Answer:
The lion is the most ferocious of all the animals. (S.D)
No other animal is so ferocious as the lion. (P.D)

Question 9.
The sword is not so mighty as the pen. (P.D)
Answer:
The pen is mightier than the sword. (C.D).

Question 10.
Copper is more useful than most other metals. (C.D)
Answer:
Copper is one of the most useful metals. (S.D)
Very few metals are so useful as copper. (P.D)

Question 11.
Mount Everest i.s higher than any other peak in the world. (C.D)
Answer:
Mount Everest is the highest of all the peaks in the world. (S.D)
No other peak in the world is so high as Mount Everest. (P.D)

Question 12.
I like you better than him. (C.D)
Answer:
I didn’t like him as well as I like you. (P.D)

Question 13.
A deer runs faster than a horse. (C.D)
Answer:
A horse does not run so fast as a deer. (P.D)

TS Inter 1st Year English Grammar Transformation of Sentences

Question 14.
Sangeetha is the tallest girl in the class. (S.D)
Answer:
No other girl in the class is so tall as Sangeetha. (P.D)

Question 15.
This is one of the most powerful earthquakes that occurred. (S.D)
Ans. This is more powerful than most other earthquakes that occurred. (C.D)
Very few earthquakes that occurred are as powerful as this earthquake. (P.D)

More Examples :

1. For me, dancing is easier to learn than singing. (C.D)
For me, singing is not as easy to learn as dancing. (P.D)

2. Singing is the best of all art forms. (S.D)
Singing is better than any other art forms. (C.D)
No other art form is as good as singing. (P.D)

3. The sentence is more impressive than the earlier one. (C.D)
The earlier sentence is not so impressive as this one. (P.D)

4. A car, of course, is costlier than a bike. (C.D)
A bike, of course, is not as costly as a car. (P.D)

5. Uttar Pradesh is the largest state in India. (S.D)
Uttar Pradesh is larger than any other state in India. (C.D)
No other state in India is as large as Uttar Pradesh. (P.D)

TS Inter 1st Year English Grammar Transformation of Sentences

6. Bill Gates is the wealthiest man in the world. (S.D)
Bill Gates is wealthier than any other man in the world. (C.D)
No other man in the world is as wealthy as Bill Gates. (P.D)

7. English is the most widely used language in the world. (S.D)
English is more widely used than any other language in the world. (C.D)
No other language in the world is as widely used as English. (P.D)

Types of transformation :
TS Inter 1st Year English Grammar Transformation of Sentences 17

EXERCISES

I. Change the following sentences into other Degrees.

1. LIC is one of the most popular insurance companies in India.
2. The custard apple is better for health than the apple.
3. A computer works faster than the human brain.
4. A Governor is sometimes more powerful than a Chief Minister.
5. The teaching profession is the best of all professions.
6. Laxmi Mittal is one of the most popular industrialists.
7: No other bank in India has as many branches as SBI.
8. Virus infects a person faster than bacteria.
9. Cancer is one of the most dangerous diseases.
10. No other boy in the class is as active as Surya Teja.
11. The Amazon is one of the longest rivers in the world.
12. No other animal lives as long as the turtle.
13. Jupiter is bigger than any other planet.
14. A rainbow is one of the most beautiful sights in nature.
15. Very few English poets are as great as John Keats.
16. The lotus is the most beautiful flower.

TS Inter 1st Year English Grammar Transformation of Sentences

17. Mathematics is more difficult than most other subjects.
18. Shimla is cooler than Ooty.
19. He can’t run as fast as I.
20. Vinay is not as mischievous as some other boys in the college.
21. There are some vegetarian food as healthy as eggs.
22. Of all the Telugu singers S.R Balasubramanyam has the most melodious voice.
23. Health is more important than wealth.
24. I cannot speak as fast as you.
25. Very few TV channels are as popular as E TV.
Answers:
1. Very few insurance companies in India are as popular as LIC. (P.D)
LIC is more popular than many other insurance companies in India. (C.D)

2. The apple is not as good for health as the custard apple. (P.D)

3. The human brain does not work as fast as a computer. (P.D)

4. Sometimes a Chief Minister is not as powerful as a Governor. (P.D)

5. The teaching profession is better than any other profession. (C.D)
No other profession is as good as the teaching profession. (P.D)

6. Very few industrialists are as popular as Laxmi Mittal. (P.D)
Laxmi Mittal is more popular than many other industrialists. (C.D)

7. SBI has the most number of branches. (S.D)
SBI has more branches than any other bank in India. (C.D)

8. Bacteria does not infect a person as fast as virus. (P.D)

9. Cancer is more dangerous than many other diseases. (C.D)
Very few diseases are as dangerous as cancer. (P.D)

10. Surya Teja is more active than any other boy in the class. (C.D)
Surya Teja is the most active boy in the class. (S.D)

TS Inter 1st Year English Grammar Transformation of Sentences

11. The Amazon is longer than many other rivers in the world. (C.D)
Very few rivers in the world are as long as the Amazon. (P.D)

12. The turtle lives longer than any other animal. (C.D)
The turtle lives the longest of all animals. (S.D)

13. No other planet is as big as Jupiter. (P.D)
Jupiter is the biggest planet. (S.D)

14. A rainbow is more beautiful than many other sights in nature. (C.D)
Very few sights in nature are as beautiful as a rainbow. (P.D)

15. John Keats is one of the greatest poets of English. (S.D)
John Keats is greater than many other poets of English. (C.D)

16. The lotus is more beautiful than any other flower. (C.D)
No other flower is as beautiful as the lotus. (P.D)

17. Mathematics is one of the most difficult subjects. (S.D)
Very few subjects are as difficult as Mathematics. (P.D)

18. Ooty is not as cool as Shimla. (P.D)

19. I can run faster than he. (C.D)

20. Vinay is one of the most mischievous boys in the college. (S.D)
Vinay is more mischievous than many other boys in the college. (C.D)

21. Eggs are not healthier than some vegetarian foods. (C.D)

22. No other Telugu singer has a voice as melodious as S.R Balu’s. (P.D)
S.R Balu’s voice is more melodious than that of any other Telugu singer. (C.D)

23. Wealth is not as important as health. (P.D)

24. You can speak faster than I. (C.D)

25. E TV is more popular than many other TV channels. (C.D)
E TV is one of the most popular TV channels (S.D)

TS Inter 1st Year English Grammar Transformation of Sentences

II. Rewrite the following comparisons as directed.

1. The taste of Pizza is more pleasing than that of Burger. (into the other degree)
2. Sheela is getting smarter and smarter than Neela. (into the other degree)
3. Raj is one of the bravest fighters. (into comparative)
4. Radha speaks more fluently than Sudha. (into the other degree)
5. ’ Riding a horse is not as easy as riding a motorbike. (into the other degree)
6. ‘Silence’ is the most potent weapon to win an argument. (into positive)
7. Rachana’s sister is taller than yours. (into the other degree)
8. Dogs don’t look as cute as rabbits. (into the other degree)
9. He is not the worst student in the class. (into comparative)
10. Very few heroes are as great as Gandhiji in the world history. (into superlative)
Answers:
1. The taste of Burger is not so pleasing as that of Pizza. (P.D)
2. Neela is not getting as smart as Sheela. (P.D)

3. Raj is braver than any other fighter. (C.D)
No other fighter is as brave as Raj. (P.D)

4. Sudha does not speak as fluently as Radha. (P.D)

5. Riding a motorbike is easier than riding a horse. (C.D)

6. No other weapon is so potent as silence to win an argument. (P.D)
Silence is more potent than any other weapon to win an argument. (C.D)

7. Your sister is not so tall as Rachana’s sister. (P.D)
8. Rabbits look cuter than dogs. (C.D)

9. He is not worse than most students in the class. (C.D)
Many students in the class are as bad as he. (P.D)

10. Gandhi is one of the greatest heroes in the world history. (S.D)
Gandhi is greater than many other heroes in the world history. (C.D)

TS Inter 1st Year English Grammar Transformation of Sentences

III. Change the following sentences into other degrees of comparison.

1. Bus journey is not as comfortable as train journey.
2. Radhakrishnan is more highly respected than any other teacher.
3. Robert Frost is one of the best American poets.
4. No other road in the world is as long as the Pan American Highway.
5. Kashmir is one of the coolest places in India.
6. A foolish friend can be more dangerous than a wise enemy.
7. Money is not as important as character.
8. Modern culture is not as stable as Traditional culture.
9. For many Indians, cricket gives greater pleasure than football.
10. Natural flowers appeal more to our senses than artificial flowers.
Answers:
1. Train journey is more comfortable than bus journey. (C.D)

2. Radhakrishnan is the most highly respected teacher. (S.D)
No other teacher is so highly respected as Radhakrishnan. (P.D)

3. Robert Frost is better than many other American poets. (C.D)
Very few American poets are as good as Robert Frost. (P.D)

4. Pan American Highway is longer than any other road in the world. (C.D)
Pan American highway is the longest road in the world. (S.D)

5. Kashmir is cooler than many other places in India. (C.D)
Very few places in India are so cool as Kashmir. (P.D)

6. A wise enemy cannot be so dangerous as a foolish friend. (P.D)
7. Character is more important than money. (C.D)
8. Traditional culture is more stable than modern culture. (C.D)
9. For many Indians, football doesn’t give as much pleasure as cricket. (P.D)
10. Artificial flowers do not appeal to our senses as much as natural flowers. (P.D)

TS Inter 1st Year English Grammar Transformation of Sentences

D. QUESTION TAGS

Question tags are short questions added to statements. They seek confirmation or agreement. (ఏకీభావాన్ని లేదా ద్రువీకరణను ఆశిస్తూ, ఒక వాక్యానికి అనుబంధంగా చేర్చబడే చిన్న ప్రశ్నలే Question tags.)

Question tags have a fixed structure. It is represented as : Helping verb + (n’t) + pronoun ? ((n’t) in brackets means it is optioned.)
e.g. She loves her children, doesn’t she?
(Q.T.) does (H.V.) n’t she (pronoun)

1. While constructing a tag, selecting the suitable helping verb is the first and the most important step. If the given sentence has a helping verb, then that helping verb is used in the tag too.
E.g : She has answered all the questions, hasn’t she?
has → Helping Verb in the sentence used in the tag too.

When the sentence doesn’t have a helping verb, the verb is either in the simple present Or in the simple past and in the affirmative. In case of the simple present, the suitable helping verb is “do/does”. If the verb in the sentence is in the simple past, then we must use ‘did’ in the tag.
Eg : a) She hates smokers, doesn’t she ? Simple present, hence ‘does’
b) They grow vegetables, do n’t they ? Simple present
c) He sold his car, didn’t he ? Simple past; hence ‘did’.

2. The second step is to decide whether to use ‘n’t’ or not. The guiding principle is quite simple. If the given sentence doesn’t have ‘rio/not’, use ‘n’t’ is the tag. If the given sentence has ‘no/not’ then the tag doesn’t have ‘n’t’.
Eg : a) He was sleeping in the class, was n’t he ?
‘not’ is not used n’t in the tag
b) They don’t grow paddy, do they?
‘n’t’ in sentence ‘n’t’ not used in tag
Remember to use the short form ‘n’t’ in the tag.

3. The last part of the tag as a pronoun. This corresponds to the subject of the given sentence. If the subject of the sentence is a pronoun, the same pronoun is used in the tag. If the subject is a noun, select a suitable pronoun as shown below.

SI.No. Subject in the sentence Pronoun used in the tag
1. Name of a man he
2. Name of a woman she
3. Name of a single thing it
4. Name referring to, a group of persons, places, things they

Eg : a) Gourav is a good cricketer, isn’t he? ?
b) Sania Mirza played well, didn’t she ?
c) Ooty is a beautiful hill station, isn’t it ?
d) Mangoes aren’t good this season, are they ?

TS Inter 1st Year English Grammar Transformation of Sentences

4. Note that ‘amn’t’ is not used. Instead, aren’t is used.
Eg : lam rather slow, aren’t I ?

5. Imperative sentences take ‘will’ as the helping verb in the tags.
Eg : a) Close the door, Won’t you ? (Will + n’t = won’t)
b) Don’t leave the place, will you ?

6. Sentences expressing proposals with the help of “Let us ……………..” have for their tags “Shall we?”
Eg : Let us walk fast, shall we ?

EXAMPLES

1. Srinivasa Ramanujan is a famous mathematician, isn’t he ?
2. Normally players have a lot of practice, don’t they ?
3. Sania Mirza is not a cricketer, is she ?
4. She can speak English, can’t she ?
5. He should believe us, shouldn’t he ?
6. We must all learn English, mustn’t we ?
7. The Governor administers the oath of office to ministers, doesn’t she / he ?
8. He does not support any one, does he ?
9. Most of the villagers depend on agriculture, don’t they ?
10. They do not seem to lead a happy life, do they ?
11. Children love to play with toys, don’t they ?
12. On their picnic, the children did not have a chance to play in the garden, did they ?
13. The children are not yet back home, are they ?
14. Do me a favour, Raju, can you ?
15. Take a right decision, won’t you ?
16. Don’t waste time, will you ?
17. Let’s understand their problems, shall we ?
18. No one complained against us, did they ?
19. Everyone appreciated his performance, didn’t they ?
20. Someone should take the initiative, shouldn’t they ?
21. Nothing is impossible, is it ?
22. There will be problems in that case, won’t there ?
23. One can achieve anything by faith, can’t one ?
24. I am not disturbing you, am I ?
25. It is used for present actions, isn’t it ?
26. You understand the point, don’t you ?
27. You are attending a job interview tomorrow, aren’t you ?
28. It is clear to you now, isn’t it ?
29. They are ready, aren’t they ?
30. They are not ready, are they ?
31. He did not attend the class, did he ?
32. Oh, you got two prizes, did you ? (Special case. Positive statement, positive tag. Express reaction to a surprising news.)
33. I am going home, aren’t I ? (Note that ‘aren’t is used instead of ‘amn’t.)

TS Inter 1st Year English Grammar Transformation of Sentences

EXERCISES

I. Add an appropriate question tag to each one of the following statements.

1. Sandeep has attended all classes, ……………….. ?
2. We are lucky to be born in India, ………………..?
3. English is an interesting language, ……………….. ?
4. He was very busy yesterday, ……………….. ?
5. I am very happy now, ……………….. ?
6. I can face challenges, ……………….. ?
7. Ravi always thinks positively, ……………….. ?
8. He does not criticize, ……………….. ?
9. Some people always depend on others, ……………….. ?
10. Discipline must be maintained at any cost, ……………….. ?
11. Let us keep to the pavement, ……………….. ?
12. Don’t blame others for everything, ……………….. ?
13. One can do wonders with knowledge, ……………….. ?
14. Nothing is permanent except change, ……………….. ?
15. Students are our best judges, ……………….. ?
Answers:
1. hasn’t he ?
2. aren’t we ?
3. isn’t it ?
4. wasn’t he ?
5. aren’t I ?
6. can’t I ?
7. doesn’t he ?
8. does he ?
9. Don’t they
10. mustn’t it be ?
11. shall we ?
12. will you ?
13. can’t one ?
14. is it ?
15. aren’t they ?

TS Inter 1st Year English Grammar Transformation of Sentences

II. Add an appropriate question tag to each one of the following statements.

1. You don’t lime me, ……………….. ?
2. It is not raining, ……………….. ?
3. You have done your homework, ……………….. ?
4. I am not late, ……………….. ?
5. I am invited to your party, ………………..?
6. You like fast food, ……………….. ?
7. You will come to my party, ……………….. ?
8. You remembered to feed the cat, ……………….. ?
9. Let’s play tennis, ……………….. ?
10. There’s a problem here, ……………….. ?
11. He never says a word, ……………….. ?
12. Nobody came to your party, ……………….. ?
13. Don’t forget, ……………….. ?
14. You think you’re clever, ……………….. ?
15. So you think you’re clever, ……………….. ?
16. We don’t have to go to the party, ……………….. ?
17. It stopped raining, ……………….. ?
18. Have a seat, ……………….. ?
19. Help yourself to some cake, ……………….. ?
20. Children, be quiet, ……………….. ?
Answers:
1. do you
2. is it
3. haven’t you
4. am I (Note . possible tag-am ; negative tag are in the place of ami
5. aren’t I
6. don’t you
7. won’t you
8. didn’t you
9. shall we
10. isn’t there
11. does he (never = not; negative statement; hence positive tag)
12. did they
13. will you
14. don’t you (you think is the main clause)
15. do you (expressing sudden reaction)
16. do we
17. didn’t it
18. won’t you
19. will you
20. will you

TS Inter 1st Year English Grammar Transformation of Sentences

III. Add an appropriate question tag to each one of the following statements.

1. I am unable to answer your question, ………………..?
2. Rahul’s first rank is at stake, ……………….. ?
3. The noise in my ears was that of the faithful Oxford crowd, ……………….. ?
4. The stop-watches held the answer, ……………….. ?
5. It belongs to both of you, ……………….. ?
Answers:
1. am I (unable = not able)
2. isn’t it
3. wasn’t it
4. didn’t they
5. doesn’t it ?

TS Inter 1st Year English Grammar Correction of Errors in Sentences

Telangana TSBIE TS Inter 1st Year English Study Material Grammar Correction of Errors in Sentences Exercise Questions and Answers.

TS Inter 1st Year English Grammar Correction of Errors in Sentences

Q.No. 14 (4 × 1 = 4 Marks)

Exercises

I. Correct the underlined parts of the following sentences :

1. Your informations are wrong.
2. He has bought expensive furnitures.
3. Children should learn the alphabets with joy.
4. He has deep knowledges of various fields.
5. The sceneries of Darjeeling are very beautiful.
6. Keep your surrounding clean.
7. We must express thank to those who help us.
8. Economics are an interesting subject.
9. Athletics are an interesting sport.
10. The news of the earthquake have spread like wildfire.
11. Measles are an infectious disease.
12. Ocean sands are not used for construction.
13. C.V. Raman’s knowledges of all branches of physics are amazing.
14. There is a scarcity of man-servants nowadays.
15. Many passer-bys observed the accident.
16. Mouses have spoiled the crop.
17. There are five womans in the team.
18. My cousin brother is a doctor.
19. We should wash our foots before coming into the house.
20. He has many sheeps.

TS Inter 1st Year English Grammar Correction of Errors in Sentences

21. One of my classmates are an army officer.
22. One should respect her teachers.
23. Every men are responsible for this situation.
24. His both sons are lawyers.
25. The principal and the chairman has attended the meeting.
26. Each of them were given a gift.
27. Student’s must avail the opportunities.
28. The two players blamed one another for their defeat.
29. All Indians must respect each other.
30. Yourself are responsible for your future.
31. There are no less than ten employed persons in their village.
32. He and me are brothers.
33. As there are only few students, I can interact with them easily.
34. My all friends are very active.
35. Gandhi is more truthful than any political leader.
36. This is taller than many buildings in Hyderabad.
37. Raghu is my older brother.
38. The streets of Hyderabad are wider than Warangal.
39. Suma is an popular anchor.
40. I waited for a hour.
41. Sun rises in east.
42. Onions cost Rs. 20 kilogram.
43. They are staying in the same flat for the last many years.
44. How long are you waiting here ?
45. He is interested to do a job.
46. They have moved to the new house last week.
47. He is having many imported clothes.
48. As soon as I opened the doors, the birds flu away.
49. If I will stand on my own legs, my parents will feel happy.

TS Inter 1st Year English Grammar Correction of Errors in Sentences

50. If you consult me, I would have advised you what to do.
51. He is visiting the library daily.
52. He walks very fastly.
53. We don’t , hardly believe it.
54. They don’t do anything careful.
55. She scarce attends classes.
56. He is walking very slow.
57. The property was divided between the four brothers.
58. I prefer fruits than sweets.
59. He is afraid with darkness.
60. We entered into the hall to watch the play.
61. Beside being a poet, Tagore is also a short story writer.
62. The shops will be open between 10 a.m. to 8 p.m.
63. Either you must take up a job or start a business.
64. Neither she drinks tea nor coffee.
65. Sheela is as proud like a peacock.
66. They asked me that where SBI was.
67. They asked me what was my name.
68. This article is made with cotton.
69. We look forward to meet the minister.
70. I know them for the last many years.
71. Why is she hating classical music ?
72. It is raining since yesterday.
73. I am good in English.
74. If cleanliness will be maintained, we will be healthy.
75. We had seen them two weeks ago.
76. The river has overflown its bank in many places.
77. He has hanged his coat on a nail.
78. All banks are open from 10.30 a.m. and 4 p.m.
79. He is not an expert in grammar, isn’t it ?
80. Children are fond for chocolates.
Answer:
1. Your informations is wrong.
2. He has bought expensive furniture.
3. Children should learn the alphabet with joy.
4. He has deep knowledge of various fields.
5. The scenery of Darjeeling are very beautiful.
6. Keep your surroundings clean.
7. We must express thanks to those who help us.
8. Economics is an interesting subject.
9. Athletics is an interesting sport.
10. The news of the earthquake has spread like wildfire.

TS Inter 1st Year English Grammar Correction of Errors in Sentences

11. Measles is an infectious disease.
12. Ocean sands is not used for construction.
13. C.V. Raman’s knowledge of all branches of physics are amazing.
14. There is a scarcity of men-servants nowadays.
15. Many passer-by observed the accident.
16. Mice have spoiled the crop.
17. There are five womens in the team.
18. My cousin is a doctor.
19. We should wash our feet before coming into the house.
20. He has many sheep.
21. One of my classmates is an army officer.
22. One should respect one’s teachers.
23. Every men is responsible for this situation.
24. Both his sons are lawyers.
25. The principal and the chairman have attended the meeting.
26. Each of them was given a gift.
27. Student’s must avail themselves of the opportunities.
28. The two players blamed each another for their defeat.
29. All Indians must respect one other.
30. You are responsible for your future.
31. There are no fewer than ten employed persons in their village.
32. He and I are brothers.
33. As there are only a few students, I can interact with them easily.
34. All my friends are very active.
35. Gandhi is more truthful than any other political leader.
36. This is taller than many other buildings in Hyderabad.
37. Raghu is my elder brother.
38. The streets of Hyderabad are wider than those of Warangal.

TS Inter 1st Year English Grammar Correction of Errors in Sentences

39. Suma is a popular anchor.
40. I waited for an hour.
41. The sun rises in east.
42. Onions cost Rs. 20 a kilogram.
43. They have been staying in the same flat for the last many years.
44. How long have you been waiting here ?
45. He is interested in doing a job.
46. They moved to the new house last week.
47. He has many imported clothes.
48. As soon as I opened the doors, the birds flew away.
49. If I stand on my own legs, my parents will feel happy.
50. If you had consulted me, I would have advised you what to do.
51. He visits the library daily.
52. He walks very fast.
53. We don’t beleive it/. We hardly believe it.
54. They don’t do anything careful.
55. She scarcely attends classes.
56. He is walking very slowly.
57. The property was divided among the four brothers.
58. I prefer fruits to sweets.
59. He is afraid of darkness.
60. We entered the the hall to watch the play.
61. Besides being a poet, Tagore is also a short story writer.
62. The shops will be open between 10 a.m. and 8 p.m.
63. You must either take up a job or start a business.
64. She drinks neither tea nor coffee.

TS Inter 1st Year English Grammar Correction of Errors in Sentences

65. Sheela is as proud as a peacock.
66. They asked me where SBI was.
67. They asked me what my name was.
68. This article is made of cotton.
69. We look forward to meetimg the minister.
70. I have know them for the last many years.
71. Why does she hate classical music ?
72. It has been raining since yesterday.
73. I am good at English.
74. If cleanliness is maintained, we will be healthy.
75. We saw them two weeks ago.
76. The river has overflowed its bank in many places.
77. He has hung his coat on a nail.
78. All banks are open from 10.30 a.m. to 4 p.m.
79. He is not an expert in grammar, is he ?
80. Children are fond of chocolates.

II. Correct the following sentences :

1. Very good morning.
2. What is your good name ?
3. Why you are late today ?
4. The staff meeting has been pre-poned.
5. 1 will report it to the concerned teacher.
6. We go home by walk.
7. Where you come from ?
8. 1 do not know what is your name.
9. He went to the back-side of the house.
10. Please bring your luggages here.
11. This road is more shorter than that.
12. We often chit-chat with our friends.
13. Please shut the TV.
14. I and my wife went to a movie.
15. Mohan and myself will come.
16. I’m having a scooter.
17. This costed me a lot.

TS Inter 1st Year English Grammar Correction of Errors in Sentences

18. I doubt that he will succeed.
19. We are living in Bengaluru since 2015.
20. We have a lot of furnitures in our house.
Answer:
1. Good morning.
2. What is your name ?
3. Why are late today ?
4. The staff meeting has been advanced.
5. I will report it to the teacher concerned.
6. We go home on foot.
7. Where are you coming from ?
8. 1 do not know what your name is.
9. He went to the back of the house.
10. Please bring your luggage here.
11. This road is shorter than that.
12. We often chat with our friends.
13. Please switch of the TV.
14. My wife and I went to a movie.
15. Mohan and I will come.
16. 1 have a scooter.
17. This cost me a lot.
18. I doubt if he will succeed.
19. We have been living in Bengaluru since 2015.
20. We have a lot of furniture in our house.

TS Inter 1st Year English Grammar Correction of Errors in Sentences

III. Rewrite the following sentences after correcting the errors :

1. Can you read the Urdu alphabets ?
2. The police is investigating the case.
3. Here is your glasses.
4. Look at the man in the blue jean.
5. Have you seen the table of content of this textbook ?
6. Mumps are a kind of disease.
7. There were a series of programmes to mark the occasion.
8. She bought a toothpaste.
9. This box has twelve dozens of apples.
10. The athlete ran a four-miles race.

TS Inter 1st Year English Grammar Correction of Errors in Sentences

11. I received five thousands rupees from the manager.
12. Most male deers have horns.
13. Eight hundred rupees are too much for a pen.
14. A black and white dog are following me.
15. A black and a white dog is following me.
16. Many a man were cheated in this way.
17. I lost my all belongings.
18. Neither he nor his wife have arrived yet.
19. More than one person are working here.
20. The first inning is over.
Answer:
1. Can you read the Urdu alphabet ?
2. The police are investigating the case.
3. Here are your glasses.
4. Look at the man in the blue jeans.
5. Have you seen the table of contents of this textbook ?
6. Mumps is a kind of disease.
7. There was a series of programmes to mark the occasion.
8. She bought a tube of toothpaste.
9. This box has twelve dozen of apples.
10. The athlete ran a four-mile race.
11. I received five thousand rupees from the manager.
12. Most male deer have horns.
13. Eight hundred rupees is too much for a pen.
14. A black and white dog is following me.
15. A black and a white dog are following me.
16. Many a man was cheated in this way.
17. I lost all my belongings.
18. Neither he nor his wife has arrived yet.
19. More than one person is working here.
20. The first innings is over.

TS Inter 1st Year English Grammar Correction of Errors in Sentences

IV. Rewrite the following sentences after correcting the errors :

1. It is myself.
2. She and me are twins.
3. Each of these girls have wide eyes.
4. Neither of these cars are worth the money.
5. Both didn’t attend the meeting.
6. We all didn’t go.
7. Sharma plays cricket better than me.
8. Any one of these two boys are sent for training.
9. I haven’t got some pens.
10. If I were him. I wouldn’t have played the game.
11. Only they who have admit passes will be allowed in.
12. Drink water which tastes better.
13. Every woman raised their voice.
14. Sheila and Nancy like one another.
15. My neighbour that works in a bank has gone to Mumbai.
16. My three sisters like each other.
17. Divide the pieces of bread between him and me.
18. Shrika is senior than Srihan.
19. These all mangoes are ripe.

TS Inter 1st Year English Grammar Correction of Errors in Sentences

20. There are no less than ten thousand books in this library..
21. She is worst than her cousin.
22. This picture is the best of the two.
Answer:
1. It is I.
2. She and I are twins.
3. Each of these girls has wide eyes.
4. Neither of these cars is worth the money.
5. Neither attend the meeting.
6. None of us went.
7. Sharma plays cricket better than I.
8. Either of these two boys is sent for training.
9. I haven’t got any pens.
10. If I were he, I wouldn’t have played the game.
11. Only those who have admit passes will be allowed in.
12. Drink water that tastes better.
13. Every woman raised her voice.
14. Sheila and Nancy like each other.
15. My neighbour who works in a bank has gone to Mumbai.
16. My three sisters like one other.
17. Divide the pieces of bread between he and I.
18. Shrika is senior to Srihan.
19. All these mangoes are ripe.
20. There are no fewer than ten thousand books in this library.
21. She is worse than her cousin.
22. This picture is the better of the two.

TS Inter 1st Year English Grammar Correction of Errors in Sentences

V. Rewrite the following sentences after correcting the errors.

1. I need an advice from an expert.
2. He is more better than she.
3. This is the most best book I have read.
4. Virat Kohli is better than any cricketer in India.
5. This is strongest of any other metals.
6. She has been helping the poors.
7. The two first chapters are very interesting.
8. I am hopeless about his success.
9. She was not smart early.
10. This is a worth reading novel.
11. He hasn’t written much stories.
12. Open your book at six page.
13. This is a best book.
14. Ooty is cool than Thirupathi.
15. I paid him rupees hundred.
Answer:
1. I need a piece of advice from an expert.
2. He is better than she.
3. This is the best book I have read.
4. Virat Kohli is better than any other cricketer in India.
5. This the strongest of all metals.
6. She has been helping the poor.
7. The first two chapters are very interesting.
8. I have no hope of his success.
9. She was not smart earlier.
10. This is a novel worth reading.
11. He hasn’t written many stories.
12. Open your book at page six.
13. This is a very good book.
14. Ooty is cooler than Thirupathi.
15. I paid him a hundred rupees.

TS Inter 1st Year English Grammar Correction of Errors in Sentences

VI. Rewrite the following sentences after correcting the errors.

1. Sania Mirza is more popular than any tennis player.
2. Of the two this is the best article.
3. Our apartment is on third floor.
4. When Rome was burning, Nero is playing on the flute.
5. She enjoys to sing patriotic songs.
6. Why you were absent yesterday ?
7. She scarce blames others.
8. This is different to others.
9. She resembles to her mother.
10. I was prevented to do my work.
11. Would you mind to open the door ?
Answer:
1. Sania Mirza is more popular than any other tennis player.
2. Of the two this is the better article.
3. Our apartment is on the third floor.
4. When Rome was burning, Nero was playing on the flute.
5. She enjoys singing patriotic songs.
6. Why were you absent yesterday ?
7. She scarcely blames others.
8. This is different from others.
9. She resembles her mother.
10. I was prevented from doing my work.
11. Would you mind opening the door ?

TS Inter 1st Year English Grammar Correction of Errors in Sentences

VII. Rewrite the following sentences after correcting the errors.

1. My brother is working in tribal area.
2. I have an urgent business.
3. Kaleshwaram Project is built on Godavari.
4. Moon is very bright today.
5. I shall be visiting UK next month.
6. Himalayas form the northern boundary of India.
7. We should love the nature.
8. The Calcutta is a big city.
9. I have read Ramayana thrice.
10. David goes to the church every Sunday.
11. The gold is a precious metal.
12. He can play sitar well.
13. Lion is the king of beasts.
14. I had the lunch at noon.
15. I met my friend at college.
Answer:
1. My brother is working in a tribal area.
2. I have (some) urgent business.
3. Kaleshwaram Project is built on the Godavari.
4. The Moon is very bright today.
5. I shall be visiting the UK next month.
6. The Himalayas form the northern boundary of India.
7. We should love nature.
8. Calcutta is a big city.
9. I have read the Ramayana thrice.
10. David goes to church every Sunday.
11. Gold is a precious metal.
12. He can play the sitar well.
13. The Lion is the king of beasts.
14. I had lunch at noon.
15. I met my friend at the college.

TS Inter 1st Year English Grammar Correction of Errors in Sentences

VIII. Rewrite the following sentences after correcting the errors.

1. One of my friends have gone to the UAE.
2. Each of the girls were given the medals.
3. Everyone of the workers have stayed away from work.
4. Neither of the participants were able to win the match.
5. Age and experience bring wisdom to man.
6. Bread and butter are my favourite breakfast.
7. Where you are going ?
8. When vou will come here again ?
9. He asked me if I am going to Dubai.
10. I asked her if she is learning dance.
11. You are married, isn’t it ?
12. I like skating, do I ?
13. As I was ill so I could not go.
14. Both Hari as well as Krishna came to see me.
15. She said that she saw him last night.
16. The train left before I arrived.
17. I had been to Vijayawada yesterday.
18. I took my supper.
19. He knows to swim.

TS Inter 1st Year English Grammar Correction of Errors in Sentences

20. She cut her pencil.
21. I said to him to go.
22. He gave a speech.
23. He made a lecture.
24. My tooth is painting.
25. He made a goal.
Answers:
1. One of my friend has gone to the UAE.
2. Each of the girls was given the medals.
3. Everyone of the workers has stayed away from work.
4. Neither of the participants was able to win the match.
5. Age and experience brings wisdom to man.
6. Bread and butter is my favourite breakfast.
7. Where are you going ?
8. When will you come here again ?
9. He asked me if I was going to Dubai.
10. I asked her if she was learning dance.
11. You are married, aren’t you ?
12. I like skating, don’t I ?
13. As I was ill I could not go. (OR)
I was ill so I could not go.
14. Both Hari and Krishna came to see me. (OR)
Hari as well as Krishna came to see me.
15. She said that she had seen him last night.
16. The train had left before I arrived.
17. I went to Vijayawada yesterday.
18. I had my supper.
19. He knows how to swim.
20. She sharpened her pencil.

TS Inter 1st Year English Grammar Correction of Errors in Sentences

21. I told him to go.
22. He made a speech.
23. He gave a lecture.
24. My tooth is aching.
25. He scored a goal.

IX. Rewrite the following sentences after correcting the errors.

1. I am too glad to see you.
2. This coffee is very hot to drink.
3. She is very much sorry.
4. You are leaving back your bag.
5. You can lift it by and by.
6. We scarcely see a lion.
7. He behaved cowardly.
8. Sarojini Naidu was called as the Nightingale of India.
9. She works very hardly.
10. He speaks English very good.
11. His version is somewhat true.
12. She speaks the truth always.
13. He comes to me often.
14. Most likely the shops will remain closed tomorrow.
15. The whole India is proud of his achievement.
Answer:
1. I am very glad to see you.
2. This coffee is too hot to drink.
3. She is very sorry.
4. You are leaving behind your bag.
5. You can lift it little and little.
6. We rarely see a lion.
7. He behaved in a cowardly manner.
8. Sarojini Naidu was called the Nightingale of India.
9. She works very hard.
10. He speaks English very well.
11. His version is partly true.
12. She always speaks the truth.
13. He often comes to me.
14. Most probably the shops will remain closed tomorrow.
15. The whole of India is proud of his achievement.

TS Inter 1st Year English Grammar Correction of Errors in Sentences

X. Rewrite the following sentences after correcting the errors.

1. I have ordered for three dishes.
2. He entered into the hall.
3. She has married with her cousin.
4. We are awaiting for the train.
5. He has been suffering with Corona.
6. She covered her head by a shawl.
7. They waited three hours.
8. I enquired her where her husband was.
9. He went for riding.
10. She is called with different names.
11. Sion the document with ink.
12. This is a comfortable house to live.
13. I filled water in the bucket.
14. I shall explain them this.
15. I travelled by my Principal’s car.
16. She was accused for stealing a gold ring.
17. He congratulated me for my success.
18. She got down the bus at Mancherial.
19. I don’t agree for your proposal.
20. This is the road to go.

TS Inter 1st Year English Grammar Correction of Errors in Sentences

21. Though he is fat, but he runs fast.
22. Scarcely had he gone than the phone rang.
23. No sooner had he gone when the officer came.
24. She is not only beautiful but intelligent.
25. I doubt that he will get through the exam.
26. He was handsome but everyone admired him.
27. You are not right nor wrong.
28. Wait while I come.
29. Unless you do not try, you will never succeed.
30. City life is tense and village life is relaxed.
Answers:
1. I have ordered three dishes.
2. He entered the hall.
3. She has married her cousin.
4. We are awaiting the train./We are waiting for the train.
5. He has been suffering from Corona.
6. She covered her head with a shawl.
7. They waited for three hours.
8. I enquired of her where her husband was.
9. He went riding. OR He went for a ride.
10. She is called by different names.
11. Sign the document in ink.
12. This is a comfortable house to live in.
13. I filled the bucket with water.
14. I shall explain this to them.
15. I travelled in my Principal’s car.
16. She was accused of stealing a gold ring.
17. He congratulated me on my success.
18. She got down from the bus at Mancherial.
19. I don’t agree to your proposal.
20. This is the road to go by.

TS Inter 1st Year English Grammar Correction of Errors in Sentences

21. Though he is fat, he runs fast.
22. Scarcely had he gone when the phone rang.
23. No sooner had he gone than the officer came.
24. She is not only beautiful but also intelligent.
25. I doubt whether he will get through the exam.
26. He was handsome and everyone admired him.
27. You are neither right nor wrong.
28. Wait till I come.
29. Unless you try, you will never succeed.
30. City life is tense but village life is relaxed.

XI. Rewrite the following sentences after correcting the errors.

1. A bouquet of yellow roses lend colour and fragrance.
2. Here is the keys.
3. Two miles are too far to walk.
4. If I was a bird, I would fly.
5. I wish it was Sunday.
6. All the staff are here.
7. The captain with his men were killed.
8. It is a two days programme.
9. Neither he came nor he wrote.
10. One of my friend is here.
11. He enioyed at the party.
12. He is in class tenth.
13. He gave his examination.
14. Columbus invented America.
15. Edison discovered electric bulb.
16. Never I have seen such a mess.
17. Should I cut this word ?
18. He asked a help.
19. They insisted to pay.
20. Choose the best of the two options.

TS Inter 1st Year English Grammar Correction of Errors in Sentences

21. He went to foreign.
22. I asked a question to him.
23. We are doing Yoga every day.
24. All the roads are covered by snow.
25. He does not care for my words.
Answers:
1. A bouquet of yellow roses lends colour and fragrance.
2. Here are the keys.
3. Two miles is too far to walk.
4. If I were a bird, I would fly.
5. I wish it were Sunday.
6. All these staff is here.
7. The captain with his men was killed.
8. It is a two day programme.
9. Neither did he come nor did he write.
10. One of my friends is here.
11. He enjoyed himself at the party.
12. He is in class ten.
13. He took his examination.
14. Columbus discovered America.
15. Edison invented electric bulb.
16. Never have I seen such a mess.
17. Should I erase this word ?
18. He asked for help.
19. They insisted on paying.
20. Choose, the better of the two options.
21. He went abroad.
22. I, asked him a question.
23. We do Yoga every day.
24. All the roads are covered with snow.
25. He pays no attention to what I say.

TS Inter 1st Year English Grammar Correction of Errors in Sentences

XII. Rewrite the following sentences after correcting the errors.

1. We elected Ram as President.
2. Did you went to school yesterday ?
3. She explained me the matter.
4. Are you really interested with English grammar ?
5. Bring me half glass water.
6. Every Sunday we go to the church.
7. He plays tennis, isn’t he ?
8. I returned back from London.
9. A bend in the road is not an end of the road.
10. I must change my cloths at once.
Answers:
1. We elected Ram President.
2. Did you go to school yesterday ?
3. She explained the matter to me.
4. Are you really interested in English Grammar ?
5. Bring me half a glass water.
6. Every Sunday we go to church.
7. He plays tennis, doesn’t he ?
8. I returned from London.
9. A bend in the road is not the end of the road.
10. I must change my clothes at once.

TS Inter 1st Year English Grammar Correction of Errors in Sentences

TS Inter 2nd Year Accountancy Study Material Chapter 7 Computerised Accounting System

Telangana TSBIE TS Inter 2nd Year Accountancy Study Material 7th Lesson Computerised Accounting System Textbook Questions and Answers.

TS Inter 2nd Year Accountancy Study Material 7th Lesson Computerised Accounting System

Very Short Answer Questions

Question 1.
What is Computerized Accounting?
Answer:

  1. Computerised Accounting is the maintaining of accounts through computers by use of special software.
  2. computerized accounting is an accounting system formed by computer (Automation) and accounting rules and procedures.
    Computerised accounting = Computer (Automation) + Accounting (Rules & Procedures)

TS Inter 2nd Year Accountancy Study Material Chapter 7 Computerised Accounting System

Question 2.
What is the need for using Computerized Accounting?
Answer:

  1. Computerized accounting system provides various services to business concerns to meet all the purposes.
  2. A computerized accounting system automates the accounting process by improving efficiency and cutting down the cost.
  3. A computerized accounting system saves time, and effort, considerably reduces/ eliminates mathematical errors and allows for much more timely information.
  4. Data within the computerized accounting system is accurate and upto date. Management can request online report in real-time and make decisions more reliable and timely.

Question 3.
How can you say that computerized accounting Is useful than Manual Accounting?
Answer:
Computerized Accounting is more useful than manual accounting because it have unique features and several advantages over then manual accounting. They are:

  1. Fast, Simple and Integreated.
  2. Accuracy and error free.
  3. Reliability, scalability and security.
  4. Upto date information and helps to make Quick Decisions.

Question 4.
What is the Feature of Scalability?
Answer:

  1. Computerized Accounting has the flexibility to record transactions with the changing volume of business.
  2. Computerized Accounting is designed to meet the current and future needs of the companies irrespective of their size and style.

Question 5.
Write about the following features of Computerized Accounting.
Answer:
1. Total Visibility: Computerized Accounting provides enough time to plan to increase the customer base and enhance customer satisfaction. Companies will have greater visibility into the day-to-day business operations and access to very important information.

2. Supremacy: Computerized Accounting is capable of storing huge volumes of transactions with greater retrieval capacity and efficiency.

3. Accuracy and Spread: Computerized accounting has customized templates for users which allow fast and accurate data entry. Thus, after recording the transactions it generates the information and reports automatically and it is very simple to operate with a greater speed.

4. Simple and Integrated: Computerized Accounts helps all business by automating and integrating all business activities. Such activities may be sales, finance, purchase, inventory, and manufacturing etc. At also facilitates the arrangement of accurate and up-to-date business information in a readily usable form.

TS Inter 2nd Year Accountancy Study Material Chapter 7 Computerised Accounting System

Question 6.
Write any two of the limitations of Computerized Accounting.
Answer:
1. Cost of Training: The computerized accounting packages generally require specialized staff personnel. As a result, huge training costs are incurred to understand the use of hardware and software on a continuous basis because newer types of hardware and software are acquired to ensure efficient and effective use of computerized accounting systems.

2. Health Issues: The extensive use of computer systems may lead to the development of various health problems such as bad backs, eyestrain, muscular pains, etc. This affects adversely the working efficiency of accounting staff on one hand and increased medical expenditure on such staff.

Question 7.
Write any two of the differences between Manual and Computerized Accounting.
Answer:

Manual Accounting System Computerized Accounting System
1. Definition/Meaning: Manual Accounting is the system which physical register is maintained for keeping the records. In Computerized Accounting system where we use computer and different accounting software to maintained for digital records.
2. Measurements/Calculations:
All Calculations of adding, subtracting and balancing are done manually.
All the calculations are done by computer system.

Question 8.
What do you know about the following software?
Answer:
1. Profit Book:

  • This software offers complete inventory management and detailed tax reports that help in stabilized controlling of the business.
  • Whether, the firm is a manufacturing unit, wholesaler, or retailer, Profit Books offers a steady platform to track management process and file tax returns.
  • From managing income and expense statements to tracking the entire cash flow, Profit Books serve as the best accounting and inventory management solution.

2. Giddh:

  • It is an all-inclusive, modern accounting software in India, which uses local database and delivers custom reports for the successful growth of the business. The software is not only for financial management, but also deals in inventory, stock management and handles bank accounts with high-level security.
  • Giddh is GST compliance and delivers insight reports for better analysis of accounting stability. The software supports multi-currency features that enable to manage globalized departments form one place.

3. Vyapar:

  • This accounting software is a free platform that allows maintaining invoice, getting inventory records, managing books of accounts, and tracking daily business activities while focusing on business growth rate.
  • Since, most of the small sector business needs a digital upgrade, Vyapar acts as an effective solution.
  • Vyapar is GST compliant and allows error-free tax returns while eliminating errors occurred with manual calculations.
  • Vyapar takes-charge to control individual units of the business, creates customizable invoices, and automates payment reminders.

4. Logic:

  • It is an online accounting software in India that satisfies the demand of having a strategic ERP system in the accounting and financial module.
  • Logic is advanced computerized software that facilitates error-free financial management, budgeting and planning, assists forecasting, renders efficient performance analysis and integrates general ledger and accounting data.
  • Business management can hold cross-communication with different departments and facilitate collaborations across business delegates using comprehensive data offered by Logic.

5. myBooks:

  • This software is an excellent accounting solution for entrepreneurs, accountants, small IT and financial companies and free lancers. myBooks GST Accounting Software designed for all small business owner.
  • my books designed from the small business owners’ perspective, kept easy user experience as the central objective in designing product. So, there will not be any need for formed training.

6. Zoho Books:

  • This is popular online accounting software in India, which acts as an integrated platform for end-to-end financial solutions. Zoho Books is GST compliant, automates business workflow, and manages financial accounting and help in managing departments collectively from one single source.
  • Right from maintaining sales orders and invoicing, Zoho Books mundane GST invoices, bookkeeping, huge, ledgers, and various accounting tasks.
  • Zoho Books is feature-packed to manage cash receivables, payables, banking, inventory, timesheets, and business contacts and generate reports.

TS Inter 2nd Year Accountancy Study Material Chapter 7 Computerised Accounting System

Short Answer Questions

Question 1.
Explain the importance of Computerized Accounting.
Answer:
A computerized accounting system is a system used by businesses for recording their financial information.
The importance of computerized accounting is given belows:
1) Time and Cost Savings: The use of computers makes in putting accounting information so simple. Business transactions are entered into the system and the system posts transactions accordingly. Thus, a computerized accounting system saves time and money,

2) Organization: A computerized accounting system help business to stay organized when information is entered into the system. It makes finding the information easy. Employees can see any financial information whenever it is needed.

3) Storage: In a Computerized accounting system data can be stored quickly after the information is entered into the system and the information is stored indefinitely. Companies perform backups on the system regularly to avoid loss of any information.

4) Distribution: Computerized accounting systems allows companies to distribute financial information easily. Financial statements are printed directly from the system and are distributed internally and externally to those needs the information.

5) Management Reports: Data within the computerized accounting system is accurate and up-to-date. Management can request online report in real-time and that makes management decisions more reliable and timely.

6) Regulatory Compliance: Reports are required on a regular basis from various government Agencies. A computer system can organize their data and reports to comply with these statutory requirements.

Question 2.
What are the features of Computerized Accounting?
Answer:
1) Accuracy and Speed: Computerized accounting has customized templates for users which allow fast and accurate data entry. Thus, after recording the transactions it generates the information and reports automatically and it is very simple to operate with a greater speed.

2) Quick Decision Making: This system generates real-time, comprehensive Management Information System (MIS) reports and ensures access to complete and critical information, instantly.

3) Scalability: It has the flexibility to record transactions with the changing volume of business. It is designed to meet the current and future needs of the companies irrespective of their size and style.

4) Security: Secured data and information can be kept confidential as compared to the „ . traditional accounting system.

5) Simple and Integrated: Computerized Accounting helps all businesses by automating and integrating all the business activities. Such activities may be sales, finance, purchase, inventory and manufacturing etc. it also facilitates the arrangement of accurate and up-to-date business information in a readily usable form.

6) Supremacy: Computerized Accounting is capable of storing huge volumes of transactions with greater retrieval capacity and efficiency.

Question 3.
Explain the five Advantages of Computerized Accounting.
Answer:
1) Accuracy: The possibility of error is eliminated in a computerized accounting system, because the primary accounting data is entered once for all the subsequent usage and processes in preparing the accounting reports.

2) Automation: Most of computerized accounting systems have standardized, user-defined formats of accounting reports that are generated automatically. The accounting reports such as Cash book, Trial balance, and Statement of accounts are obtained just by click of a mouse in a computerized accounting environment.

3) Efficiency: The computer-based accounting systems ensure better use of resources and time. This brings about efficiency in generating decisions, useful information and reports.

4) Management Information System Reports: The computerized accounting system facilitates the real-time production of management information reports, which will help management to monitor and control the business effectively.

Question 4.
Write any five limitations of Computerized Accounting.
Answer:
1) Cost of Training: The computerized accounting packages generally require specialized staff personnel. As a result, huge training costs are incurred to understand the use of hardware and software on a continuous basis because newer types of hardware and software are acquired to ensure efficient and effective use of computerized accounting systems.

2) Health Issues: The extensive use of computer systems may lead to development of various health problems such as bad backs, eyestrain, muscular pains, etc. This affects adversely the working efficiency of accounting staff on one hand and increased medical expenditure on such staff.

3) Reduction of Manpower: The introduction of computers in accounting work reduces the number of employees in an organization. Thus, it leads to greater amount of unemployment.

4) Security Issues: Computer-related crimes are difficult to detect. The alteration of records in a manual accounting system is easily detected. Fraud and embezzlement are usually committed on a computerized accounting system by alteration of data or programs. Hacking of passwords or user rights may change the accounting records.

5) Staff Resistance: Whenever the accounting system is computerized, there is a Significant degree of resistance from the existing accounting staff, partly because of the fear that they shall be made redundant and largely, because of the perception that they shall be less important to the organization.

6) System Failure: The danger of the system crashing due to hardware failures and the subsequent loss of work is a serious limitation of the computerized accounting system. Software damage and failure may occur due to attacks by viruses. No full proof solutions are available as of now to tackle the menace of attacks on software by viruses.

7) Unanticipated Errors: Since, the computers lack capability to judge, they cannot detect unanticipated errors as human beings commit.

TS Inter 2nd Year Accountancy Study Material Chapter 7 Computerised Accounting System

Question 5.
Explain the difference between Manual and a Computerized Accounting system.
Answer:

Basis Manual Accounting System Computerized Accounting System
Definition Manual Accounting is the system in which physical register of Journal and Ledger is maintained for keeping the records of each transaction. In this system of accounting, computer and different accounting software are maintained for digital record of each transaction.
Identification Based on application of Accounting Principles. Based on application of Accounting Principles software is designed.
Measurement All calculations of adding, subtracting and balancing are done manually. All the calculations are done by computer system.
Recording Recording of financial transac­tions is through Journal (book of original entry). Data content of these transactions is stored in well-designed database.
Adjustments Adjustment Entries are to be made in Journal and Ledger. We create Ledgers for adjustment record voucher entry.
Rectification of Errors Rectification of Errors requires recording of adjustment entries. Easy to rectify by deleting the wrong entry and record correct entry or correcting the figure.
Backup Incase of fire or other miship, it is not possible to backup and save the paper records, unless many copies of all pages are made and stored in different places. All transactions can be saved and backed up in Computerized Accounting.
Speed and Accuracy User can flip to the pages to the needed, and even spread the books out of a table if needed. Quicker as far as entering the transactions is concerned.

 

Question 6.
What are the different factors influencing the selection of Prepackaged Accounting Software?
Answer:
1) Cost of installation: The choice of the software obviously requires consideration of organization’s ability to afford the hardware and software. A simple guideline to take such a decision is the cost-benefit analysis of the available options and the financing opportunities available to the firm. Sometimes, certain software which appears cheap to buy, involve heavy maintenance and alternation costs.

2) Data Facility:The transfer of database to other systems or other software is sometimes expected from the accounting software. Organizations may need to transfer information directly from the ledger into spreadsheet software such as Lotus or Excel for more flexible reporting. The software should allow the hygienic, untouched data transfer.

3) Ease of Adaptation: The software consider must be capable of attracting users and, if it requires simple training, should be able to motivate its potential users.

4) An important consideration before sourcing accounting software is flexibility, viz., data entry and the availability and design of various reports expected from it. The user should be able to run the software on a variety of platforms and machines.

5) MIS Reports: The MIS reports and the degree to which they are used in the organization also determine the acquisition of software. For example, software that requires simply producing the final accounts or cashflow or ratio analysis may be ready-to-use software. However, the software, which is expected to produce cost records, needs to be customized as per user requirements.

6) Security Features: Another consideration before buying accounting software is the security features, which prevent unauthorized personnel from accessing and/or manipulating data in the accounting system.

7) Size of Organisation: The size of the organization and the volume of business transactions do affect the software choices. Small organizations, e.g., in non-profit organizations, where the number of accounting transactions are not so large, may opt for simple, single-user operated software. While, a large organization may require sophisticated software to meet the multiuser requirements, geographically scattered and connected through complex networks.

8) Vendors Reputation: Another important consideration is the reputation and capability of the vendor. This depends upon how long has been the vendor is in business of software development, whether there are other users of the software.

Question 7.
Explain the types of Accounting Packages.
Answer:
Every Computerized Accounting System is implemented to perform the accounting activity. Accounting Software is are an integral part of the computerized accounting system such as recording and storing of accounting data and generate reports as per the requirements of the user. As per this, accounting software is classified into three categories. They are:
TS Inter 2nd Year Accountancy Study Material Chapter 7 Computerised Accounting System 1
1) Read-to-Use Software:

  1. This software is suited for organizations running small or conventional business where the frequency or volume of accounting transactions is very low.
  2. The cost of installation is low and number of users is limited. It is relatively easier to learn and accountant adaptability is very high.
  3. This implies that level of secrecy is relatively low and the software is prone to data frauds. The training needs are simple and sometimes the supplier of software offers the training on the software free.

TS Inter 2nd Year Accountancy Study Material Chapter 7 Computerised Accounting System

2) Customized Software:

  1. This may be customized to meet the special requirement of the business orginizations. Customized software is suited for medium businesses and can be linked to the other information systems.
  2. The cost of installation and maintenances is relatively high because the high cost is to be paid to the vendor for customization.
  3. Secrecy of data and software can be better maintained in this software.

3) Tailored Software:

  1. The accounting software is generally tailored in large business organizations such as multi-national companies with multi-users and geographically scattered locations.
  2. This software requires specialized training to the users.
  3. The secrecy and authenticity checks are robust in such type of software and they offer high flexibility in terms of number of users.

TS Inter 2nd Year Accountancy Study Material Chapter 6 Retirement and Death of a Partner

Telangana TSBIE TS Inter 2nd Year Accountancy Study Material 6th Lesson Retirement and Death of a Partner Textbook Questions and Answers.

TS Inter 2nd Year Accountancy Study Material 6th Lesson Retirement and Death of a Partner

Very Short Answer Questions

Question 1.
State how a partner may retire from partnership firm.
Answer:
1. An existing partner may retire from a firm due to many factors such as old age, better business prospects elsewhere, differences with other partners, health problems etc.

2. According to Section 32(i) of the partnership Act 1932, a partner may retire
a) With the consent of all other partners,
b) In accordance with an express agreement with the partners.
c) By circulating a written notice among other partners, incase of partnership will.

TS Inter 2nd Year Accountancy Study Material Chapter 6 Retirement and Death of a Partner

Question 2.
What is Ratio of Gaining?
Answer:

  1. The ratio at which the share of retiring partner is taken by the continuing partners is called Ratio of Gaining.
  2. Ratio of Gaining = New Profit sharing Ratio – Old profit sharing ratio

Question 3.
Why ratio of gaining is to be ascertained?
Answer:

  1. Calculation of ratio of gaining is very important because, the share of goodwill to be paid to the retiring partner, shall be contributed by the remaining partners in their respective share of gaining.
  2. The more the gain, the more the goodwill, one has to contribute. The less the gain, the less the goodwill one has to contribute.

Question 4.
X, Y and Z are partners sharing profits and losses in the ratio of 3: 2: 2. Calculate new profit sharing of;
a) X and Y if Z retires from the business.
b) Y and Z if X retires from the business.
c) X and Z if Y retires from the business.
Answer:
XYZ profit & loss ratio = 3:2:2
TS Inter 2nd Year Accountancy Study Material Chapter 6 Retirement and Death of a Partner 1

Question 5.
A, B and C are partners sharing profits and losses equally. Mr. C retires from the business A and B decided to continue the business and sharing profits and losses in the ratio of 3: 2 respectively. Calculate the ratio of gaining of A and B.
Answer:
AB & C profit sharing ratio = 1:1:1
A & B new profit sharing ratio = 3:2
Ratio of Gaining = New Ratio – Old ratio.
TS Inter 2nd Year Accountancy Study Material Chapter 6 Retirement and Death of a Partner 2

Question 6.
P, Q and R are partners sharing profits and losses in the ratio of 4: 3: 2 respectively. R retires from the business and his share is purchased by P and Q in the ratio of 2:1. Calculate New Profit sharing ratio of P and Q.
Answer:
P, Q, R old profit sharing ratio = 4:3:2 i.e., 4/9: 3/9: 2/9
R’s share of profit 2/9 being purchased by
TS Inter 2nd Year Accountancy Study Material Chapter 6 Retirement and Death of a Partner 3
New profit sharing ratio of P = P’s old share + proportion of R’s share purchased
TS Inter 2nd Year Accountancy Study Material Chapter 6 Retirement and Death of a Partner 4
New profit sharing ratio of Q = Q’s old share + proportion of R’s share purchased
TS Inter 2nd Year Accountancy Study Material Chapter 6 Retirement and Death of a Partner 5
The new profit sharing ratio of P & Q is 16/27: 11/27 (or) 16: 11.

Question 7.
Ram, Rahim and Akbar are partners sharing profits and losses in the ratio of 3: 2: 3 respectively. Akbar retires from the business and Rahim purchased the share of Akbar. Calculate new profit sharing ratio of Ram and Rahim.
Answer:
Ram, Rahim and Akbar profit sharing ratio = 3:2:1 (or) 3/6: 2/6: 1/6
Rahim purchased Akbar shares then
TS Inter 2nd Year Accountancy Study Material Chapter 6 Retirement and Death of a Partner 6
Ram: Rahim New Profit sharing Ratio = 3/6: 3/6 = 3: 3 = 1: 1.

TS Inter 2nd Year Accountancy Study Material Chapter 6 Retirement and Death of a Partner

Question 8.
X, Y and Z are partners with profit sharing ratio of 5: 4: 3 respectively. Z retires from the business. X and Y decided to share future profits in the ratio of 3: 2. Calculate the ratio of gaining of X and Y.
Answer:
X, Y and Z profit sharing ratio = 5:4:3
X and Y new (future) profit ratio = 3:2
Gaining ratio = New ratio – Old ratio.
TS Inter 2nd Year Accountancy Study Material Chapter 6 Retirement and Death of a Partner 7

Question 9.
A, B and C are partners sharing profits and losses at the ratio of 5: 4: 3 respectively. C retires from business. A and B decided to continue the business and sharing future profits in the ratio of 4: 3. Calculate the ratio of gaining of A and B.
Answer:
A, B and C profit sharing ratio = 5:4:3
A and B new (future) profit ratio = 4:3
Gaining ratio = New ratio – Old ratio.
TS Inter 2nd Year Accountancy Study Material Chapter 6 Retirement and Death of a Partner 8

Question 10.
Sitha, Geetha and Savitha are partners sharing profits and losses in the ratio of 4: 3: 2 respectively. Savitha retired from the business. The value of goodwill is estimated at Rs. 72,000. There is no goodwill balance in the books. Create/Raise goodwill account in the books.
Answer:
Sitha, Geetha and Savitha profit sharing ratio = 4:3:2
When the Goodwill raised worth Rs. 72,000.
Journal entry when goodwill is raised:
TS Inter 2nd Year Accountancy Study Material Chapter 6 Retirement and Death of a Partner 9
TS Inter 2nd Year Accountancy Study Material Chapter 6 Retirement and Death of a Partner 10

Question 11.
Vani, Rani, Radha are partners sharing profits and losses equally. Radha retires from the business. Goodwill of the firm is valued at Rs. 40,000. Goodwill account showing a balance of Rs. 10,000 in the books. The pass journal entry to raise goodwill in the books.
[Hint: Goodwill to be created is Rs. 30,000 only as goodwill existing in the books is Rs. 10,000].
Answer:
Journal entries when goodwill is raised:
TS Inter 2nd Year Accountancy Study Material Chapter 6 Retirement and Death of a Partner 11

TS Inter 2nd Year Accountancy Study Material Chapter 6 Retirement and Death of a Partner

Question 12.
Ramesh, Suresh and Rajesh are partners sharing profits and losses in the ratio of 3:2:1 respectively. Suresh retires from the business. Ramesh and Rajesh decided to continue the business and share future profits in the ratio of 3: 2, goodwill of the firm valued at Rs. 60,000. Give necessary journal entries to create and writeoff goodwill.
Answer:
Journal Entries when goodwill is raised and written-off
TS Inter 2nd Year Accountancy Study Material Chapter 6 Retirement and Death of a Partner 12
TS Inter 2nd Year Accountancy Study Material Chapter 6 Retirement and Death of a Partner 13

Question 13.
X, Y and Z are partners sharing profits and losses equally. Goodwill of the firm is valued at Rs. 45,000. X retires from the business. Y and Z divided to continue the business by sharing future profits and losses in the ratio of 3: 2 respectively. Give necessary journal entries without raising goodwill account.
Answer:
X, Y, Z’s old profit sharing ratio =1:1:1
Y and Z new profit sharing ratio = 3:2
Ratio of gaining = New ratio – Old ratio
TS Inter 2nd Year Accountancy Study Material Chapter 6 Retirement and Death of a Partner 14
Goodwill of the firm is Rs. 45,000
The share of goodwill payable to ‘X’ is 45,000 x 1/3 = 15,000 Rs. 15,000 payable to ‘X’ will be contributed by Y and Z in their ratio of gaining 4:1.

Journal Entries without raising Goodwill account
TS Inter 2nd Year Accountancy Study Material Chapter 6 Retirement and Death of a Partner 15

Question 14.
What is joint Life policy?
Answer:
On death of a partner, firm has to pay huge amount of cash to the executors of the deceased partner. This may adversely affect the resources of the firm. To over come this problem, firm may take a insurance policy as the live of the partners to guarclthe risk. This insurance policy is known as Joint Life Policy.

In the event of death of any partner, the insurance company pays the sum assured to the firm. In this way the firm add comes the problem of setting the amount due to the decreased partner.

Question 15.
How do you ascertain share of profit/loss payable to deceased partner?
Answer:

  1. Share of profit/loss payable to deceased partner is ascertain till the date of his/her death during the current financial year.
  2. Partnership deed contains a provisions for ascertainment of profit in the event of death of partner.
  3. Accordingly, the share of profit/loss of deceased partner will be ascertained and paid to legal representatives of deceased partner along with another amount due.

Question 16.
What are the amounts payable to deceased partner?
Answer:
The amount payable to deceased partner includes:

  1. Capital contributed.
  2. Share in undistributed profits/losses.
  3. Share in accumulated reserves.
  4. Share in the goodwill of the firm.
  5. Share in profit/loss on revaluation of Assets and Liabilities.
  6. Share in profit/loss of the business till the date of death.

TS Inter 2nd Year Accountancy Study Material Chapter 6 Retirement and Death of a Partner

Question 17.
State the methods of accounting for payment of share of profit to deceased partner.
Answer:
After ascertaining the profit, there are two ways of recording the profit ascertained till the date of death.

1. Distribute the profit among all the partners in their respective old profit-sharing ratio.
TS Inter 2nd Year Accountancy Study Material Chapter 6 Retirement and Death of a Partner 16
2. Record the share of profit payable to decreased partner only in such a case the journal entry is
TS Inter 2nd Year Accountancy Study Material Chapter 6 Retirement and Death of a Partner 17
3. Sometimes, the continuing partners, instead of debiting to profit and loss a/c. They may contribute the share of profit of decreased partner by debiting to their capital accounts in their gaining ratio.
The entry is —> TS Inter 2nd Year Accountancy Study Material Chapter 6 Retirement and Death of a Partner 18

Textual Problems

When Goodwill is created / Raised:

Question 1.
X, Y and Z are partners sharing profits and losses equally. Their balance sheet as on 31 March 2020 was as under;
TS Inter 2nd Year Accountancy Study Material Chapter 6 Retirement and Death of a Partner 19
On the above date, Z retires from the business on the following conditions;
a) Stock and Machinery to be depreciated by 10%.
b) Provided for bad debts @ 5% on debtors.
c) Land revalued at Rs. 35,000.
d) Goodwill of the firm valued at Rs. 60,000.
Give necessary journal entries, ledger accounts and opening balance sheet of X and Y.
Answer:
Journal entries in the books of X, Y, Z partnership firm.
TS Inter 2nd Year Accountancy Study Material Chapter 6 Retirement and Death of a Partner 20
TS Inter 2nd Year Accountancy Study Material Chapter 6 Retirement and Death of a Partner 21
TS Inter 2nd Year Accountancy Study Material Chapter 6 Retirement and Death of a Partner 22
TS Inter 2nd Year Accountancy Study Material Chapter 6 Retirement and Death of a Partner 23

X and Y Balance Sheet as on 31 – 3 – 2020
TS Inter 2nd Year Accountancy Study Material Chapter 6 Retirement and Death of a Partner 24
TS Inter 2nd Year Accountancy Study Material Chapter 6 Retirement and Death of a Partner 25

TS Inter 2nd Year Accountancy Study Material Chapter 6 Retirement and Death of a Partner

Question 2.
X and Y are partners sharing profits and losses in the ratio of 3: 2. Their balance sheet as on 31 March, 2020 was as follows;
TS Inter 2nd Year Accountancy Study Material Chapter 6 Retirement and Death of a Partner 26
X retires from the business on the following terms:
a) Goodwill is valued at Rs. 20,000.
b) Depreciate stock and machinery by 10%.
c) Provide for bad debts at 6%.
d) Buildings are valued at Rs. 35,000.
Give Journal entries, necessary Ledger accounts and the Balance sheet.
Answer:
Journal entries in the books of X, Y, Z partnership firm.
TS Inter 2nd Year Accountancy Study Material Chapter 6 Retirement and Death of a Partner 27
TS Inter 2nd Year Accountancy Study Material Chapter 6 Retirement and Death of a Partner 28
TS Inter 2nd Year Accountancy Study Material Chapter 6 Retirement and Death of a Partner 29
TS Inter 2nd Year Accountancy Study Material Chapter 6 Retirement and Death of a Partner 30
TS Inter 2nd Year Accountancy Study Material Chapter 6 Retirement and Death of a Partner 31
Balance Sheet of Y as on 31 – 3 – 2015
TS Inter 2nd Year Accountancy Study Material Chapter 6 Retirement and Death of a Partner 32

Question 3.
S, P and G were partners sharing profits and loss in the ratio of 4: 3: 3. Their balance sheet as on 31st March, 2020 was as under;
TS Inter 2nd Year Accountancy Study Material Chapter 6 Retirement and Death of a Partner 33
G Retires from the business on the following terms:
a) Buildings valued at Rs. 1,30,000.
b) Depreciate Furniture and Machinery by 10%.
c) Provide for bad debts at Rs. 1,600.
d) Creditors Rs. 6,000 need not be paid.
e) Goodwill valued at Rs. 27,000.
f) G will be paid Rs. 17,700 immediately and the balance is transferred to his loan account. Give journal entries, ledger accounts and balance sheet of S and R
Answer:
Journal entries in the books of S, P & G Partnership firm.
TS Inter 2nd Year Accountancy Study Material Chapter 6 Retirement and Death of a Partner 34
TS Inter 2nd Year Accountancy Study Material Chapter 6 Retirement and Death of a Partner 35
TS Inter 2nd Year Accountancy Study Material Chapter 6 Retirement and Death of a Partner 36
TS Inter 2nd Year Accountancy Study Material Chapter 6 Retirement and Death of a Partner 37
TS Inter 2nd Year Accountancy Study Material Chapter 6 Retirement and Death of a Partner 38
TS Inter 2nd Year Accountancy Study Material Chapter 6 Retirement and Death of a Partner 39
Balance Sheet of ‘S’ and P’ as on 31.3.2020
TS Inter 2nd Year Accountancy Study Material Chapter 6 Retirement and Death of a Partner 40

TS Inter 2nd Year Accountancy Study Material Chapter 6 Retirement and Death of a Partner

Question 4.
Ajay, Vijay and Vinay were partners sharing profits and losses in the ratio of 5:3:2. Their balance sheet as on 31 March, 2020 was as under.
TS Inter 2nd Year Accountancy Study Material Chapter 6 Retirement and Death of a Partner 41
Vinay retires on the above date on the following conditions:
a) Goodwill of the firm is valued at Rs. 50,000.
b) Appreciate buildings by 20%.
c) Create a provision for bad debts at Rs. 1,000.
d) Depreciate plant and machinery by 10%.
e) Ajay and Vijay bring in cash Rs. 25,500 and Rs. 19,300 towards additional capital to pay the amount due to retiring partner Vinay.
Give journal entries and necessary ledger accounts and balance sheet of a new firm.
Answer:
Journal entries in the books of Ajay, Vijay and Vinay partnership firm.
TS Inter 2nd Year Accountancy Study Material Chapter 6 Retirement and Death of a Partner 42
TS Inter 2nd Year Accountancy Study Material Chapter 6 Retirement and Death of a Partner 43
TS Inter 2nd Year Accountancy Study Material Chapter 6 Retirement and Death of a Partner 44
TS Inter 2nd Year Accountancy Study Material Chapter 6 Retirement and Death of a Partner 45

Ajay, Vijay Balance Sheet as on 31-3-2020
TS Inter 2nd Year Accountancy Study Material Chapter 6 Retirement and Death of a Partner 46

Question 5.
Ganga, Yamuna and Saraswathi are partners sharing profits and losses in the ratio of 3:2:1 respectively. Their balance sheet as on 31st March 2019 was under.
TS Inter 2nd Year Accountancy Study Material Chapter 6 Retirement and Death of a Partner 47
Saraswathi retired from the business on the following conditions:
a) Depreciate machinery by 10% and furniture by 15%.
b) Stock to be appreciated by 20%.
c) Buildings are to be appreciated by 10%.
d) Goodwill of the firm is valued at Rs. 36,000.
Write up necessary Journal entries, ledger accounts and balance sheet of new firm.
Answer:
Journal entries in the books of Ganga, Yamuna and Saraswathi partnership firm.
TS Inter 2nd Year Accountancy Study Material Chapter 6 Retirement and Death of a Partner 48
TS Inter 2nd Year Accountancy Study Material Chapter 6 Retirement and Death of a Partner 49
TS Inter 2nd Year Accountancy Study Material Chapter 6 Retirement and Death of a Partner 50
TS Inter 2nd Year Accountancy Study Material Chapter 6 Retirement and Death of a Partner 51
Ganga and Yamuna balance sheet as on 31-3-2019
TS Inter 2nd Year Accountancy Study Material Chapter 6 Retirement and Death of a Partner 52

TS Inter 2nd Year Accountancy Study Material Chapter 6 Retirement and Death of a Partner

Question 6.
Kamala, Amala and Vimala were partners sharing profits and losses in the ratio of 5: 3: 2 respectively. Their balance sheet as on 31st March, 2020 was given below;
TS Inter 2nd Year Accountancy Study Material Chapter 6 Retirement and Death of a Partner 53
On the above date Vimala retired from the business on the following terms:
a) Appreciate Machinery by 20%.
b) Provide for Bad Debts @ 5% on debtors.
c) Stock to be depreciated by Rs. 6,000.
d) Goodwill is valued at Rs. 20,000.
e) Amount payable to Vimala transferred to her loan a/c.
Prepare necessary ledger accounts and balance sheet of Kamala and Amala.
Answer:
Ledger a/c’s in the books of Kamala, Amala and Vimala
Partnership firm as on 31-3-2020
TS Inter 2nd Year Accountancy Study Material Chapter 6 Retirement and Death of a Partner 54
TS Inter 2nd Year Accountancy Study Material Chapter 6 Retirement and Death of a Partner 55
TS Inter 2nd Year Accountancy Study Material Chapter 6 Retirement and Death of a Partner 56

Question 7.
K, S and N are sharing profits and losses in the ratio of 4: 3: 2 respectively. Their balance sheet as on 31 March 2020 was as under;
TS Inter 2nd Year Accountancy Study Material Chapter 6 Retirement and Death of a Partner 57
On 31st March 2020, N retires from the business on the following conditions:
a) Buildings are revalued at Rs. 60,000.
b) Provide for bad debts Rs. 3,000.
c) Stock to be depreciated by Rs. 2,500.
d) Goodwill is valued at Rs. 27,000.
The amount payable to N transferred to N’s Loan account by carrying 10% Interest per annum.
Prepare necessary ledger accounts and balance sheet of a new firm.
Answer:
TS Inter 2nd Year Accountancy Study Material Chapter 6 Retirement and Death of a Partner 58
TS Inter 2nd Year Accountancy Study Material Chapter 6 Retirement and Death of a Partner 59
K, S Balance Sheet as on 31 – 3 – 2020
TS Inter 2nd Year Accountancy Study Material Chapter 6 Retirement and Death of a Partner 60

TS Inter 2nd Year Accountancy Study Material Chapter 6 Retirement and Death of a Partner

Question 8.
X, Y and Z are partners in a firm sharing profits and losses equally. Their balance sheet as on 31 March, 2020 was as under;
TS Inter 2nd Year Accountancy Study Material Chapter 6 Retirement and Death of a Partner 61
On the above date Mr. Z decided to retire from the business on the following terms:
a) The assets are to be revalued as under;
Stock Rs. 15,000; Furniture Rs. 18,000; Machinery Rs. 25,000.
b) Goodwill of the firm valued at Rs. 30,000.
Give necessary ledger accounts and balance sheet of X and Y.
Answer:
TS Inter 2nd Year Accountancy Study Material Chapter 6 Retirement and Death of a Partner 62
TS Inter 2nd Year Accountancy Study Material Chapter 6 Retirement and Death of a Partner 63
TS Inter 2nd Year Accountancy Study Material Chapter 6 Retirement and Death of a Partner 64

When Goodwill is created and written off:

Question 9.
Dravid, Ganguly and Sachin are partners sharing profits and losses equally. Their balance sheet as on 31st March, 2020 was as under:
TS Inter 2nd Year Accountancy Study Material Chapter 6 Retirement and Death of a Partner 65
On the above date Dravid decided to retire from the business on the following terms.
a) Fixed assets are revalued at Rs. 80,000.
b) Create a provision for bad debts @ 6% on debtors.
c) Goodwill of the firm is valued at Rs. 45,000 and it is decided to writen off immediately.
d) Ganguly and Sachin will share future profits in the ratio of 3: 2 respectively.
Give necessary journal entries and ledger accounts and balance sheet of new firm.
Answer:
Journal entries in the books of Dravid, Ganguly and Sachin partnership firm.
TS Inter 2nd Year Accountancy Study Material Chapter 6 Retirement and Death of a Partner 66
TS Inter 2nd Year Accountancy Study Material Chapter 6 Retirement and Death of a Partner 67
TS Inter 2nd Year Accountancy Study Material Chapter 6 Retirement and Death of a Partner 68
TS Inter 2nd Year Accountancy Study Material Chapter 6 Retirement and Death of a Partner 69

Ganguly and Sachin Balance sheet as on 31-3-2020
TS Inter 2nd Year Accountancy Study Material Chapter 6 Retirement and Death of a Partner 70

TS Inter 2nd Year Accountancy Study Material Chapter 6 Retirement and Death of a Partner

Question 10.
P, Q and R are partners sharing profits and losses in the ratio of 2: 1: 1 respectively. Their balance sheet as on 31st March 2020 is as follows;
TS Inter 2nd Year Accountancy Study Material Chapter 6 Retirement and Death of a Partner 71
On the above date Mr. R decides to retire from the business on the following terms;
a) Goodwill of the firm is to be valued at Rs. 20,000 and written off completely after the retirement of R.
b) Stock to be depreciated by 5% and Furniture by 10%.
c) Buildings valued at Rs. 43,000.
d) The amount payable to R is to be transferred to his loan a/c by carrying 6% interest per annum.
e) P and Q share the future profits in the ratio of 3: 2 respectively.
Give necessary ledger accounts and balance sheet of new firm.
Answer:
TS Inter 2nd Year Accountancy Study Material Chapter 6 Retirement and Death of a Partner 72
TS Inter 2nd Year Accountancy Study Material Chapter 6 Retirement and Death of a Partner 73
TS Inter 2nd Year Accountancy Study Material Chapter 6 Retirement and Death of a Partner 74
PQ Balance Sheet as on 31-3-2020
TS Inter 2nd Year Accountancy Study Material Chapter 6 Retirement and Death of a Partner 75

Question 11.
Raju, Rani and Prince are partners sharing profits and losses in the ratio of their capitals. Their balance sheet as on 31st March, 2020 was as under.
TS Inter 2nd Year Accountancy Study Material Chapter 6 Retirement and Death of a Partner 76
On the above date Rani retired from the business and Raju, Prince decided to continue the business sharing profits and losses in the ratio of 3: 2 respectively. The following are agreed;
a) Value of buildings to be appreciated by Rs. 10,000.
b) Depreciate machinery by Rs. 5,000 and stock by Rs. 2,000.
c) Goodwill of the firm valued at Rs. 10,000 and decided to write off immediately.
d) The amount due to Rani is to be transferred to her loan a/c by carrying 10% interest per annum.
Give necessary ledger accounts and balance sheet.
Answer:
Raju, Rani, Prince profit sharing ratio 50,000: 30,000: 20,000 5:3:2
TS Inter 2nd Year Accountancy Study Material Chapter 6 Retirement and Death of a Partner 77
TS Inter 2nd Year Accountancy Study Material Chapter 6 Retirement and Death of a Partner 78
TS Inter 2nd Year Accountancy Study Material Chapter 6 Retirement and Death of a Partner 79
Raju and Prince Balance Sheet as on 31-3-2020
TS Inter 2nd Year Accountancy Study Material Chapter 6 Retirement and Death of a Partner 80

Question 12.
Harish, Sathish and Mahesh are partners sharing profits and losses equally. Their balance sheet as on 31 March 2020 was as under;
TS Inter 2nd Year Accountancy Study Material Chapter 6 Retirement and Death of a Partner 81
On the above date Mahesh retired from the business on the following terms;
a) Land is valued at Rs. 38,000.
b) Depreciate machinery by Rs. 5,000 and Stock by Rs. 2,000.
c) Goodwill of the firm valued at Rs. 24,000 and decided to give the Mahesh’s share of goodwill without raising goodwill in the books.
d) Harish and Sathish share future profits in the ratio of 2: 3 respectively.
Give necessary journal entries and ledger accounts and balance sheet.
Hint: Goodwill payable to retiring partner is Rs. 8,000, contributed in the ratio of gaining i.e., 1:4 between Harish and Sathish.
Answer:
Journal entries in the books of Harish, Sathish and Mahesh partnership firm as on 31-3 2020.
TS Inter 2nd Year Accountancy Study Material Chapter 6 Retirement and Death of a Partner 82
TS Inter 2nd Year Accountancy Study Material Chapter 6 Retirement and Death of a Partner 83
TS Inter 2nd Year Accountancy Study Material Chapter 6 Retirement and Death of a Partner 84
Working Notes:
Calculation of Gaining Ratio = (New Ratio – Old Ratio)
Old ratio 1:1:1
Harish, Satish new Raju 2:3.
TS Inter 2nd Year Accountancy Study Material Chapter 6 Retirement and Death of a Partner 85
Gaining ratio =1:4.

TS Inter 2nd Year Accountancy Study Material Chapter 6 Retirement and Death of a Partner 86
TS Inter 2nd Year Accountancy Study Material Chapter 6 Retirement and Death of a Partner 87
TS Inter 2nd Year Accountancy Study Material Chapter 6 Retirement and Death of a Partner 88
Harish and Sathish Balance Sheet as on 31-3-2020
TS Inter 2nd Year Accountancy Study Material Chapter 6 Retirement and Death of a Partner 89

TS Inter 2nd Year Accountancy Study Material Chapter 6 Retirement and Death of a Partner

Question 13.
Sit Chandra, Bhaskar; Rah a are partners sharing profits and losses in the ratio oRs. 3:2: 1 respectively. Their balance sheet as on 31st March, 2013 IMS as under ;
TS Inter 2nd Year Accountancy Study Material Chapter 6 Retirement and Death of a Partner 90
On the above date Raghu retired from the business on the following’ conditions:
a) Fixed assets are revalued at Rs. 42,000.
b) Depreciate stock by Rs. 1,700.
c) Provide for Bad Debts Rs. 700.
d) Goodwill of the firm is valued at Rs. 18,000. The share of goodwill payable to Raghu will be contributed by continuing partners without raising goodwill account.
e) Ratio of gaining of Chandra and Bhaskar is 1:1 respectively.
Show necessary ledger accounts and balance sheet of Chandra and Bhaskar.
[Hint: Raghu’s share of goodwill Rs. 3,000 contributed by Chandra and Bhaskar in their ratio of gaining i.e., 1: 1 i.e., Rs. 1,500 each]
Answer:
TS Inter 2nd Year Accountancy Study Material Chapter 6 Retirement and Death of a Partner 91
TS Inter 2nd Year Accountancy Study Material Chapter 6 Retirement and Death of a Partner 92
Chandra and Bhaskar Balance sheet as on 31-3-2015
TS Inter 2nd Year Accountancy Study Material Chapter 6 Retirement and Death of a Partner 93
Working Note:
Value of Goodwill of the firm is Rs. 18,000
Raghu’s Share in Goodwill = 18,000 x 1/6 = 3,000
Raghu’s share of goodwill Rs. 3,000 is contributed by Chandra and Bhaskar in ratio of gaining i.e., 1: 1 i.e., Rs. 1,500 each.

Question 14.
Star, Sun and Moon are partners sharing profits and losses in the ratio of 5: 3: 2 respectively. Their balance sheet as on 31st March 2020 was as under;
TS Inter 2nd Year Accountancy Study Material Chapter 6 Retirement and Death of a Partner 94
Moon retired from the business on the above date with the following terms;
a) Goodwill of the firm is valued at Rs. 20,000 and it is decided not to raise goodwill account in the books.
b) Buildings revalued at Rs. 42,000.
c) Provide for bad debts @ 5% on debtors.
d) Trade creditors Rs. 1,000 need not be paid.
e) Star and Sun share future profits equally.
f) Amount due to Moon will be transferred to his loan account with 12% interest per annum.
Prepare necessary ledger accounts and Balance sheet of new firm.
[Hint: On retirement of Moon, Sun alone gaining star is not gaining anything. So, the share of goodwill of Moon Rs. 4,000 given by Sun only.
Answer:
TS Inter 2nd Year Accountancy Study Material Chapter 6 Retirement and Death of a Partner 95
TS Inter 2nd Year Accountancy Study Material Chapter 6 Retirement and Death of a Partner 96
Working Mole:
Calculation of Gaining ratio of star & sun (New ratio – old ratio)
Old Ratio = 5:3:2, New 1: 1
TS Inter 2nd Year Accountancy Study Material Chapter 6 Retirement and Death of a Partner 97
Gaining ratio = 0:2 (Means star not gaining anything) So, total share of moon is contributed by sun.

Star and Sun Balance Sheet as an 31-3-2015
TS Inter 2nd Year Accountancy Study Material Chapter 6 Retirement and Death of a Partner 98

Textual Examples

Question 1.
X, Y and Z are partners sharing profits and losses in the ratio of 3:2:1 respectively the find out the new profit shaiiag ratio in the case of;
a) X retires from the business.
b) Y retires from the business.
c) Z retires from the business.
Answer:
The old profit sharing ratio of X, Y and Z is 3:2:1 respectively.
a) If X retires from the business, Y and Z share the profits in the ratio of 2:1 i.e., 2/3 and 1/3
b) If Y retires from business X and Z share the profits in the ratio of 3:1 respectively i.e., 3/4 and 1/4.
c) If Z retires from the business, X and Y share the profits in the ratio of 3: 2 respectively, i.e., 3/5 and 2/5 respectively.

Question 2.
A, B and C are partners sharing profits and losses in the ratio of 2:1:1 respectively. Mr. C retires from the business. Calculate new profit sharing ratio of A and B.
Answer:
Elimination Method:
The old profit sharing ratio of A, B and C is 2:1:1.
Eliminate C’s share of profit from old profit sharing ratio.
The new profit sharing ratio of continuing partners A and B is 2:1 respectively i.e., 2/3: 1/3.
Alternative Method:
Alternatively, the new profit-sharing ratio may be calculated as follows:
Profit sharing ratio of A, B and C is 2:1:1 respectively = 2/4: 1/4: 1/4.
Retiring partner C’s share is 1/4.
Retiring partner’s share is acquired in the old ratio by A and B i.e., 2:1. This is also called gaining ratio.
Gaining ratio of A and B is 2:1 (or) 2/3: 1/3.
Gaining ratio = Retiring partners share x Partners gaining ratio.
TS Inter 2nd Year Accountancy Study Material Chapter 6 Retirement and Death of a Partner 99
New profit sharing ratio = Old share + Share gained
TS Inter 2nd Year Accountancy Study Material Chapter 6 Retirement and Death of a Partner 100

Question 3.
P, Q and R partners sharing profits and losses in the ratio of 5:4:3 respectively. R Retires from the business and his share of profit purchased by P and Q in the ratio of 2:1 respectively. Calculate the new profit sharing ratio of P and Q,
Answer:
Old profit sharing ratio of P, Q and R is 5:4:3 = 5/12: 4/12: 3/12
R’s share of profit 3/12 being purchased by P and Q in the ratio of 2:1 = 2/3 : 1/3 respectively.
TS Inter 2nd Year Accountancy Study Material Chapter 6 Retirement and Death of a Partner 101

New profit sharing ratio of P = P’s old share + proportion of R’s share purchased
TS Inter 2nd Year Accountancy Study Material Chapter 6 Retirement and Death of a Partner 102

New profit sharing ratio Q = Q’s old share + proportion of R’s share purchased
TS Inter 2nd Year Accountancy Study Material Chapter 6 Retirement and Death of a Partner 103

The new profit-sharing ratio of P and Q is 7:5 respectively i.e., 7/12 and 5/12.

Question 4.
X, Y and Z are partners sharing profits and losses in the ratio of 2:4:3 respectively. Mr. X retires from the business. Y and Z share future profits in the ratio of 3:2. respectively. Calculate the ratio of gaining.
Answer:
Ratio of gaining = New profit sharing ratio – Old profit sharing ratio
Old ratio of X, Y and Z is 2:4:3.
New ratio of Y and Z is 3:2.
TS Inter 2nd Year Accountancy Study Material Chapter 6 Retirement and Death of a Partner 104

Question 5.
A, B and C are partners sharing profits and losses in the ratio of 5:3:2 respectively. C retires from the business. Calculate ratio of gaining and new profit Sharing ratio of A and B.
Answer:
In this problem, new profit sharing ratio is not given. Hence, after eliminating C’s share of profit from old ratio, whatever that is left will be the new profit sharing ratio of A and B. Old ratio, of A, B and C is 5:3:2
New ratio of A and B is 5:3 i.e., 5/8 and 3/8 (C’s share eliminated).
In the absence of new ratio given in the problem, the continuing partners gain in the same ratio in which, they were sharing earlier. Even, it is calculated it will be the same.
Ratio of gaining = New ratio – Old ratio
TS Inter 2nd Year Accountancy Study Material Chapter 6 Retirement and Death of a Partner 105
The ratio of gain between A and B is 5:3 respectively.
In other words, the continuing partners are gaining in the same ratio in which they are sharing profits earlier after eliminating C’s share.

TS Inter 2nd Year Accountancy Study Material Chapter 6 Retirement and Death of a Partner

Question 6.
X, Y and Z are partners sharing profits or losses in the ratio of 4:2:2. Mr. Z retires from the business. X and Y will gain in the ratio of 7:3 respectively. Calculate new profit sharing ratio of X and Y.
Answer:
TS Inter 2nd Year Accountancy Study Material Chapter 6 Retirement and Death of a Partner 106
New profit sharing ratio of X and Y is 27/40 and 13/40 = 27 : 13 respectively.

Question 7.
X, Y and Z are partners sharing profits and losses in the the ratio of 3:2:1. Goodwill Of the firm is valued at Rs. 60,000. Mr. Z retires from the business, X & Y decided to continue the business shearing profits and losses in the ratio of 3:2 respectively
Give journal entries and prepare the goodwill account when;
a) Goodwill is raised in the books for full value.
b) Goodwill is raised and writtenoff in the books.
Answer:
a) Journal entries when goodwill is raised
TS Inter 2nd Year Accountancy Study Material Chapter 6 Retirement and Death of a Partner 107
Note: In this case, goodwill appear at Rs. 60,000 on the assets side of the balance sheet of new firm.
b) Journal Entries when goodwill is raised and writtenoff.
TS Inter 2nd Year Accountancy Study Material Chapter 6 Retirement and Death of a Partner 108
TS Inter 2nd Year Accountancy Study Material Chapter 6 Retirement and Death of a Partner 109
Note: In this case, the goodwill account is closed, so it will not appear in balance sheet of new firm in which X and Y are partners.

Question 8.
A, B and C are partners sharing profits and losses in the ratio of 2:1:1 respectively. Their balance sheet as on 31-3-2020 was as under;
TS Inter 2nd Year Accountancy Study Material Chapter 6 Retirement and Death of a Partner 110
On the above date Mr. C retired from the business. The following are agreed among partners;
a) Machinery revalued at Rs. 23,000 and Buildings at Rs. 40,000.
b) Depreciate furniture by 10%.
c) Outstanding expenses Rs. 1,000 need not be paid.
d) Goodwill of the firm valued at Rs. 20,000.
e) A should bring Rs. 20,000 and B Rs. 10,000 as additional capital to pay the amount due to retiring partner, Mr. C.
Give journal entries and necessary ledger accounts and new balance sheet.
Answer:
Journal Entries
TS Inter 2nd Year Accountancy Study Material Chapter 6 Retirement and Death of a Partner 111
TS Inter 2nd Year Accountancy Study Material Chapter 6 Retirement and Death of a Partner 112
TS Inter 2nd Year Accountancy Study Material Chapter 6 Retirement and Death of a Partner 113
Ledger Accounts:
TS Inter 2nd Year Accountancy Study Material Chapter 6 Retirement and Death of a Partner 114
TS Inter 2nd Year Accountancy Study Material Chapter 6 Retirement and Death of a Partner 115
Balance Sheet of A and B as on 31-03-2020
TS Inter 2nd Year Accountancy Study Material Chapter 6 Retirement and Death of a Partner 116

TS Inter 2nd Year Accountancy Study Material Chapter 6 Retirement and Death of a Partner

Question 9.
Ganga, Yamuna and Saraswathi are partners sharing profits and losses in the ratio of 3:2:2 respectively. Their balance sheet as on 31 March 2020 was under.
TS Inter 2nd Year Accountancy Study Material Chapter 6 Retirement and Death of a Partner 117
On the above date Saraswathi retired from the business. Ganga and Yamuna decided to continue the business. The following were agreed among partners;
a) Goodwill of the firm is valued at Rs. 56,000.
b) Stock and Motor car to be depreciated by 10%.
c) Provide for bad debts Rs. 1,000.
d) Buildings appreciated byl5%.
e) Trade creditors reduced by Rs. 300.
It is decided to pay Rs. 18,800 to Saraswathi and transfer the balance in her capital account to her loan account.
Give necessary Journal entries and ledger accounts and opening balance sheet of Ganga and Yamuna.
Answer:
Journal entries
TS Inter 2nd Year Accountancy Study Material Chapter 6 Retirement and Death of a Partner 118
TS Inter 2nd Year Accountancy Study Material Chapter 6 Retirement and Death of a Partner 119
TS Inter 2nd Year Accountancy Study Material Chapter 6 Retirement and Death of a Partner 120
TS Inter 2nd Year Accountancy Study Material Chapter 6 Retirement and Death of a Partner 121
TS Inter 2nd Year Accountancy Study Material Chapter 6 Retirement and Death of a Partner 122
TS Inter 2nd Year Accountancy Study Material Chapter 6 Retirement and Death of a Partner 123
TS Inter 2nd Year Accountancy Study Material Chapter 6 Retirement and Death of a Partner 124
Note: Goodwill created in the books. Hence, it appears on assets side of the balance sheet.

TS Inter 2nd Year Accountancy Study Material Chapter 6 Retirement and Death of a Partner

Question 10.
Ram, Rahim and Robert are partners sharing profits and losses in the ratio of 3:1:2 respectively. The following is the balance sheet as on 31 March 2020.
TS Inter 2nd Year Accountancy Study Material Chapter 6 Retirement and Death of a Partner 125
Mr. Rahim Retires on the above date on the following conditions;
a) Goodwill of the firm be valued at Rs. 45,000.
b) Provision for bad debts not necessary.
c) An outstanding liability in respect of workmen compensation Rs. 2,500 to be brought into books.
d) Patents have no value.
e) Stock to be appreciated by Rs. 2,490.
f) Buildings be appreciated by 10%.
Give necessary Journal entries and ledger accounts and balance sheet of Ram and Robert. Partners capital accounts are maintained under fixed capital method.
Answer:
Journal Entries
TS Inter 2nd Year Accountancy Study Material Chapter 6 Retirement and Death of a Partner 126
TS Inter 2nd Year Accountancy Study Material Chapter 6 Retirement and Death of a Partner 127
TS Inter 2nd Year Accountancy Study Material Chapter 6 Retirement and Death of a Partner 128
Ledger Accounts:
TS Inter 2nd Year Accountancy Study Material Chapter 6 Retirement and Death of a Partner 129
TS Inter 2nd Year Accountancy Study Material Chapter 6 Retirement and Death of a Partner 130
TS Inter 2nd Year Accountancy Study Material Chapter 6 Retirement and Death of a Partner 131
Note: Capital Accounts are maintained under fixed capital method. Current a/c of retiring partner Rahim transferred to his capital a/c and then to his loan A/c.

When Goodwill is created and written off:

Question 11.
X, Y and Z are partners sharing profits and losses in the ratio of 3:2:1 respectively. Their balance sheet as on 31 March 2015 was as follows;
TS Inter 2nd Year Accountancy Study Material Chapter 6 Retirement and Death of a Partner 132
On the above date Mr. Y retires from the business. X and Z decided to continue the business with the following terms;
a) Goodwill of the firm is valued at Rs. 18,000.
b) Provision for bad debts required is Rs. 1,500.
c) Stock to be depreciated by Rs. 6,000.
d) Land to be appreciated by Rs. 5,000.
e) It is decided to write off goodwill in the new firm.
f) New profit-sharing ratio of X and Z will be 3:2.
Give journal entries and necessary ledger accounts and opening balance sheet of X and Z.
Answer:
Journal Entries
TS Inter 2nd Year Accountancy Study Material Chapter 6 Retirement and Death of a Partner 133
TS Inter 2nd Year Accountancy Study Material Chapter 6 Retirement and Death of a Partner 134

Ledger Accounts:
TS Inter 2nd Year Accountancy Study Material Chapter 6 Retirement and Death of a Partner 135
TS Inter 2nd Year Accountancy Study Material Chapter 6 Retirement and Death of a Partner 136
Balance Sheet of X and Z as on 31-03-2020
TS Inter 2nd Year Accountancy Study Material Chapter 6 Retirement and Death of a Partner 137

Note: Goodwill and shared in old profit sharing ratio and written – off in new profit sharing ratio.

TS Inter 2nd Year Accountancy Study Material Chapter 6 Retirement and Death of a Partner

Question 12.
Ramesh, Ganesh and Suresh are partners sharing profits and losses equally. Their balance sheet as on 31 March 2020 stood as follows;
TS Inter 2nd Year Accountancy Study Material Chapter 6 Retirement and Death of a Partner 138
a) Buildings to be appreciated to Rs. 45,000.
b) Furniture revalued at Rs. 23,000.
c) Goodwill of the firm valued at Rs. 40,000.
d) New profit sharing ratio of Ganesh and Suresh will be 3:2 respectively and decided to write off goodwill.
Give journal entries and necessary ledger accounts and opening balance sheet.
Answer:
Journal Entries
TS Inter 2nd Year Accountancy Study Material Chapter 6 Retirement and Death of a Partner 139
TS Inter 2nd Year Accountancy Study Material Chapter 6 Retirement and Death of a Partner 140
TS Inter 2nd Year Accountancy Study Material Chapter 6 Retirement and Death of a Partner 141
TS Inter 2nd Year Accountancy Study Material Chapter 6 Retirement and Death of a Partner 142
Ledger Accounts:
TS Inter 2nd Year Accountancy Study Material Chapter 6 Retirement and Death of a Partner 143
TS Inter 2nd Year Accountancy Study Material Chapter 6 Retirement and Death of a Partner 144
TS Inter 2nd Year Accountancy Study Material Chapter 6 Retirement and Death of a Partner 145

Note:

  1. Goodwill created to the extent of Rs. 30,000 because already Rs. 10,000 value of goodwill appears in the books. Now the goodwill of the firm will be 40,000 i.e., 10,000 + 30,000 created.
  2. P & L a/c Dr. balance (loss), transferred to old partners capital a/cs.
  3. The amount payable to Ramesh, the retiring partner, after all the adjustments are transferred to his loan account.

TS Inter 2nd Year Accountancy Study Material Chapter 6 Retirement and Death of a Partner

Question 13.
Amar, Akbar, and Anthony are partners sharing profits and losses equally. Their balance sheet as on 31s1 March 2020, was as follows;
TS Inter 2nd Year Accountancy Study Material Chapter 6 Retirement and Death of a Partner 146
On the above date Mr. Akbar retired from the business. The following adjustments are agreed.
a) Land & Buildings appreciated by Rs. 20,000.
b) Stock and Machinery are to be depreciated by 10%.
c) Provide for Bad debts Rs. 2,000.
d) Goodwill of the firm is valued at Rs. 60,000 and it is decided to pay the share of Goodwill of retiring partner by continuing partners without raising goodwill account in the books.
e) Rs. 70,000 to be sharing ratio of Amar and Anthony is 3 : 2 respectively.
f) New profit sharing ratio of Amar and Anthony is 3:2 respectively.
Give journal entries and necessary ledger accounts and opening balance sheet of Amar and Anthony.
Answer:
Journal Entries
TS Inter 2nd Year Accountancy Study Material Chapter 6 Retirement and Death of a Partner 147
TS Inter 2nd Year Accountancy Study Material Chapter 6 Retirement and Death of a Partner 148
Ledger Accounts:
TS Inter 2nd Year Accountancy Study Material Chapter 6 Retirement and Death of a Partner 149
TS Inter 2nd Year Accountancy Study Material Chapter 6 Retirement and Death of a Partner 150
TS Inter 2nd Year Accountancy Study Material Chapter 6 Retirement and Death of a Partner 151
TS Inter 2nd Year Accountancy Study Material Chapter 6 Retirement and Death of a Partner 152
Notes:
1) Calculation of Gaining ratio:
TS Inter 2nd Year Accountancy Study Material Chapter 6 Retirement and Death of a Partner 153

TS Inter 2nd Year Accountancy Study Material Chapter 6 Retirement and Death of a Partner

2) The share of goodwill payable to retiring partner, Ameer is (60,000 x 1/3 ) = Rs. 20,000. It
is given by continuing partners in their respective share of gaining. Amar gives (20,000 x 1/5) = 16,000 and Anthony gives (20,000 x 1/5) = Rs. 4,000 from their capital accounts and the same (i.e., 20,000) credited to retiring partner’s capital account, without raising goodwill a/c in the books.

TS Inter 1st Year Maths 1A Product of Vectors Important Questions Long Answer Type

Students must practice these Maths 1A Important Questions TS Inter 1st Year Maths 1A Product of Vectors Important Questions Long Answer Type to help strengthen their preparations for exams.

TS Inter 1st Year Maths 1A Product of Vectors Important Questions Long Answer Type

Question 1.
By the vector method, prove that altitudes of a triangle are concurrent.
Answer:
Let A, B, C be the vertices of a triangle.
Let \(\overline{\mathrm{OA}}\) = a̅, \(\overline{\mathrm{OB}}\) = b̅, \(\overline{\mathrm{OC}}\) = c̅
Let the altitudes through A, B meet at H and \(\overline{\mathrm{OH}}\) = r̅ (say)
TS Inter First Year Maths 1A Product of Vectors Important Questions Long Answer Type 1
Now \(\overline{\mathrm{AH}} \perp \overline{\mathrm{BC}} \Rightarrow \overline{\mathrm{AH}} \cdot \overline{\mathrm{BC}}=0 \Rightarrow(\overline{\mathrm{OH}}-\overline{\mathrm{OA}}) \cdot(\overline{\mathrm{OC}}-\overline{\mathrm{OB}})\) = 0
⇒ (r̅ – a̅). (c̅ – b̅) = 0
⇒ r̅ . (c̅ – b̅) – a̅. (c̅ – b̅) = 0 ……………(1)

Also \(\overline{\mathrm{BH}} \perp \overline{\mathrm{AC}} \Rightarrow \overline{\mathrm{BH}} \cdot \overline{\mathrm{AC}}=0 \Rightarrow(\overline{\mathrm{OH}}-\overline{\mathrm{OB}}) \cdot(\overline{\mathrm{OC}}-\overline{\mathrm{OA}})\) = 0
⇒ (r̅ – b̅). (c̅ – a̅) = 0
⇒ r̅ .(c – a̅) – b̅.(c̅ – a̅) = 0 ………….(2)

(1) – (2) ⇒ r̅ . (c̅ – b̅) – a̅. (c̅ – b̅) – r . (c̅ – a̅) + b̅. (c̅ – a̅) = 0
TS Inter First Year Maths 1A Product of Vectors Important Questions Long Answer Type 2
⇒ r̅ . (a̅ – b̅) – c̅ (a̅ – b̅) = 0
⇒ (r̅ – c̅) . (a̅ – b̅) = 0
⇒ \((\overline{\mathrm{OH}}-\overline{\mathrm{OC}}) \cdot(\overline{\mathrm{OA}}-\overline{\mathrm{OB}})\) = 0
⇒ \((\overline{\mathrm{OH}}-\overline{\mathrm{OC}}) \cdot(\overline{\mathrm{OA}}-\overline{\mathrm{OB}})=0 \Rightarrow \overline{\mathrm{CH}} \cdot \overline{\mathrm{BA}}=0 \Rightarrow \overline{\mathrm{CH}} \perp \overline{\mathrm{BA}}\)
∴ The altitude through C also passes through H.
∴ The altitudes of a Ale are concurrent.

Question 2.
By vector method, prove that the perpendicular bisectors of the sides of a triangle are concurrent. [Mar. ’92]
Answer:
Let A, B, C be the vertices of a triangle. Let \(\overline{\mathrm{OA}}\) = a, \(\overline{\mathrm{OB}}\) = b, \(\overline{\mathrm{OC}}\) = c
TS Inter First Year Maths 1A Product of Vectors Important Questions Long Answer Type 3
Let D, E, F are the midpoints of BC, CA, AB respectively
TS Inter First Year Maths 1A Product of Vectors Important Questions Long Answer Type 4
∴ The bisector of AB passes through ‘O’.
∴ The perpendicular bisectors of a triangle are concurrent.

TS Inter First Year Maths 1A Product of Vectors Important Questions Long Answer Type

Question 3.
If a̅, b̅, c̅ be three vectors. Then show that (a̅ × b̅) × c̅ = (a̅. c̅) b̅ – (b̅ . c̅) a̅.
Answer:
Let a̅ = a1 i̅ + a2 j̅ + a3k̅, b̅ = b1 i̅ + b2 j̅ + b3k̅ and c̅ = c1 i̅ + c2 j̅ + c3
= i̅ (a2b3 – a3b2) – j̅ (a1b3 – a1b3) + k̅ (a1b2 – a2b1)

(a̅ × b̅) × c̅ = \(\left|\begin{array}{ccc}
\bar{i} & \bar{j} & \bar{k} \\
a_2 b_3-a_3 b_2 & a_3 b_1-a_1 b_3 & a_1 b_2-a_2 b_1 \\
c_1 & c_2 & c_3
\end{array}\right|\)
= i̅(a3b1c3 – a1b3c3 – a1b2c2 + a2b1c2) – j̅(a2b3c3 – a3b2c3 – a1b2c1 + a2b1c1) + k̅ (a2b3c2 – a3b2c2 – a3b1c1 + a1b3c1)
c̅.a̅ = (c1i̅ + c2j̅ + c3k̅). (a1i̅ + a2j̅ + a3k̅) = c1a1 + c2a2 + c3a3
c̅.b̅ = (c1i̅ + c2j̅ + c3k̅). (b1̅ + b2j̅ + b3k̅) = c1b1 + c2b2 + c3b3

Now (c̅.a̅)b̅ – (c̅.b̅)a̅ = (c1a1 + c2a2 + c3a3) (b1 i + b2 j + b3k) – (c1b1 + c2b2 + c2b3) (a1 i̅ + a2j̅ + a3k̅)
= a1b1c1 i̅ + a1b2c1 j̅ + a1b3c1 k̅ + a2b1c2 i̅ + a2b2c2j̅ + a2b3c2 k̅ + a3b1c3 i̅ + a3b2c3 i̅ + a3b2c3 j̅ + a3b3c3 k̅ – a1b1c1i̅ – a2b1c1j̅ – a3b21c1 k̅ – a1b2c2 i̅ – a1b2c2 j̅ – a3b2c2k̅ – a1b3c3i̅ – a2b3c3j̅ – a3b3c3
= i̅(a2b1c2 + a3b1c3 – a1b2c2 – a1b3c3) – j̅(-a1b2c1 – a3b2c3 + a2b1c1 + a22b3c3) + k̅(a1b3c1 + a2b3c2 – a3b1c1 – a3b2c2)
∴ (a̅ × b̅) × c̅ = (a̅. c̅) b̅ – (b̅ . c̅) a̅

Question 4.
Find the equation of the plane passing through the points A = (2, 3, -1), B = (4, 5, 2) and C = (3, 6, 5).
Answer:
Let the position vectors of the points A, B and C with respect to the origin ‘O’ are
\(\overline{\mathrm{OA}}\) = 2 i̅ + 3 j̅ – k̅; \(\overline{\mathrm{OB}}\) = 4 i̅ + 5 j̅ + 2k̅; \(\overline{\mathrm{OC}}\) = 3 i̅ + 6 j̅ + 5k̅
Let r̅ = OP = x i̅ + y j̅ + zk̅ be the position vector of any point P in the plane of ΔABC.
AP = OP-OA = xi̅ + yj̅ + zk̅ – 2i̅ – 3j̅ + k̅ = (x – 2)i̅ + (y – 3)j̅ +(z + 1)k̅
AB = OB – OA = 4i̅ + 5j̅ + 2k̅ – 2i̅ – 3j̅ + k̅ = 2i̅ + 2j̅ + 3k̅
AC = OC -OA = 3i̅ + 6j̅ + 5k̅ – 2i̅ – 3j̅ + k̅ = i̅ + 3j̅ + 6k̅
The equation of the plane passing through the points A, B and C is \([\overline{\mathrm{AP}} \overline{\mathrm{AB}} \overline{\mathrm{AC}}]\) = 0
⇒ \(\left|\begin{array}{ccc}
x-2 & y-3 & z+1 \\
2 & 2 & 3 \\
1 & 3 & 6
\end{array}\right|\) = 0
⇒ (x – 2) [12 – 9] – (y – 3) [12 – 3] + (z + 1) [6 – 2] = 0
⇒ (x – 2) (3) – (y – 3) (9) + (z + 1) (4) = 0
⇒ 3x – 6 – 9y + 27 + 4z + 4 = 0
⇒ 3x – 9y + 4z + 25 = 0.

Question 5.
Find the equation of the plane passing through the point A = (3, -2, -1) and parallel to the vectors b̅ = i̅ – 2j̅ + 4k̅ and c̅ = 3i̅ + 2j̅ – 5k̅. [May ’01]
Answer:
The position vector of the point with respect to origin O’ is OA = 3 i̅ – 2 j̅ – k̅
Given b = i̅ – 2j̅ + 4k̅, c = 3i̅ + 2j̅ – 5k̅
Let r̅ = \(\overline{\mathrm{OP}}\) = xi̅ + yj̅ + zk̅ be the position vectqr of any point P in the plane of AABC.
\(\overline{\mathrm{AP}}=\overline{\mathrm{OP}}-\overline{\mathrm{OA}}\) = xi̅ +yj̅ + zk̅ – 3i̅ +2j̅ + k̅ = (x – 3)i̅ +(y + 2)j̅ +(z + 1)k̅

The equation of the plane passing through the point A parallel to the vectors b̅ & c̅ is [\(\overline{\mathrm{AP}} b̅ c̅ ] = 0
⇒ \left|\begin{array}{ccc}
x-3 & y+2 & z+1 \\
1 & -2 & 4 \\
3 & 2 & -5
\end{array}\right|\) = 0
⇒ (x – 3)[10 – 8] – (y + 2)[-5 – 12] + (z + 1)[2 + 6] = 0
⇒ (x + 3)(2) – (y + 2)(-17) + (z + 1)(8) = 0
⇒ 2x – 6 + 17y + 34 + 8z + 8 = 0
⇒ 2x + 17y + 8z + 36 = 0.

Question 6.
Find the shortest distance between the skew lines r̅ = (6i̅ + 2j̅ + 2k̅) + t (i̅ – 2j̅ + 2k̅) and r̅ = (-4i̅ – k̅) + s (3i̅ – 2j̅ – 2k̅).
Answer:
Given equations of the straight lines are r̅ = (6 i̅ + 2j̅ +2k̅) + t(i̅ – 2j̅ + 2k̅)
TS Inter First Year Maths 1A Product of Vectors Important Questions Long Answer Type 5
Comparing this equation with r̅ = a̅ + tb̅
a̅ = 6 i̅ + 2 j̅ + 2k̅, b̅ = i̅ – 2j̅ + 2k̅
r̅ = (- 4 i̅ – k̅) + s (3 i̅ – 2 j̅ – 2k̅)

Comparing this equation with r̅ = c̅ + sd̅
c̅ = -4i̅ – k̅, d̅ = 3i̅ – 2j̅ – 2k̅
a̅ – c̅ = 6i̅ + 2j̅ + 2k̅ + 4i̅ + k ̅= 10i̅ + 2j̅ + 3k̅
[a̅ – c̅ b̅d̅] = \(\left|\begin{array}{ccc}
10 & 2 & 3 \\
1 & -2 & 2 \\
3 & -2 & -2
\end{array}\right|\) = 10(4 + 4) – 2(-2-6) + 3(-2 + 6)
= 10(8) – 2(-8) + 3(4) = 80 + 16 + 12 = 108

b̅ × d̅ =
= i̅(4 + 4) – j̅(-2-6) + k̅(-2+6) = 8i̅ + 8j̅ + 4k̅

|b̅ × d̅| = \(\sqrt{8^2+8^2+4^2}\)
= \(\sqrt{64+64+16}=\sqrt{144}\)
= 12

The shortest distance between the two skew lines is
PQ = \(\frac{\mid\left[\begin{array}{ll}
\overline{\mathrm{a}}-\overline{\mathrm{c}} & \overline{\mathrm{b}} \overline{\mathrm{d}}]
\end{array} \mid\right.}{|\overline{\mathrm{b}} \times \overline{\mathrm{d}}|}=\frac{|108|}{12}=\frac{108}{12}\) = 9

Question 7.
If A = (1, – 2, – 1), B = (4,0, – 3), C = (1, 2, – 1) and D = (2, – 4, – 5), find the distance between \(\overline{\mathrm{A B}}\) and \(\overline{\mathrm{C D}}\).
Answer:
Given points are A = (1, – 2, – 1), B = (4, 0, – 3), C = (1, 2, – 1), D = (2, -4,-5)
TS Inter First Year Maths 1A Product of Vectors Important Questions Long Answer Type 6
The vector equation of the straight line passing through the points A and B is
r = (1 – t)a̅ + tb̅, t ∈ R = (1 – t) (i̅ – 2j̅ – k̅) + t(4 i̅ – 3k̅) = i̅ – 2j̅ – k̅ – ti̅ + 2t j̅ + tk̅ + 4ti̅ – 3tk̅
= (i̅ – 2j̅ – k̅) + 3ti̅ +2tj̅ – 2tk̅
r = (i̅ – 2j̅ – k̅) + t(3i̅ + 2j̅ – 2k̅)

Comparing this equation with r̅ = a̅ + tb̅
We get a̅ = i̅ – 2 j̅ – k̅, b̅ = 3 i̅ + 2 j̅ – 2k̅

The vector equation of a straight line passing through the points C and D is
r̅ = (1 – s) c̅ + sd̅, s ∈ R = (1 – s) (i̅ + 2j̅ – k̅) + s(2i̅ – 4j̅ – 5k̅)
= i̅ + 2j̅ – k̅ – si̅ — 2s j̅ + sk̅ + 2si̅ – 4s j̅ – 5sk̅
= i̅ + 2j̅ – k̅ + si̅ – 6sj̅ – 4sk̅
r = (i̅ – 2 j̅ – k̅) + s(i̅ – 6j̅ – 4k̅)

Comparing this equation with r = c̅ + sd̅, we get c̅ = i̅ + 2j̅ – k̅, d̅ = i̅ – 6j̅ – 4k̅
a̅ – c̅ = i̅ – 2j̅ – k̅ – i̅ – 2j̅ + k̅ = – 4j̅
[a̅ – c̅ b̅d̅] = \(\left|\begin{array}{rrr}
0 & -4 & 0 \\
3 & 2 & -2 \\
1 & -6 & -4
\end{array}\right|\)
= 0(-8 – 12) + 4(-12 + 2) + 0(-18 – 2) = 0 + 4(-10) + 0 = -40

b̅ × d̅ = \(\left|\begin{array}{ccc}
\overline{\mathbf{i}} & \overline{\mathrm{j}} & \overline{\mathrm{k}} \\
3 & 2 & -2 \\
1 & -6 & -4
\end{array}\right|\)
= i̅(-8 – 12) – j̅(-12 + 2) + k̅(-18 – 2) = 20i̅ + 10j̅ – 20k̅

b̅ × d̅ = \(\sqrt{(-20)^2+(10)^2+(-20)^2}\)
= \(\sqrt{400+100+400}=\sqrt{900}\)
= 30

The shortest distance between the two skew lines is PQ = \(\frac{\left|\left[\begin{array}{ll}
\bar{a}-\bar{c} & \bar{b} \bar{d}
\end{array}\right]\right|}{|\bar{b} \times \bar{d}|}=\frac{|-40|}{30}=\frac{4}{3}\)

TS Inter First Year Maths 1A Product of Vectors Important Questions Long Answer Type

Question 8.
If a̅ = i̅ – 2j̅ + k̅, b̅ = 2i̅ + j̅ + k̅, c̅ = i̅ + 2j̅ – k̅ find a̅ × (b̅ × c̅) and |(a̅ × b̅) × c̅|.
Answer:
Given vectors are a̅ = i̅ – 2j̅ + k̅, b̅ = 2i̅ + j̅ + k̅, c̅ = i̅ + 2j̅ – k̅
TS Inter First Year Maths 1A Product of Vectors Important Questions Long Answer Type 7

Question 9.
If a̅ = i̅ – 2j̅ – 3k̅, b̅ = 2i̅ + j̅ – k̅ and c̅ = i̅ + 3j̅ – 2k̅, verify that a̅ × (b̅ × c̅) = (a̅ × b̅) × c̅. [Mar ’11, ’98; Mar. ’08, ’04; B.P]
Answer:
Given vectors a̅ = i̅ – 2j̅ – 3k̅, b̅ = 2i̅ + j̅ – k̅, c̅ = i̅ + 3j̅ – 2k̅
TS Inter First Year Maths 1A Product of Vectors Important Questions Long Answer Type 8

Question 10.
If a̅ = 2i̅ + j̅ – 3k̅, b̅ = i̅ – 2j̅ + k̅, c̅ = – i̅ + j̅ – 4k̅ and d̅ = i̅ + j̅ + k̅, then compute |(a̅ × b̅) × (c̅ × d̅)|. [Mar. ’15(TS); Mar. ’03]
Answer:
Given vectors are a̅ = 2i̅ + j̅ – 3k̅, b̅ = i̅ – 2j̅ + k̅, c̅ = – i̅ + j̅ – 4k̅, d̅ = i̅ + j̅ + k̅
TS Inter First Year Maths 1A Product of Vectors Important Questions Long Answer Type 9

Question 11.
If a̅ = i̅ – 2j̅ + 3k̅, b̅ = 2i̅ + j̅ + k̅, c̅ = i̅ + j̅ + 2k̅, then find |(a̅ × b̅) × c̅| and |a̅ × (b̅ × c̅)|. [Mar. ’18(TS); Mar ’13]
Answer:
Given vectors are a̅ = i̅ – 2j̅ + 3k̅, b̅ = 2i̅ + j̅ + k̅, c̅ = i̅ + j̅ + 2k̅
Now (a̅ × b̅) × c̅ = (a̅. c̅)b̅ – (b̅. c̅) a̅
= [(i̅ – 2j̅ + 3k̅). (i̅ + j̅ + 2k̅)] b̅ – [(2i̅ + j̅ + k̅). (i̅ + j̅ + 2k̅)]a̅
= (1 – 2 + 6)b̅ – (2 + 1 + 2)a̅ = 5b̅ – 5a̅
= 5 [2i̅ + j̅ + k̅ – i̅ + 2j̅ – 3k̅] = 5 [i̅ + 3j̅ – 2k̅]
|(a̅ × b̅) × c̅| = 57l + 9 + 4 = 57l4

a̅ × (b̅ × c̅) = (a̅. c̅)b̅ – (a̅. b̅) c̅
= [(i̅ – 2j̅ + 3k̅). (i̅ + j̅ + 2k̅)] b̅ – [(i̅ – 2j̅ + 3k̅). (2i̅ + j̅ + k̅)]c̅
= (1 – 2 + 6) b̅ – (2 – 2 + 3) c̅ = 5b̅ – 3c̅
= 5 (2 i̅ + j̅ + k̅) — 3(i̅ + j̅ + 2k̅) = 7 i̅ + 2 j̅ – k̅
Hence |a̅ × (b̅ × c̅) | = |7i̅ + 2j̅ – k̅|
= \(\sqrt{49+4+1}=\sqrt{54}\) = 3√6

Question 12.
Let a̅ = 2i + j – 2k, b̅ = i + j. If c isavec- tor such that a̅.c̅ = |c̅|,|c̅-a̅| = 2√2 and the angle between a̅ × b̅ and c is 30°, then find the value of |(a̅ × b̅) × c̅|. [May ’15(TS)]
Answer:
Given that a̅ = 2i̅ + j̅ – 2k̅, b̅ = i̅ + j̅
⇒ |a̅| = \(\sqrt{4+1+4}\) = √9 =3, |b̅| = \(\sqrt{1+1}\) = √2
also, a̅ . c̅ = |c̅| and |c̅ – a̅| = 2√2
⇒ (c̅ – a̅)2 = 8 ⇒ |c̅|2 + |a̅|2 – 2c̅.a̅ = 8
⇒ |c| + 9 – 2|c̅| = 8 ⇒ |c̅| — 2|c̅| + 1 = 0
⇒ (|c̅| – 1) = 0 ⇒ |c̅| = 1

Now a̅ × b̅ = \(\left|\begin{array}{ccc}
\overline{\mathrm{i}} & \overline{\mathrm{j}} & \overline{\mathrm{k}} \\
2 & 1 & -2 \\
1 & 1 & 0
\end{array}\right|\)
= i̅(0 + 2) – j̅(0 + 2) + k̅ (2 – 1) = 2i̅ – 2j̅ + k̅
|a̅ × b̅| = ^/4 + 4 + l =3
|(a̅ × b̅) × c̅| = |a̅ × b̅| |c̅| sin (a̅ × b̅, c̅)
= |a̅ × b̅| |c̅| sin 30° = 3.1.\(\frac{1}{2}=\frac{3}{2}\)

Some More Maths 1A Product of Vectors Important Questions

Question 1.
If a̅ = 6i̅ + 2j̅ + 3k̅ and b̅ = 2i̅ – 9j̅ + 6k̅ then find a̅. b̅ and the angle between a̅ and b̅.
Answer:
Given a̅ = 6i̅ + 2j̅ + 3k̅ and b̅ = 2i̅ – 9j̅ + 6k̅
Now a̅.b̅ = (6i̅ + 2j̅ + 3k̅).(2i̅ – 9j̅ + 6k̅) = 12 – 18 + 8 = 12
TS Inter First Year Maths 1A Product of Vectors Important Questions Long Answer Type 10
Let ‘θ’ be the angle between a̅ & b̅ then cos θ = \(\frac{\overline{\mathrm{a}} \cdot \overline{\mathrm{b}}}{|\overline{\mathrm{a}}||\overline{\mathrm{b}}|}=\frac{12}{7.11}=\frac{12}{77}\)
∴ θ = cos-1\(\left(\frac{12}{77}\right)\)

Question 2.
For what values of λ, the vectors i̅ – λj̅ + 2k̅ and 8i̅ + 6 j̅ – k̅ are at right angles ?
Answer:
Let a̅ = i̅ – λj̅ + 2k̅ and b̅ = 8i̅ + 6j̅ – k̅
Since a,b form a right angle i.e., the vectors a and b are perpendicular then a̅ b̅ =0
(i̅ – λj̅ + 2k̅). (8i̅ + 6j̅ – k̅) = 0
⇒ 8 – 6λ – 2 = 0
⇒ 6 – 6λ = 0
⇒ 6λ = 6
⇒ λ = 1.

TS Inter First Year Maths 1A Product of Vectors Important Questions Long Answer Type

Question 3.
If the vectors λi̅ – 3j̅ + 5k̅ and 2λi̅ – A,j̅ – k̅ are perpendicular to each other then find X.
Answer:
Let a̅ = λi̅ – 3j̅ + 5k̅ and b̅ = 2λi̅ – λj̅ – k̅
Since the vector a̅ = λi̅ – 3j̅ + 5k̅ and b̅ = 2λi̅ – λj̅ – k̅
(λi̅ – 3j̅ + 5k̅). (2λ.i̅ – λ j̅ -k̅) = 0
2 + 3λ – 5 = 0
2 + 5λ – 2λ – 5 = 0

λ(2λ + 5) – 1(2λ + 5) = 0
(2λ + 5) (λ – 1) = 0
2λ + 5 = 0, λ – 1 = 0
λ = \(\frac{-5}{2}\), λ = 1
∴ λ = \(\frac{-5}{2}\) (or) 1.

Question 4.
If a̅ = i̅ – j̅ – k̅ and b̅ = 2i̅ – 3j̅ + k̅, then find the projection vector of b on a and its magnitude.
Answer:
Given vectors are a̅ = i̅ – j̅ – k̅ and b̅ = 2 i̅ – 3 j̅ + k̅
The projection vector of b̅ on a̅
TS Inter First Year Maths 1A Product of Vectors Important Questions Long Answer Type 11

Question 5.
Find the area of the parallelogram for which the vectors a̅ = 2i̅ – 3j̅ and b̅ =3i̅ – k̅ are adjacent sides.
Answer:
Given vectors are = 2j̅ – 3j̅ and b̅ = 3i̅ – k̅
The area of the parallelogram for which the vectors and 6 are adjacent sides
= a̅ × b̅ = \(\left|\begin{array}{ccc}
\overline{\mathrm{i}} & \overline{\mathrm{j}} & \overline{\mathrm{k}} \\
2 & -3 & 0 \\
3 & 0 & -1
\end{array}\right|\)
= i̅(3 – o) – j̅(-2 – o) + k̅(0 + 9) = 3i̅ + 2j̅ + 9k̅
∴ Area of the parallelogram = |a̅ × b̅| = \(\sqrt{(3)^2+(2)^2+(9)^2}=\sqrt{9+4+81}=\sqrt{94}\) sq.units.

Question 6.
If a̅ = 2i̅ – 3j̅ + 5k̅, b̅ = -i̅ + 4j̅ + 2k̅ then find a̅ × b̅ and unit vector perpendicular to both a̅ and b̅.
Answer:
Given a̅ = 2i̅ – 3j̅ + 5k̅, b̅ = -i̅ + 4j̅ + 2k̅
a̅ × b̅ =
= i̅(-6 – 20) – j̅(4 + 5) + k(8 – 3) = 26i̅ – 9j̅ + 5k̅
|a̅ × b̅| = \(\sqrt{(-26)^2+(-9)^2+(5)^2}=\sqrt{676+81+25}\)
= \(\sqrt{782}\)
∴ The unit vector perpendicular to both a̅ & b̅ is = \(\frac{(\overline{\mathrm{a}} \times \overline{\mathrm{b}})}{|\overline{\mathrm{a}} \times \overline{\mathrm{b}}|}=\pm \frac{(-26 \overline{\mathrm{i}}-9 \overline{\mathrm{j}}+5 \overline{\mathrm{k}})}{\sqrt{782}}\)

Question 7.
Find unit vector perpendicular to both i̅ + j̅ + k̅ and 2i̅ + j̅ + 3k̅.
Answer:
Let a̅ = i̅ + j̅ + k̅, b̅ = 2i̅ + j̅ + 3k̅
a̅ × b̅ = \(\left|\begin{array}{ccc}
\overline{\mathrm{i}} & \overline{\mathrm{j}} & \overline{\mathrm{k}} \\
1 & 1 & 1 \\
2 & 1 & 3
\end{array}\right|\)
= i̅(3 – 1) – j̅(3 – 2) + k̅(1 – 2)
= 2i̅ – j̅ – k̅
|a̅ × b̅| = \(\sqrt{(2)^2+(-1)^2+(-1)^2}=\sqrt{4+1+1}\) = √6
∴ The unit vector perpendicular to both a̅ & b̅ is = \(\pm \frac{(\overline{\mathrm{a}} \times \overline{\mathrm{b}})}{|\overline{\mathrm{a}} \times \overline{\mathrm{b}}|}=\pm \frac{(2 \overline{\mathrm{i}}-\overline{\mathrm{j}}-\overline{\mathrm{k}})}{\sqrt{6}}\)

Question 8.
If θ is the angle between the vector i̅ + j̅ and j̅ + k̅, then find sin θ.
Answer:
Let a̅ = i̅ + j̅ , b̅ = j̅ + k̅
a̅ × b̅ = \(\left|\begin{array}{ccc}
\overline{\mathrm{i}} & \overline{\mathrm{j}} & \overline{\mathrm{k}} \\
1 & 1 & 0 \\
0 & 1 & 1
\end{array}\right|\)
= i̅(1 – 0) – j̅(1 – 0) + k̅(1 – 0) = i̅ – j̅ + k̅
TS Inter First Year Maths 1A Product of Vectors Important Questions Long Answer Type 12
If ‘θ’ is the angle between the vector a̅ & b̅ then sin θ = \(\frac{(\overline{\mathrm{a}} \times \overline{\mathrm{b}})}{|\overline{\mathrm{a}}| \overline{\mathrm{b}} \mid}=\frac{\sqrt{3}}{\sqrt{2} \cdot \sqrt{2}}=\frac{\sqrt{3}}{2}\)

Question 9.
If a̅ = (1, – 1, -6), b̅ = (1, -3, 4) and c̅ = (2, -5, 3), then compute a̅.(b̅ × c̅).
Answer:
Given a̅ = (1, – 1, -6), b̅ = (1, -3, 4), c̅ = (2, -5, 3)
Now a̅.(b̅ × c̅) = [a̅ b̅ c̅]= 1 —3 4
= 1(-9 + 20) + 1(3 – 8) – 6(-5 + 6)
= 11 – 5 – 6 = 0

Question 10.
Find the volume of the parallelopiped whose coterminus edges are represented by the vectors 2i̅ – 3j̅ + k̅, i̅ -j̅ + 2k̅ and 2i̅ + j̅ – k̅ .
Answer:
Let a̅ = 2i̅ – 3j̅ + k̅, b̅ = i̅ -j̅ + 2k̅, c̅ = 2i̅ + j̅ – k̅
Volume of the parallelopiped
V = |[a̅ b̅ c̅]|
[a̅ b̅ c̅] = \(\left|\begin{array}{rrr}
2 & -3 & 1 \\
1 & -1 & 2 \\
2 & 1 & -1
\end{array}\right|\) = 2(1 – 2) + 3(-1-4) + 1(1 + 2)
= -2 – 15 + 3 = -14

∴ |[a̅ b̅ c̅]| = 14 cubic units

Question 11.
Find ‘t’ for which the vectors 2i̅ – 3j̅ + k̅, i̅ + 2j̅ – 3k̅ and j̅ – tk̅ are coplanar.
Answer:
Let a̅ = 2i̅ – 3j̅ + k̅, b̅ = i̅ + 2j̅ – 3k̅, c̅ = j̅ – tk̅
Since the vectors are coplanar then [a̅ b̅ c̅] = 0
⇒ \(\) = 0
⇒ 2(-2t + 3) + 3(-t – 0) + 1(1 – 0) = 0
⇒ -4t + 6 – 3t + 1 = 0
⇒ -7t + 7 = 0
⇒ t = 1

TS Inter First Year Maths 1A Product of Vectors Important Questions Long Answer Type

Question 12.
If the vectors a̅ = 2i̅ – j̅ + k̅, b̅ = i̅ + 2j̅ – 3k̅ and c̅ = 3i̅ + pj̅ + 5k̅ are coplanar then find p.
Answer:
Given a̅ = 2i̅ – j̅ + k̅, b̅ = i̅ + 2j̅ – 3k̅, c̅ = 3i̅ + pj̅ + 5k̅
Since the vectors are coplanar then [a̅ b̅ c̅] = 0
⇒ \(\left|\begin{array}{ccc}
2 & -1 & 1 \\
1 & 2 & -3 \\
3 & \mathrm{p} & 5
\end{array}\right|\) = 0
= 2(10 + 3p) + 1(5 + 9) + 1(p – 6) = 0
⇒ 20 + 6p + 14 + p – 6 = 0
⇒ 7p + 28 = 0
⇒ p = -4

Question 13.
In ΔABC if \(\overline{\mathrm{B C}}\) = a̅, \(\overline{\mathrm{C A}}\) = b̅ and \(\overline{\mathrm{A B}}\) = c̅ then show that a̅ × b̅ = b̅ × c̅ = c̅ × a̅.
Answer:
a̅ + b̅ + c̅ = \(\overline{\mathrm{BC}}+\overline{\mathrm{CA}}+\overline{\mathrm{AB}}=\overline{\mathrm{BA}}+\overline{\mathrm{AB}}=\overline{0}\) (by vector addition)
∴ a̅ + b̅ = -c̅
TS Inter First Year Maths 1A Product of Vectors Important Questions Long Answer Type 13
⇒ a̅ × b̅ = c̅ × a̅ ………….(1) (∵ a̅ × a̅ = 0)
Again a̅ + b̅ = -c̅
(a̅ + b̅) × b̅ = -c̅ × b̅ ⇒ a̅ × b̅ + b̅ × b̅ = b̅ × c̅
⇒ a̅ × b̅ = b̅ × c̅ ……………..(2) (∵ b̅ × b̅ = 0)
∴ From (1) and (2); a̅ × b̅ = b̅ × c̅ = c̅ × a̅

Question 14.
Find a unit vector perpendicular to the plane determined by the points P(1, – 1, 2), Q(2, 0, – 1) and R (0, 2, 1).
Answer:
Let O be the origin.
\(\overline{\mathrm{OP}}\) = i̅ – j̅ + 2k̅, \(\overline{\mathrm{OQ}}\) = 2i̅ – k̅, \(\overline{\mathrm{OR}}\) = 2j̅ + k̅
\(\overline{\mathrm{PQ}}=\overline{\mathrm{OQ}}-\overline{\mathrm{OP}}\) = (2i̅ – k̅)-(i̅ – j̅ + 2k̅) = i̅ + j̅ – 3k̅
\(\overline{\mathrm{PR}}=\overline{\mathrm{OR}}-\overline{\mathrm{OP}}\) = (2j̅ + k̅) – (i̅ – j̅ + 2k̅) =-i̅ + 3j̅ – k̅

Now \(\overline{\mathrm{PQ}} \times \overline{\mathrm{PR}}\) = \(\left|\begin{array}{ccc}
\overline{\mathrm{i}} & \overline{\mathrm{j}} & \overline{\mathrm{k}} \\
1 & 1 & -3 \\
-1 & 3 & -1
\end{array}\right|\)
= i̅(-1 + 9) – j̅(-1 – 3) + k̅(3 + 1)
= 8i̅ + 4j̅ + 4k̅
= 4(2i̅ + j̅ + k̅)

\(|\overline{\mathrm{PQ}} \times \overline{\mathrm{PR}}|=4 \sqrt{4+1+1}\) = 4√6
∴ Unit vector perpendicular to the plane determined by the points P, Q and R is
= \(\pm \frac{(\overline{\mathrm{PQ}} \times \overline{\mathrm{PR}})}{|\overline{\mathrm{PQ}} \times \overline{\mathrm{PR}}|}=\pm \frac{4(2 \overline{\mathrm{i}}+\overline{\mathrm{j}}+\overline{\mathrm{k}})}{4 \sqrt{6}}=\pm\left(\frac{2 \overline{\mathrm{i}}+\overline{\mathrm{j}}+\overline{\mathrm{k}}}{\sqrt{6}}\right)\)

Question 15.
If a̅, b̅ and c̅ are non coplanar vectors, then prove that the four points with position vectors 2a̅ + 3b̅ – c̅, a̅ – 2b̅ + 3c̅, 3a̅ + 4b̅ – 2c̅ and a̅ – 6b̅ + 6c̅ are coplanar.
Answer:
Suppose A, B, C, D are the given points with respect to a fixed origin ‘O’ and given that
\(\overline{\mathrm{OA}}\) = 2a̅ + 3b̅ – c̅,
\(\overline{\mathrm{OB}}\) = a̅ – 2b̅ + 3c̅ ,
\(\overline{\mathrm{OC}}\) = 3a̅ + 4b̅ – 2c̅ and
\(\overline{\mathrm{OD}}\) = a̅ – 6b̅ + 6c̅
\(\overline{\mathrm{AB}}=\overline{\mathrm{OB}}-\overline{\mathrm{OA}}\) = (a̅ – 2b̅ + 3c̅) – (2a̅ + 3b̅ – c̅) = – a̅ – 5b̅ + 4c̅
\(\overline{\mathrm{AC}}=\overline{\mathrm{OC}}-\overline{\mathrm{OA}}\) = (3a̅ + 4b̅ – 2c̅) – (2a̅ + 3b̅ – c̅) = a̅ + b̅ – c̅
\(\overline{\mathrm{AD}}=\overline{\mathrm{OD}}-\overline{\mathrm{OA}}\) =(a̅ – 6b̅ + 6c̅) – (2a̅ + 3b̅ – c̅) = -a̅ – 9b̅ + 7c̅
∴ \(\left[\begin{array}{lll}
\overline{\mathrm{AB}} & \overline{\mathrm{AC}} & \overline{\mathrm{AD}}
\end{array}\right]=\left|\begin{array}{rrr}
-1 & -5 & 4 \\
1 & 1 & -1 \\
-1 & -9 & 7
\end{array}\right|\) [a̅ b̅ c̅]
=[-1(7 – 9)+ 5(7 – 1)+ 4 (-9 + 1)] [a̅ b̅ c̅]
= [-1(- 2) + 5 (6) + 4 (- 8)] [a b c]
= (2 + 30 – 32) [a̅ b̅ c̅] = 0
Hence the given points A, B, C, D are coplanar.

Question 16.
If a, b, c are three vectors, then show that a̅ × (b̅ × c̅) = (a̅ . c̅) b̅ – (b̅. c̅) a̅.
Answer:
Case – (i) : If a and b are parallel, then the result is true.
Case – (ii) : If a and b are not parallel, then suppose \(\overline{\mathrm{OA}}\) = a̅ and \(\overline{\mathrm{OB}}\) = b̅ with respect to an origin O. Since a and b are not parallel we have O, A, B are non collinear and hence determine a plane.
Let i̅ be a unit vector along OA and j̅ be a unit vector perpendicular to i̅ in XY plane, k̅ is a unit vector perpendicular to XZ plane such that i̅, j̅, k̅ form a right handed system and k̅ = i̅ × j̅
TS Inter First Year Maths 1A Product of Vectors Important Questions Long Answer Type 14
∴ a̅ = a1i̅, b̅ = b1i̅ + b2j̅, c̅ = c1i̅ + c2j̅ + c3k̅ for a1, b1, c1, c2, c3, b2 being scalars.
Since a̅ and b̅ are non parallel,
a̅ × b̅ = a1i̅ × (b1j̅ i̅ + b2j̅) = a1b2
∴ (a̅ × b̅) × c̅ = (a1b2k) × (c1i̅  + c2j + c3k) = a1b2c1j̅ – a1b2c2i̅ ……………….(1)
(a̅.c̅)b̅ —(b̅.c̅)a̅ = a1c1 (b1i̅ + b2j̅) – (b1c1 + b2c2) a1i̅ = a1c1b2j̅ – a1b2c2i̅ ……………. (2)
From (1) and (2),
∴ (a̅ × b̅) × c̅ = (a̅.c̅)b̅ – (b̅.c̅)a̅

Question 17.
Find the cartesian equation of the plane through the point A (2, – 1, – 4) and parallel to the plane 4x – 12y – 3z – 7 = 0.
Answer:
The equation of the parallel plane is 4x – 12y – 3z = p
It passes through A (2, – 1, – 4) then 4 (2) – 12 (- 1) – 3 (- 4) = p
⇒ 8 + 12 + 12 = p
⇒ p = 32
∴ The equation of the required plane is 4x – 12y – 3z = 32

TS Inter First Year Maths 1A Product of Vectors Important Questions Long Answer Type

Question 18.
Find the angle between the planes 2x – 3y – 6z = 5 and 6x + 2y – 9z = 4.
Answer:
Equation of the plane is 2x – 3y – 6z = 5 ⇒ r̅ . (2 i̅ – 3 j̅ – 6k̅) = 5 …………….(1)
Similarly 6x + 2y- 9z = 4 ⇒ r̅ . (6i̅ + 2 j̅ – 9k̅) = 4 ………………(2)
If the angle between the planes r̅. n̅1 = d1 and r̅.n̅2 = d2 is θ then
cos θ = \(=\frac{\overline{\mathrm{n}}_1 \cdot \overline{\mathrm{n}}_2}{\left|\overline{\mathrm{n}}_1\right|\left|\overline{\mathrm{n}}_2\right|}\)
= \(\frac{(2 \overline{\mathrm{i}}-3 \overline{\mathrm{j}}-6 \overline{\mathrm{k}}) \cdot(6 \overline{\mathrm{i}}+2 \overline{\mathrm{j}}-9 \overline{\mathrm{k}})}{\sqrt{4+9+36} \sqrt{36+4+81}}=\frac{12-6+54}{7(11)}\)
= \(\frac{60}{77}\)
∴ θ = cos-1\(\left(\frac{60}{77}\right)\)

Question 19.
a̅ = 2i̅ – j̅ + k̅, b̅ = i̅ – 3 j̅ – 5k̅. Find the vector c̅ such that a̅, b̅ and c̅ form the sides of a triangle.
Answer:
a̅ = 2i̅ – j̅ + k̅, b̅ = i̅ – 3j̅ – 5k̅
TS Inter First Year Maths 1A Product of Vectors Important Questions Long Answer Type 15
∵ a̅, b̅, c̅ form the sides of a triangle a̅ + b̅ + c̅ = 0 (∵ \(\overline{\mathrm{AB}}+\overline{\mathrm{BC}}+\overline{\mathrm{CA}}\) = 0)
∴ c̅ = -a̅ – b̅ = -(2i̅ – j̅ + k̅) – (i̅ – 3j̅ – 5k̅) = -3i̅ + 4j̅ + 4k̅

Question 20.
Find the angle between the planes r̅ (2i̅ – j̅ + 2k̅) = 3 and r̅ . (3i̅ + 6j̅ + k̅) = 4. [Mar. ’15(TS)]
Answer:
If the angle between planes r̅.n̅1 = p1 and r̅.n̅2 = p2 is θ
then cos θ = \(\frac{\bar{n}_1 \cdot \bar{n}_2}{\left|\bar{n}_1\right| \cdot\left|\bar{n}_2\right|}=\frac{(2 \overline{\mathrm{i}}-\overline{\mathrm{j}}+2 \overline{\mathrm{k}}) \cdot(3 \overline{\mathrm{i}}+6 \overline{\mathrm{j}}+\overline{\mathrm{k}})}{\sqrt{4+1+4} \sqrt{9+36+1}}\)
= \(\frac{6-6+2}{3 \sqrt{46}}=\frac{2}{3 \sqrt{46}}\)
∴ θ = cos-1\(\left(\frac{2}{3 \sqrt{46}}\right)\)

Question 21.
If a̅ + b̅ + c̅ = 0, |a̅| = 3, |b̅| =5 and |c̅| = 7, then find the angle between a̅ and b̅.
Answer:
Given a̅ + b̅ + c̅ = 0 ⇒ c̅ =-(a̅ + b̅)
⇒ |c̅|2 = (a̅ + b̅) = a̅2 + b̅2 + 2(a̅ b̅)
⇒ 49 = 9 + 25 + 2(a̅ b̅)
⇒ 2(a̅.b̅) = 49 – 34 = 15
⇒ a̅ . b̅ = \(\frac{15}{2}\)

If θ is the angle between a and b then cos θ = \(\frac{\overline{\mathrm{a}} \cdot \overline{\mathrm{b}}}{|\overline{\mathrm{a}}||\overline{\mathrm{b}}|}=\frac{\frac{15}{2}}{3(5)}\)
= \(\frac{15}{2} \cdot \frac{1}{15}=\frac{1}{2}\)
∴ θ = cos-1\(\left(\frac{1}{2}\right)=\frac{\pi}{3}\)
∴ Angle between a̅ and b̅ is \(\frac{\pi}{3}\)

Question 22.
If |a̅| = 2, |b̅| =3 and |c̅| = 4 and each of a̅, b̅, c̅ is perpendicular to the sum of the other two vectors, then find the magnitude of a̅ + b̅ + c̅.
Answer:
Given |a̅| = 2, |b̅| = 3 and |c̅| = 4
Since each of a̅, b̅, c̅ is perpendicular to the sum of other two vectors i.e., a̅ is perpendicular to b̅ + c̅.
.\a̅ – (b̅ + c̅) = 0
⇒ a̅ – b̅ + a̅ – c̅= 0
Similarly b̅ (c̅ + a̅) = 0
⇒ b̅ c̅ + b̅ a̅ = 0 and c̅.(a̅ + b̅) = 0
⇒ c̅.a̅ + c̅.b̅ = 0
Adding we get 2 [(a̅. b̅) + (b̅. c̅) + (c̅ . a̅)] = 0 ……………..(1)
Also (a̅ + b̅ + c̅) =|a̅|2 + |b̅|2 + |c̅|2 + 2(a̅b̅ + b̅c̅ + c̅a̅)
=4 + 9 + 16 + 2(a̅b̅ + b̅c̅ + c̅a̅)
= 4 + 9 + 16 + 2 (0) = 29
∴ |a̅ + b̅ + c̅| = \(\sqrt{29}\)

Question 23.
For any two vectors a̅ and b̅ show that |a̅ × b̅|2 = \(\overline{\mathrm{a}^2} \overline{\mathrm{b}^2}-(\overline{\mathrm{a}} \cdot \overline{\mathrm{b}})^2\)
Answer:
We know that |a̅ × b̅| = |a̅| |b̅| sin θ, where ‘θ’ is the angle between a̅ and b̅.
Squaring on both sides |a̅ × b̅| = |a̅|2 |b̅|2 sin2 θ = |a̅| |b̅| (1 – cos2 θ)
= |a̅| |b̅̅| – |a̅|2 |b̅|2 cos2 θ
= \(\overline{\mathrm{a}^2} \overline{\mathrm{b}^2}-(\overline{\mathrm{a}} \cdot \overline{\mathrm{b}})^2\)

Question 24.
Find the area of the triangle formed by the two sides a̅ = i̅ + 2j̅ + 3k̅ and b̅ = 3i̅ + 5j̅ – k̅.
Answer:
Given a̅ = i̅ + 2 j̅ + 3k̅ and b̅ = 3 i̅ + 5 j̅ – k̅
Then a̅ × b̅ = \(\left|\begin{array}{rrr}
\overline{\mathrm{i}} & \overline{\mathrm{j}} & \overline{\mathrm{k}} \\
1 & 2 & 3 \\
3 & 5 & -1
\end{array}\right|\)
= i̅(-2 – 15) – j̅(-1 – 9) + k̅(5 – 6)
= -17i̅ + 10j̅ – k̅
Area of the triangle = \(\frac{1}{2}\)|a̅ × b̅| = \(\frac{1}{2} \sqrt{289+100+1}=\frac{1}{2} \sqrt{390}\)

Question 25.
For any vector g show that |a̅ × i̅|2 + |a̅ × j̅|2 +|a̅ × k̅|2 = 2|a̅|2.
Answer:
Let a̅ = xi̅ + yj̅ + zk̅, then a̅ × i̅ = -yk̅ + zj̅
|a̅ × i̅|2 = y2 + z2
Similarly |a̅ × j̅|2 = z2 + x2 and |a̅ × k̅| = x2+ y2
∴ |a̅ × i̅|2 + |a̅ × j̅|2 + |a̅ × k̅|2 = 2(x2 + y2 + z2) = 2|a̅|2

Question 26.
Find the area of the triangle having 3i̅ + 4j̅ and – 5i̅ + 7j̅ as two of its sides.
Answer:
Area of the triangle = \(\frac{1}{2}|\overline{\mathrm{AB}} \times \overline{\mathrm{AC}}|\)
\(\overline{\mathrm{AB}} \times \overline{\mathrm{AC}}\) = (3i̅ + 4 j̅) × (- 5i̅ + 7j̅) =-15(i̅ × i̅) – 20(j̅ × j̅) + 21(i̅ × j̅) + 28(j̅ × j̅)
= 20k̅ + 21k̅ = 41k̅
∴ Area of the ΔABC = \(\frac{1}{2}\)(41) = 20.5 sq. units

TS Inter First Year Maths 1A Product of Vectors Important Questions Long Answer Type

Question 27.
If a̅ = 2i̅ + j̅ – k̅, b̅ = -i̅ + 2j̅ – 4k̅ and c̅ = i̅ + j̅ + k̅, then find (a̅ × b̅) . (b̅ × c̅).
Answer:
Given a̅ = 2i̅ + j̅ – k̅, b̅ = -i̅ + 2j̅ – 4k̅ and c̅ = i̅ + j̅ + k̅
Then a̅ × b̅ = \(\left|\begin{array}{rrr}
\bar{i} & \bar{j} & \bar{k} \\
2 & 1 & -1 \\
-1 & 2 & -4
\end{array}\right|\)
= i̅(-4 + 2) – j̅(-8 – 1) + k̅(4 + 1) = -2i̅ + 9j̅ + 5k̅

b̅ × c̅ = \(\left|\begin{array}{rrr}
\overline{\mathrm{j}} & \overline{\mathrm{j}} & \overline{\mathrm{k}} \\
-1 & 2 & -4 \\
1 & 1 & 1
\end{array}\right|\)
= i̅(2 + 4) – j̅(-1 + 4) + k̅(-1 – 2) = 6i̅ – 3j̅ – 3k̅
(a̅ × b̅).(b̅ × c̅) = (-2i̅ + 9j̅ + 5k̅).(6i̅ – 3j̅ – 3k̅) = -12 – 27 – 15 = -54

Question 28.
Find the vector area and the area of the parallelogram having a̅ = i̅ + 2j̅ – k̅ and b̅ = 2i̅ – j̅ + 2k̅ as adjacent sides.
Answer:
Given a̅ = i̅ + 2 j̅ – k̅ and b̅ = 2 i̅ – j̅ + 2k̅
Then the vector area of parallelogram = a̅ × b̅
∴ (a̅ × b̅) = \(\left|\begin{array}{rrr}
\bar{i} & \bar{j} & \bar{k} \\
1 & 2 & -1 \\
2 & -1 & 2
\end{array}\right|\)
= i̅(4 – 1) – j̅(2 + 2) + k̅(-1 – 4) = 3i̅ – 4j̅ – 5k̅
Magnitude of the area = \(\sqrt{9+16+25}=\sqrt{50}\) = 5√2 sq. units

Question 29.
If a̅ × b̅ = b̅ × c̅ ≠ 0, then show that a̅ + c̅ = pb̅, where p is some scalar.
Answer:
Consider (a̅ + c̅ – pb̅) × b̅ = (a̅ × b̅) + (c̅ × b̅) – p(b̅ × b̅) = (b̅ × c̅) – (b̅ × c̅) – p(0) = 0
∴ a̅ + c̅ – pb̅ = 0
⇒ a̅ + c̅ = pb̅

Question 30.
Let a and b be vectors, satisfying |a̅|=|b̅| = 5 and (a̅, b̅) = 45°. Find the area of the triangle having a̅ – 2b̅ and 3a̅ + 2b̅ as two of its sides. [May ’15(AP); Mar. ’07] [Mar ’18(AP)]
Answer:
Area of the triangle = \(\frac{1}{2}\)|(a̅ – 2b̅) × (3a̅ + 2b̅)| ……………(1)
Now |(a̅ – 2b̅) × (3a̅ + 2b̅)| = |3(a̅ × a̅) – 2(b̅ × a̅) – 6(b̅ × a̅) – 4(b̅ × b̅)|
= |2(a̅ × b̅) + 6(a̅ × b̅)| = |8(a̅ × b̅)| = 8|a||b| sin 45°
= 8(5)(5)\(\frac{1}{\sqrt{2}}\)
= 100√2

Question 31.
Let a̅ and b̅ be vectors, satisfying |a̅| = |b̅| = 5 and (a̅, b̅) = 45°. Find the area of the triangle having a̅ – 2b̅ and 3a̅ + 2b̅ as two of Its sides. [May ’15(AP); Mar. ’07] [Mar ’18(AP)]
Answer:
Area of the triangle = \(\frac{1}{2}\)|(a̅ – 2b̅) × (3a̅ + 2b̅)| ………….(1)
Now |(a̅ – 2b̅) × (3a̅ + 2b̅)| = |3(a̅ × a̅) – 2(b̅ × a̅) – 6(b̅ × a̅) – 4(b̅ × b̅)|
= |2(a̅ × b̅) + 6(a̅ × b̅)| = |8(a̅ × b̅)| = 8|a̅||b̅| sin 45
= 8(5)(5)\(\frac{1}{\sqrt{2}}\)
= 100√2

From (1), Area of the triangle = \(\frac{1}{2}\)(100)√2 = 50√2 sq.units

Question 32.
Find the volume of the tetrahedron having the edges i̅ + j̅ + k̅; i̅ – j̅ and i̅ + 2j̅ + k̅.
Answer:
Denoting the edges by a̅ ,b̅, c̅ of tetrahedron, then its volume is
= \(\frac{1}{6}\)[a̅ b̅ c̅] = \(\frac{1}{6}\left|\begin{array}{ccc}
1 & 1 & 1 \\
1 & -1 & 0 \\
1 & 2 & 1
\end{array}\right|\) = \(\frac{1}{6}\) [1 (- 1) – 1 (1) + 1 (2 + 1)]
= \(\frac{1}{6}\) [-1 – 1 + 3] = \(\frac{1}{6}\) cubic units.

Question 33.
If a̅, b̅, c̅ are mutually perpendicular unit vectors, then find the value of [a̅ b̅ c̅]2.
Answer:
Given a̅, b̅, c̅ are mutually perpendicular unit vectors.
We have |a̅| = |b̅| = |c̅| = 1 and taking a̅ = i̅, b̅ = j̅, c̅ = k̅
We have [a̅ b̅ c̅] = [i̅ j̅ k̅] = i̅ . (j̅ × k̅) = i̅ . i̅ = 1
∴ [a̅ b̅ c̅]2 =1

Question 34.
Show that (a̅ + b̅) – (b̅ + c̅) × (c̅ + a̅) = 2 [a̅ b̅ c̅]
Answer:
(a̅ + b̅) . (b̅ + c̅) × (c̅ + a̅) = \(\left|\begin{array}{lll}
1 & 1 & 0 \\
0 & 1 & 1 \\
1 & 0 & 1
\end{array}\right|\) [a̅ b̅ c̅]
= [1(1) – 1(-1)][a̅ b̅ c̅]
= 2[a̅ b̅ c̅]

Question 35.
Prove that a̅ × [a̅ × (a̅ × b̅)] = (a̅ . a̅) (b̅ × a̅)
Answer:
L.H.S = a̅ × [a̅ × (a̅ × b̅)] = a̅ × [(a̅ . b̅)a̅ – (a̅. a̅)b̅]
= (a̅ . b̅) (a̅ × a̅) – (a̅ . a̅) (a̅ × b̅)
= (a̅ . b̅) (0) – (a̅ a̅) (a̅ × b̅)
= (a̅.a̅)(b̅ × a̅) = R.H.S.

TS Inter First Year Maths 1A Product of Vectors Important Questions Long Answer Type

Question 36.
If a, b, c and d are coplanar vectors, then show that (a̅ × b̅) × (c̅ × d̅) = 0.
Answer:
Given a,b,c,d are coplanar vectors ⇒ a̅ × b̅ is perpendicular to the plane S.
In the similar way c̅ × d̅ is perpendicular to the plane S.
a̅ × b̅ and c̅ × d̅ are parallel vectors.
⇒ (a̅ × b̅) × (c̅ × d̅) = 0 (or) (a̅ × b̅) × (c̅ × d̅) = [a̅ c̅ d̅]b̅ – [b̅ c̅ d̅]a̅
= 0b̅ – 0a̅ = 0 (∵ a̅, b̅, c̅, d̅ are coplanar)

Question 37.
If a, b, c are non coplanar, then show that the vectors a̅ – b̅, b̅ + c̅, c̅ + a̅ are coplanar.
Answer:
Given that a̅, b̅, c̅ are non coplanar we have [a̅ b̅ c̅] ≠ 0
[a̅ – b̅ b̅ + c̅ c̅ + a̅] = [a̅ b̅ c̅] = [1 + 1(-1)][a̅ b̅ c̅] = 0
[a̅ b̅ c̅] = 0
∴ Vectors a̅ – b̅, b̅ + c̅, c̅ + a̅ are coplanar.

Question 38.
Let a̅, b̅ and c̅ be non coplanar vectors. If [2a̅ – b̅ + 3c̅, a̅ + b̅ – 2c̅, a̅ + b̅ – 3c̅] = λ [a̅ b̅ c̅] then find the value of λ.
Answer:
Given a̅, b̅, c̅ are non coplanar vectors
We have [a̅ b̅ c̅] ≠ 0
1 1 -2 [a̅ b̅ c̅] = [2 (- 3 + 2) + 1 (- 3 + 2) + 3 (1 – 1)] [a̅ b̅ c̅]
= [-2 – 1] [a̅ b̅ c̅] = -3[a̅ b̅ c̅]
Given [2a̅ – b̅ + 3c̅, a̅ + b̅ – 2c̅, a̅ + b̅ – 3c̅] = λ [a̅ b̅ c̅]
We have – 3 [a̅ b̅ c̅] = λ [a̅ b̅ c̅]
⇒ λ = -3

Question 39.
If a̅ = (1, – 1, – 6), b̅ = (1, – 3, 4) and c̅ = (2, – 5, 3), then compute a̅ × (b̅ × c̅)
Answer:
Given a̅ = (1, – 1, – 6), b̅ = (1, – 3, 4), c̅ = (2, – 5, 3)
Now b̅ × c̅ = \(\left|\begin{array}{ccc}
\bar{i} & \bar{j} & \bar{k} \\
1 & -3 & 4 \\
2 & -5 & 3
\end{array}\right|\)
= i̅(-9 + 20) – j̅(3 – 8) + k̅(-5 + 6)
= i̅(11) – 7(-5) + k(1) = 11i̅ + 5j̅ + k̅

a̅ × (b̅ × c̅) = \(\left|\begin{array}{ccc}
\overline{\mathrm{i}} & \overline{\mathrm{j}} & \overline{\mathrm{k}} \\
1 & -1 & -6 \\
11 & 5 & 1
\end{array}\right|\) = i̅(-1 + 30) – j̅ (1 + 66) + k̅(5 + 11)
= i̅(29) – j̅(67) + k̅(16)
= 29i̅ – 67j̅ + 16k̅

Question 40.
If |a̅| = 11, |b̅| = 23 and |a̅ – b̅| = 30, then find the angle between the vectors a̅, b̅ and also find |a̅ + b̅|.
Answer:
|a̅ – b̅| = 30 ⇒|a̅ – b̅|2 = 900
⇒ |a̅|2 + |b̅|2 – 2(a̅.b̅) = 900
⇒ 121 + 529 – 2(a̅. b̅) = 900
⇒ 650 -2(a̅ . b̅) = 900
⇒ -2(a-b) = 250
⇒ -2 |a̅| |b̅| cos θ = 250
⇒ (-2)(253)cos θ = 25O
⇒ cos θ = \(\frac{125}{253}\)
⇒ θ = π – cos-1\(\left(\frac{125}{253}\right)\)

Also |a̅ + b̅|2 = |a̅|2 + |b̅|2 + 2(a̅.b̅) = 112 + 232 + 2|a̅||b̅|cos θ
= 121 + 529 + 2(11)(23)\(\left(\frac{-125}{253}\right)\) = 400
∴ |a̅ + b̅| = 20

Question 41.
Find λ in order that the four points A(3, 2, λ), B(4, λ, 5), C(4, 2, -2) and D(6, 5, – λ) be coplanar.
Answer:
\(\overline{\mathrm{OA}}\) = 3i̅ + 2j̅ + k̅; \(\overline{\mathrm{OB}}\) = 4i̅ + λj̅ + 5k̅; \(\overline{\mathrm{OC}}\) = 4i̅ + 2j̅ – 2k̅ and \(\overline{\mathrm{OD}}\) = 6i̅ + 5j̅ – k̅
\(\overline{\mathrm{AB}}=\overline{\mathrm{OB}}-\overline{\mathrm{OA}}\) = i̅ + (A – 2) j̅ + 4k̅;
\(\overline{\mathrm{AC}}=\overline{\mathrm{OC}}-\overline{\mathrm{OA}}\) = i̅ – 3k̅;
\(\overline{\mathrm{AD}}=\overline{\mathrm{OD}}-\overline{\mathrm{OA}}\) = 3i̅ + 3j̅ – 2k̅

Given A, B, C, D are coplanar
⇒ \(\overline{\mathrm{AB}}, \overline{\mathrm{AC}}, \overline{\mathrm{AD}}\) are coplanar
⇒ \(\left[\begin{array}{lll}
\overline{\mathrm{AB}} & \overline{\mathrm{AC}} & \overline{\mathrm{AD}}
\end{array}\right]\) = 0
⇒ \(\left|\begin{array}{ccc}
1 & \lambda-2 & 4 \\
1 & 0 & -3 \\
3 & 3 & -2
\end{array}\right|\) = 0
⇒ 1 (9) – (λ – 2) (- 2 + 9) + 4(3) = 0
⇒ 21 – (λ – 2) (7) = 0
⇒ λ – 2 = 3
⇒ λ = 5

TS Inter First Year Maths 1A Product of Vectors Important Questions Long Answer Type

Question 42.
For any two vectors a̅ and b̅, show that (1 + |a̅|)2 (1 + |b̅|)2 = |1 – a̅. b̅|2 + |a̅ + b̅ + a̅ × b̅|2
Answer:
Let |a̅| = a̅, |b̅| = b̅, (a̅, b̅) = θ.
LHS = (1 + a2) (1 + b2)
= 1 + a2 + b2 + a2 b2 …………..(1)
a̅. b̅ = |a̅||b̅| cos 9 = ab cos θ
|a̅ × b̅| = |a̅| |b̅| sin θ = ab sin θ
RHS = (1 – a . b)2 + (a̅ + b̅ + a̅ × b̅)2
= 1 + (a̅ b̅)2 – 2a̅ b̅ + a̅2 + b̅2 + |a̅ × b̅| + 2 a̅ . b̅ + 2(b̅ . a̅ × b̅) + 2(a̅ × b̅ . a̅)
= 1 + a̅22 cos2 θ + a̅2 + b̅2 + a̅22 sin2 θ + 0 + 0
= 1 + a̅22 (cos2 θ + sin2 θ) + a̅2 + b̅2
= 1 + a̅22 (1) + a̅2 +b̅2
= 1 + a̅22 + a̅2 + b̅2
= 1 + a̅2 + b̅2 + a̅22
= RHS.

Question 43.
If a̅ = 2i̅ – 3j̅ + k̅ and b̅ = i̅ + 4j̅ – 2k̅, then find (a̅ + b̅) × (a̅ – b̅)
Answer:
Given a̅ = 2i̅ – 3j̅ + k̅
b̅ = i̅ + 4j̅ – 2k̅
Now
a̅ + b̅ = 2i̅ – 3j̅ + k̅ + i̅ + 4j̅ – 2k̅ = 3i̅ + j̅ – k̅
a̅ – b̅ = 2i̅ – 3j̅ + k̅ – i̅ – 4j̅ + 2k̅ = i̅ – 7j̅ + 3k̅
(a̅ + b̅) x (a̅ – b̅) = \(\left|\begin{array}{rrr}
\overline{\mathrm{i}} & \overline{\mathrm{j}} & \overline{\mathrm{k}} \\
3 & 1 & -1 \\
1 & -7 & 3
\end{array}\right|\)
= i̅(3 – 7) – j̅(9 + 1) + k̅(-21 – 1)
= -4i̅ – 10j̅ – 22k̅

Question 44.
Show that the volume of a tetrahedron with a̅, b̅ and c̅ as coterminous edges is \(\frac{1}{6}\)|[a̅ b̅ c̅]|
Answer:
Let OABC be a tetrahedron and
\(\overline{\mathrm{OA}}\) = a̅, \(\overline{\mathrm{OB}}\) = b̅, \(\overline{\mathrm{OC}}\) = c̅
Let V be the volume of the tetrahedron OABC. By definition the volume V is given by V = \(\frac{1}{3}\) (area of the base ΔOAB)
(Length of the perpendicular from C to the base ΔOAB)
TS Inter First Year Maths 1A Product of Vectors Important Questions Long Answer Type 16
CN is the perpendicular from C to AOAB and CM is the perpendicular from C on to the supporting line of a̅ × b̅ so that CN = OM = Length of the projection of c onto a̅ × b̅.

Question 45.
Find the equation of the plane passing through the point (3, -2,1) and perpendicular to the vector (4, 7, -4).
Answer:
The vector equation of the plane is
[r̅ – (3 i̅ – 2 j̅ + k̅)j̅ . (4 i̅ + 7 j̅ – 4k̅) = 0
⇒ r̅ . (4i̅ + 7j̅ – 4k̅) – (12 – 14 – 4) = 0
⇒ r̅ . (4 i̅ + 7 j̅ – 4k̅) +6 = 0
The Cartesian equation is 4x + 7y – 4z + 6 = 0

TS Inter Second Year Maths 2A Random Variables and Probability Distributions Important Questions Long Answer Type

Students must practice these Maths 2A Important Questions TS Inter Second Year Maths 2A Random Variables and Probability Distributions Important Questions Long Answer Type to help strengthen their preparations for exams.

TS Inter Second Year Maths 2A Random Variables and Probability Distributions Important Questions Long Answer Type

Question 1.
The probability distribution of a random variable X is given below:

TS Inter Second Year Maths 2A Random Variables and Probability Distributions Important Questions Long Answer Type 1

Find the value of k and the mean and variance of X. [AP – Mar. 2019, AP- Mar. 2017: May ‘14, ’13, May ’14, ’12, ’10].
Solution:
Given that

TS Inter Second Year Maths 2A Random Variables and Probability Distributions Important Questions Long Answer Type 1

is the probability distribution of a random variable X.
i) We know that,
\(\) P(X = xr) = 1
i.e., Sum of probabilities = 1
P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4)+ P(X = 5) = 1
k + 2k + 3k + 4k + 5k = 1
15k = 1
k = \(\frac{1}{15}\)

ii) Mean of X is
μ = \(\sum_{r=1}^5\) P(X = xr) xr
= 1 (k) + 2 (2k) + 3 (3k) + (4k) 4 + (5k) 5
= k + 4k + 9k + 16k + 25k = 55 k
= 55(\(\frac{1}{15}\)) = \(\frac{11}{3}\)

iii) Variance of X is
σ2 = \(\sum_{r=1}^5\) P(X = xr) xr2 – μ2
= k(1)2 + 2k(2)2 + 3k(3)2 + 4k (4)2 + 5k (5)2 – (\(\frac{11}{3}\))2
= k(1) + 2k(4) + 3k(9) + 4k(16) + 5k(25) – \(\frac{121}{9}\)
= k + 8k + 27k + 64k + 125k – \(\frac{121}{9}\)
= 225k – \(\frac{121}{9}\)
= 225 (\(\frac{1}{15}\)) – \(\frac{121}{9}\)
= 15 – \(\frac{121}{9}\)
= \(\frac{135-121}{9}=\frac{14}{9}\).

TS Inter Second Year Maths 2A Random Variables and Probability Distributions Important Questions Long Answer Type

Question 2.

TS Inter Second Year Maths 2A Random Variables and Probability Distributions Important Questions Long Answer Type 2

is the probability distribution of a random variable X. find the value of k and the variance of X.
Solution:

TS Inter Second Year Maths 2A Random Variables and Probability Distributions Important Questions Long Answer Type 2

is the probability distribution of a random variable X.
We know that,
\(\sum_{r=-2}^3\) P(X = xr) = 1
i.e., Sum of probabilities = 1
P(X = – 2) + P(X = – 1) + P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) = 1
0.1 + k + 0.2 + 2k + 0.3 + k = 1
4k + 0.6 = 1
4k = 1 – 0.6
4k = 0.4
k = 0.1
k = \(\frac{1}{10}\)
Mean of X is μ = \(\sum_{r=-2}^3\) (X = xr) . xr
= (- 2) (0.1) + (- 1) k + 0(0.2) + 1(2k) + 2(0.3) + 3k
= – 0.2 – k + 0 + 2k + 0.6 + 3k
= 0.4 + 4k
= 0.4 + 4 (\(\frac{1}{10}\))
= 0.4 + 0.4 = 0.8
= \(\frac{8}{10}=\frac{4}{5}\)
Variance of X is σ2 = \(\sum_{r=1}^5\) P(X = xr) xr2 – μ2
= (- 2)2 (0.1) + k(- 1)2 + (0.2) (0)2 + 2k(1)2 0.3(2)2 + k(3)2 – (\(\frac{4}{5}\))2
= 4 . (0.1) + k . 1 + 0.2 (0) + 2k . 1 + 0.3(4) + k . 9 – \(\frac{16}{25}\)
= 0.4 + k + 0 + 2k + 1.2 + 9k – \(\frac{16}{25}\)
= 1.6 + 12k – \(\frac{16}{25}\)
= \(\frac{16}{10}+\frac{12}{10}-\frac{16}{25}\)
= \(\frac{160+120-64}{100}=\frac{216}{100}\) = 2.16.

TS Inter Second Year Maths 2A Random Variables and Probability Distributions Important Questions Long Answer Type

Question 3.
A random variable X has the following probability distribution.

TS Inter Second Year Maths 2A Random Variables and Probability Distributions Important Questions Long Answer Type 3

Find i) k
ii) the mean and
iii) P(0 < X < 5). [May ’12, ’10, ’08, March ‘09, Board Paper] [AP – May, Mar.16; TS – Mar. ‘18, ‘16]
Solution:

TS Inter Second Year Maths 2A Random Variables and Probability Distributions Important Questions Long Answer Type 3

is the probability distribution function.
i) We know that,
\(\sum_{\mathbf{r}=0}^7\) P(X = x) = 1
i.e., Sum of the probabilities = 1
P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5) + P(X = 6) + P(X = 7)=
0 + k + 2k + 2k + 3k + k2 + 2k2 + 7k2 + k = 1
10k2 + 9k – 1 = 0
10k2 + 10k – k – 1 = 0
10k (k + 1) – 1(k + 1) = 0
(k + 1) (10k – 1) = 0
k + 1 = 0 (or) 10k – 1 = 0
k = – 1 (or) k = \(\frac{1}{10}\)
k = – 1 does not satisfy the given probabilities.
∴ k = \(\frac{1}{10}\).

ii) The mean of X is
μ = \(\sum_{r=0}^7\) (X = xr) . xr
= 0 . 0 + 1(k) + 2(2k) + 3(2k) + 4(3k)+ 5(k2) + 6(2k2) + 7 (7k2 + k)
= 0 + k + 4k + 6k + 12k + 5k2 + 12k2 + 49k2 + 7k
= 66k2 + 30k
= \(66\left(\frac{1}{10}\right)^2+30\left(\frac{1}{10}\right)\)
= \(\frac{66}{100}+\frac{30}{10}\)
= 0.66 + 3 = 3.66.

iii) P(0 < X < 5)
= P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4)
= k + 2k + 2k + 3k
= 8k = 8(\(\frac{1}{10}\))
= 0.8 = \(\frac{4}{5}\).

TS Inter Second Year Maths 2A Random Variables and Probability Distributions Important Questions Long Answer Type

Question 4.
The range of a random variable X is {0, 1, 2}. Given that P(X= 0) = 3c3, P(X = 1) = 4c – 10c2, P(X = 2) = 5c – 1. Find
(i) the value of c
(ii) P(X < 1),
(iii) P (1 < X ≤ 2) and P (0 < X ≤ 3). [March ‘13. ‘11, ‘07. ‘05, ‘95; May ‘11. 09. ‘91, TS – Mar. 2015; AP – Mar. 2015]
Solution:
The range of a random variable, X is {O, 1, 2}
Given that,
P(X = 0) = 3c3, P(X = 1) = 4c – 10c2,
P(X = 2) = 5c – 1
ï) We know that,
\(\sum_{\mathrm{r}=0}^2\) P(X = xr) = 1
i.e., Sum of the probabilities = 1
P(X = 0) + P(X = 1) + P(X = 2) = 1
3c3 + 4c – 10c2 + 5c – 1 = 1
3c3 – 10c2 + 9c – 2 = 0
Let, f(c) = 3c3 – 10c2 + 9c – 2
If c = 1 then,
f(1) = 3(1)3 – 10(1)2 + 9(1) – 2
1(1) = 3 – 10 + 9 – 2
= 12 – 12 = 0
∴ c = 1 is a root of 1(c) = 0

TS Inter Second Year Maths 2A Random Variables and Probability Distributions Important Questions Long Answer Type 4

3c2 – 7c + 2 = 0
3c2 – 6c – c + 2 = 0
3c (c – 2) – 1(c – 2) = 0
(c – 2) (3c – 1) = 0
c – 2 = 0 (or) 3c – 1 = 0
c = 2 (or) c = \(\frac{1}{3}\)
∴ c = 1, 2, \(\frac{1}{3}\)
c = 1, 2 does not satisfy the given probabilities.
∴ c = \(\frac{1}{3}\)

ii) P(X < 1) = P(X = 0)
= 3c3
= 3(\(\frac{1}{3}\))3
= \(\frac{3}{27}=\frac{1}{9}\)

iii) P(1 < X ≤ 2)
= P(X = 2)
= 5c – 1
= 5 . \(\frac{1}{3}\) – 1
= \(\frac{5-3}{3}=\frac{2}{3}\)

iv)P(0 < X < 3) = P(X = 1) + P(X = 2)
= 4c – 10c2 + 5c – 1
= 9c – 10c2 – 1
= 9(\(\frac{1}{3}\)) – 10(\(\frac{1}{9}\)) – 1
= \(\frac{27-10-9}{9}=\frac{8}{9}\).

Question 5.
The range of a random variable X is {1, 2, 3, …………..} and P(X = k) = (k = 1, 2, 3, ………………). Find the value of c and P(0 < X < 3). [TS – May 2015; March 2003, May 2009]
Solution:
The range of a random variable, X is {1, 2, 3, …………..}.
Given that,
P(X = k) = \(\) k = 1, 2, 3 …………….
i) We know that,
\(\) P(X = xk) = 1
i.e, sum of the probabilities = 1
P(X = 1) + P(X = 2) + P(X = 3) + …………………. = 1
\(\frac{\mathrm{c}}{1 !}+\frac{\mathrm{c}^2}{2 !}+\frac{\mathrm{c}^3}{3 !}+\ldots \ldots\)
\(e^x=1+\frac{x}{1 !}+\frac{x^2}{2 !}+\ldots \ldots\)
\(1+\frac{\mathrm{c}}{1 !}+\frac{\mathrm{c}^2}{2 !}+\frac{\mathrm{c}^3}{3 !}+\ldots \ldots\)
ec = 2.
c = loge 2

ii) P(0 < X < 3)
= P(X = 1) + P(X = 2)
= \(\frac{c}{1 !}+\frac{c^2}{2 !}=\frac{c}{1}+\frac{c^2}{2}\)
= loge 2 + \(\frac{\left(\log _{\mathrm{e}} 2\right)^2}{2}\).

TS Inter Second Year Maths 2A Random Variables and Probability Distributions Important Questions Long Answer Type

Question 6.
A cubical die is thrown. Find the mean and variance of X, giving the number on the face that shows up. [TS – Mar. 2019] [TS – May 2016; AP – May’ 2015]
Solution:
Let S be the sample space and X be the random variable associated with S, where P(X) is given by the following table.

TS Inter Second Year Maths 2A Random Variables and Probability Distributions Important Questions Long Answer Type 5

Mean of X is μ = \(\sum_{r=1}^6\) P(X = xr) . xr

TS Inter Second Year Maths 2A Random Variables and Probability Distributions Important Questions Long Answer Type 6

Question 7.
If X is a random variable with probability distribution P(X = k) = \(\frac{(k+1) c}{2^k}\), k = 0, 1, 2, …………….. then find c. AP – Mar. 2018;
Solution:
Given that,
P(X = k) = \(\frac{(k+1) c}{2^k}\), k = 0, 1, 2, ………………. is the probability distribution of X.
We know that,
\(\sum_{k=0}^{\infty}\) P(X = xk) = 1
i.e., sum of the probabilities = 1
P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + ………………. = 1
\(\frac{1 \cdot c}{2^0}+\frac{2 \cdot c}{2}+\frac{3 \cdot c}{2^2}+\frac{4 \cdot c}{2^3}+\ldots \ldots\) = 1

TS Inter Second Year Maths 2A Random Variables and Probability Distributions Important Questions Long Answer Type 7

TS Inter Second Year Maths 2A Random Variables and Probability Distributions Important Questions Long Answer Type

Question 8.
Let X be a random variable such that P(X = – 2) = P(X = – 1) = P(X = 2) = P(X = 1) = \(\frac{1}{6}\) and P(X = 0) = \(\frac{1}{3}\). Find the mean and variance of X.
Solution:
X is a random variable.
Given that, P(X = – 2) = \(\frac{1}{6}\)
P(X = – 1) = \(\frac{1}{6}\)
P(X = 2) = \(\frac{1}{6}\)
P(X = 1)= \(\frac{1}{6}\)
P (X = 0) = \(\frac{1}{6}\)

TS Inter Second Year Maths 2A Random Variables and Probability Distributions Important Questions Long Answer Type 8

Question 9.
Two dice are rolled at random. Find the probability distribution of the sum of the numbers on them. Find the mean of the random variable.
Solution:
When two dice are rolled, the sample space S’ consists of 6 × 6 = 36.
Sample points are
S = {(1, 1), (1, 2), (1, 3), (1,4), (1, 5), (1, 6),
(2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6),
(3, 1), (3, 2), (3, 3), (3, 4), (3, 5), (3, 6)
(4, 1), (4, 2), 4, 3), (4, 4), (4. 5), (4, 6),
(5, 1), (5, 2), (5, 3), (5,4), (5, 5), (5, 6),
(6, 1), (6, 2), (6, 3), (6, 4), (6, 5), (6, 6))
Let X denote the sum of the numbers on the two dice.
Then the range of X is {2, 3, 4, 5, 6, …………………, 12)
The probability distribution for X is given here under:

TS Inter Second Year Maths 2A Random Variables and Probability Distributions Important Questions Long Answer Type 9

TS Inter Second Year Maths 2A Random Variables and Probability Distributions Important Questions Long Answer Type

Question 10.
Find the constant ‘c’, so that F(x) = c \(\left(\frac{2}{3}\right)^x\) x = 1, 2, 3, …….. is the p.d.f. of a discrete random variable X.
Solution:
Given that,
F(x) = c \(\left(\frac{2}{3}\right)^x\), x = 1, 2,3,….. is the probability distribution function.
We know that,
\(\sum_{r=1}^{\infty}\) P(X = xr) = 1
i.e., sum of the probabilities = 1
P(X = 1) + P(X = 2) + P(X = 3) + …………. = 1
\(c\left(\frac{2}{3}\right)^1+c\left(\frac{2}{3}\right)^2+c\left(\frac{2}{3}\right)^3+\ldots \ldots \ldots\) = 1
\(c\left[\frac{2}{3}+\left(\frac{2}{3}\right)^2+\left(\frac{2}{3}\right)^3+\ldots \ldots\right]\) = 1
Here, a = \(\frac{2}{3}\), r = \(\frac{2}{3}\)
S = \(\frac{a}{1-r}\)
c\(\left[\frac{\frac{2}{3}}{1-\frac{2}{3}}\right]\) = 1
\(c\left[\frac{\frac{2}{3}}{\frac{1}{3}}\right]\) = 1
c(2) = 1
c = \(\frac{1}{2}\).

Question 11.
In the experiment of tossing a coin n times, if the variable X denotes the number of heads ndP(X=4),P(X=5),P(X=6) are in arithmetic progression then find n. [March 2002]
Solution:
X follows binomial distribution with p = \(\frac{1}{2}\), q = \(\frac{1}{2}\)
Given that,
P(X = 4), P(X = 5), P(X = 6) are in A.P.
Since a, b, c are in A.P. then
∴ 2P(X = 5) = P(X = 4) + P(X = 6)
We have,
P(X = r) = \({ }^n \mathrm{C}_1\) prq1-r

TS Inter Second Year Maths 2A Random Variables and Probability Distributions Important Questions Long Answer Type 10

12 (n – 4) = 30 + (n – 5) (n – 4)
12n – 48 = 30 + n2 – 9n + 20
n2 – 21n + 98 = 0
n2 – 14n – 7n + 98 = 0
n (n – 14) – 7(n – 14) = 0
(n – 14) (n – 7) = 0
n – 14 = 0 (or) n – 7 = 0
n = 14 (or) n = 7
∴ n = 7 (or) 14.

TS Inter Second Year Maths 2A Random Variables and Probability Distributions Important Questions Very Short Answer Type

Students must practice these Maths 2A Important Questions TS Inter Second Year Maths 2A Random Variables and Probability Distributions Important Questions Very Short Answer Type to help strengthen their preparations for exams.

TS Inter Second Year Maths 2A Random Variables and Probability Distributions Important Questions Very Short Answer Type

Question 1.
Define Binomial distribution. [Mar. ’92, May ’94]
Solution:
Definition:
Let n’ be a positive integer and p be a real number such that 0 ≤ p ≤ 1. A random variable, X with range {0, 1, 2, ……., n} is said to follow (or have) binomial distribution (or) Bernoulli distribution with parameters n and p,
if P(X = r) = \({ }^n C_r\) prqn-r for r = 0, 1, 2, , n where q = 1 – p.

Question 2.
8 coins are tossed simultaneously. Find the probability of getting atleast 6 heads.
Solution:
X follows binomial distribution.
Let, X be the no. of heads getting when 8 coins are tossed.
In the experiment of tossing a coin,
the probability of getting a head, p = \(\frac{1}{2}\)
the probability of getting a tail, q = 1 – p
= 1 – \(\frac{1}{2}\) = \(\frac{1}{2}\), n = 8
The probability of getting atleast 6 heads =
P(X ≥ 6) = P(X = 6) + P(X = 7) + P(X = 8)
We have, P(X = r) = \({ }^n C_r\) prqn-r

TS Inter Second Year Maths 2A Random Variables and Probability Distributions Important Questions Very Short Answer Type 1

TS Inter Second Year Maths 2A Random Variables and Probability Distributions Important Questions Very Short Answer Type

Question 3.
The mean and variance of a binomial distribution are 4 and 3 respectively. Fix the distribution and find P(X ≥ 1).
[TS – Mar. ’17, ’15; AP – May 2015; Mar. ’11, ’08, May ’11] [AP – Mar. 2016; AP & TS – Mar. 2019]
Solution:
X follows binomial distribution.
In binomial distribution, mean = 4
np = 4 …………(1)
variance = 3
npq = 3 …………….(2)
Now, \(\frac{(2)}{(1)} \Rightarrow \frac{n p q}{n p}=\frac{3}{4}\)
q = \(\frac{3}{4}\)
p = 1 – q
= 1 – \(\frac{3}{4}\) = \(\frac{1}{4}\)
p = \(\frac{1}{4}\)
From (1), n(\(\frac{1}{4}\)) = 4
n = 16
Parameters are n = 16, p = \(\frac{1}{4}\)
Distribution = (q + p)n
= \(\left(\frac{3}{4}+\frac{1}{4}\right)^{16}\)
P(X ≥ 1) = P(X = 1) + P(X = 2) + ……………. + P(X = 16)
= 1 – P(X = 0)
We have P(X = r) = \({ }^n C_r\) prqn-r
= 1 – \({ }^{16} \mathrm{C}_0\left(\frac{1}{4}\right)^0\left(\frac{3}{4}\right)^{16-0}\)
= 1 – 1. 1 . \(\left(\frac{3}{4}\right)^{16}\)
= 1 – \(\left(\frac{3}{4}\right)^{16}\).

Question 4.
The probability that a person choosen at random is left handed (in hand writing) is 0.1. What is the probability that in a group of 10 people, there is one who is left handed? [TS – Mar. ’16, AP – Mar. ’17, ’15; May ’12]
Solution:
Solution:
X follows binomial distribution.
Given that, the probability that a person choosen at random Is left handed
p = 0.1
q = 1 – p
= 1 – 0.1 = 0.9
n = 10, r = 1
The probability of one who is left handed = P(X = 1)
We have, P(X = r) = \({ }^n C_r\) prqn-r
P(X = 1) = \(\)
= 10 . \(\frac{1}{10}\) . (0.9)9

Question 5.
One in 9 ships is likely to be wrecked, when they are set on sail, when 6 ships are on sail, find the probability for
i) Atleast one will arrive safely
ii) Exactly three will arrive safely. [March ’08]
Solution:
Since, one in 9 ships is likely to be wrecked.
The probability that a ship will be wrecked, q = \(\frac{1}{9}\)
P = 1 – q
= 1 – \(\frac{1}{9}\) = \(\frac{8}{9}\)
Let X be no. of ships arrive safely in the 6 ships which set on sail.
Now, X follows binomial distribution with parameters
n = 6, p = \(\frac{8}{9}\), q = \(\frac{1}{9}\)
i) The probability for atleast one will arrive safety
= P(X ≥ 1)
= P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P (X = 5) + P (X = 6)
= 1 – P (X = 0)
We have,
P(X = 6) = \({ }^n C_r\) prqn-r
= 1 – \({ }^6 c_0\left(\frac{8}{9}\right)^0\left(\frac{1}{9}\right)^{6-0}\)
= 1 – 1 . 1 . \(\left(\frac{1}{9}\right)^6\)
= 1 – \(\frac{1}{9^6}\)

ii) The probability for exactly three will arrive safely = P(X = 3)
P(X = r) = \({ }^n C_r\) prqn-r
= \({ }^6 \mathrm{C}_3\left(\frac{8}{9}\right)^3\left(\frac{1}{9}\right)^{6-3}\)
= \(\frac{6 \cdot 5 \cdot 4}{1 \cdot 2 \cdot 3} \cdot \frac{8^3}{9^3} \cdot \frac{1}{9^3}\)
= \(\frac{20 \cdot 512}{9^6}=\frac{10240}{9^6}\).

TS Inter Second Year Maths 2A Random Variables and Probability Distributions Important Questions Very Short Answer Type

Question 6.
If the mean and variance of a binomial variable X are 2.4 and 1.44 respectIvely, find P(1 < x ≤ 4) [AP – Mar.’18; TS – May ’15]
Solution:
X follows binomial distribution.
In binomial distribution,
Mean = 2.4
np = 2.4 ………….(1)
Variance = 1.44
npq = 144 …………..(2)
Now,

TS Inter Second Year Maths 2A Random Variables and Probability Distributions Important Questions Very Short Answer Type 2

Question 7.
On an average, rain falls on 12 days in every 30 days, find the probability that, rain will fall on just 3 days of a given week.
Solution:
X follows binomial distribution.
Given that, the probability for the day to be raining
p = \(\frac{12}{30}=\frac{2}{5}\)
q = 1 – p = 1 – \(\frac{2}{5}\) = \(\frac{3}{5}\)
n = 7, r = 3
The probability that rain will fall on just 3 days of a given week
P(X = 3) =?
We have P(X = r) = \({ }^n C_r\) pr qn-r
P(X = 3) = \({ }^7 C_3\left(\frac{2}{5}\right)^3\left(\frac{3}{5}\right)^{7-3}\)
= \(\frac{7 \cdot 6 \cdot 5}{1 \cdot 2 \cdot 3} \cdot \frac{2^3}{5^3} \cdot \frac{3^4}{5^4}\)
= 35. \(\frac{2^3 \cdot 3^4}{5^7}\).

TS Inter Second Year Maths 2A Random Variables and Probability Distributions Important Questions Very Short Answer Type

Question 8.
For a binomial distribution with mean 6 and variance 2, find the first two terms of the distribution.
Solution:
X follows binomial distribution.
In binomial distribution,
mean = 6
np = 6 ……………..(1)
variance 2
npq = 2 ……………(2)
Now,
\(\frac{(2)}{(1)} \Rightarrow \frac{n p q}{n p}=\frac{2}{6}\)
q = \(\frac{1}{3}\)
p = 1 – q
= 1 – \(\frac{1}{3}\)
= \(\frac{2}{3}\)
From (1),
n(\(\frac{2}{3}\)) = 6
The first two terms of the binomial distribution are P(X = 0) and P(X = 1).
We have P(X = r) = \({ }^n C_r\) pr qn-r
i) P(X = o) = \({ }^9 C_0\left(\frac{2}{3}\right)^0\left(\frac{1}{3}\right)^{9-0}\)
= 1 . 1 . \(\frac{1}{3^9}\) = \(\frac{1}{3^9}\)

ii) P(X = 1) = \({ }^9 C_1\left(\frac{2}{3}\right)^1\left(\frac{1}{3}\right)^{9-1}\)
= 9 . \(\frac{2}{3} \cdot \frac{1}{3^8}=\frac{2}{3^7}\)

Question 9.
Define Poisson distribution. [May ‘07]
Solution:
Poisson distribution:
Let λ > 0 be a real number. A random vari able, X with range {O, 1, 2, …………..} is said to follow (have) Poisson distribution with parameter λ if
P(X = r) = \(\frac{\mathrm{e}^{-\lambda} \lambda^{\mathrm{r}}}{\mathrm{r} !}\) for r = 0, 1, 2, ……………….

Question 10.
A Poisson variable satisfies P(X = 1) = P(X = 2). Find P(X = 5). [Mar. ‘14, ‘10, May’14, 13, ’06, Board Paper, TS – Mar. ‘18; AP & TS – May ’16]
Solution:
We have,

TS Inter Second Year Maths 2A Random Variables and Probability Distributions Important Questions Very Short Answer Type 3

TS Inter Second Year Maths 2A Random Variables and Probability Distributions Important Questions Very Short Answer Type

Question 11.
In a book of 450 pages, there are 400 typographical en-ors. Assuming that the number of errors per page follow the Poisson law. Find the probability that a random sample of 5 pages will contain no typographical error.
Solution:
The average no. of errors for page in the book is λ = \(\frac{400}{450}=\frac{8}{9}\)
Let, X be the no. of typographical errors in a page.
Assume that X follows Poisson distribution with parameter, λ = 0.2
Now, P(X = r) = \(\frac{e^{-\lambda} \lambda^r}{r !}\)
The probability that there are no errors for a page = P(X = 0)
= \(\frac{\mathrm{e}^{-8 / 9}\left(\frac{8}{9}\right)^0}{0 !}=\mathrm{e}^{-8 / 9}\)
The required probability that a random sample of 5 pages will contain no error
= P(X = 0) . P(X = 0) . P(X = 0) . P(X = 0) . P(X = 0)
= [P(X = 0)]5
= \(\left[\mathrm{e}^{-8 / 9}\right]^5\)

Question 12.
In a city 10 accidents take place in a span of 50 days. Assuming that the number of accidents for the Poisson distribution, find the probability that there will 5e 3 or more accidents In a day.
Solution:
X follows Poisson distribution.
Average of accidents take place for a day.
λ = \(\frac{10}{50}=\frac{1}{5}\) = 0.2
Let, X be the no. of accidents in a day.
Assume that X follows Poisson distribution with parameter λ = 0.2.
Now,
P(X = r) = \(\frac{e^{-\lambda} \lambda^r}{r !}\) for r = 0, 1, 2, …………
The probability of 3 or more accidents in a day = P (X ≥ 3)
P (X = 3) + P(X = 4) + …………………
= 1 – [P(X = 0) + P(X = 1) + P(X = 2)]
= 1 – \(\left[\frac{\mathrm{e}^{-0.2}(0.2)^0}{0 !}+\frac{\mathrm{e}^{-0.2}(0.2)^1}{1 !}+\frac{\mathrm{e}^{-0.2}}{} \frac{0.2)^2}{}\right]\)
= 1 – e-0.2 \(\left[1+\frac{0.2}{1}+\frac{0.04}{2}\right]\)
= 1 – e-0.2 [1 + 0.2 + 0.02]
= 1 – e-0.2 (1.22)

TS Inter 1st Year English Grammar Spelling: Missing Letters

Telangana TSBIE TS Inter 1st Year English Study Material Grammar Spelling: Missing Letters Exercise Questions and Answers.

TS Inter 1st Year English Grammar Spelling: Missing Letters

Q.No. 15 (8 × 1/2- 4 Marks)

English spelling poses problems to learners. This is because of a) no one letter-one sound relationship b) silent letters and c) words borrowed from other languages and so on.

Though there are some rules and generalizations that MAY HELP improve one’s spelling, it is always good to develop a keen eye to the spelling of the words one comes across and to practise writing words as many times as possible, that too correctly.

  • In the Intermediate Public Examination, usually the spelling of the words used in the selected lessons is tested.
  • The words that have vowel clusters (as in rec£jve, entertain etc.) or the words that have doubled consonants (as in possible, success etc.) are generally set in the question paper.
  • Careful observation of the spelling of commonly used but typically spelt words (like height, tuition etc.) will go a long way in helping the student improve spelling to a great extent.

Examples of some commonly misspelled words :
TS Inter 1st Year English Grammar Spelling Missing Letters 1
TS Inter 1st Year English Grammar Spelling Missing Letters 2

1. For adjectives that end in a consonant +y, ‘-y’ changes to ‘-ily’.
easy-easily
happy-happily
angry-angrily
Exceptions
shy-shyly
sly-slyly
coy-coyly

TS Inter 1st Year English Grammar Spelling: Missing Letters

2. For adjectives that end in a consonant +le the ‘-le’ changes to ‘-ly’ after the consonant,
probable-probably
sensible-sensibly
idle-idly
noble-nobly
For adjectives that end in – ic, we add -ally.
tragic-tragically
automatic-automatically
Exception
public-publicly
The doubling of final consonants.
When a one syllable word ends with one vowel and consonant we double the final consonant before adding a suffix that begins with a vowel.
bat-batting
dub-dubbing
sad-sadder
dig-digger
travel-travelled
confer-conferred

3. Spelling of regular verbs.
The past tense and past participle are the same in regular verbs.
i) We simply add – ed to the base form of the verb.
clear-cleared
walk-walked
visit-visited

ii) If the word ends in -e, we add -d.
like-liked
smile-smiled
hope-hoped

iii) For verbs ending in y preceded by two consonants, we change y to i before adding the suffix – ed.
hurry-hurried
reply-replied
try-tried

iv) For the verbs that end in a consonant, the final consonant is doubled when a suffix with an initial vowel letter is added.
rob-robbed
mop-mopped
drop-dropped

TS Inter 1st Year English Grammar Spelling: Missing Letters

4. For ‘ie’ and ‘ei’
The general rule is that ‘i’ comes before ‘e’.
chief
grief
relieve
But after ‘c’ ‘e’ comes before ‘i’.
receive
conceit
deceive
Note the exceptions
neighbour
weight
eight
weigh
seize
height

Here is a list of commonly misspelled words.

TS Inter 1st Year English Grammar Spelling Missing Letters 3
TS Inter 1st Year English Grammar Spelling Missing Letters 4

TS Inter 1st Year English Grammar Spelling: Missing Letters

Exercise – A

Fill in the blanks with either “ei” or “ie”

1. n _ _ ther
2. br _ _ f
3. sh _ _ ld
4. cr _ _ d
5. tr _ _ d
6. fr _ _ nd
7. th _ _ f
8. gr _ _ f
9. l _ _ sure
10. c _ _ ling
11. s _ _ ze
Answer:
1. n e i ther
2. br i e f
3. sh o u ld
4. cr e e d / cr i e d
5. tr i e d
6. fr i e nd
7. th i e f
8. gr i e f
9. l e i sure
10. c e i ling
11. s e i ze

TS Inter 1st Year English Grammar Spelling: Missing Letters

Exercise – B

Correct the following misspelled words.

1. foregn
2. lugage
3. liesure
4. knowlege
5. twelth
6. tomorow
7. gurantee
8. momonto
9. ilegal
10. restaurent
Answer:
1. foreign
2. luggage
3. leisure
4. knowledge
5. twelfth
6. tomorrow
7. guarantee
8. memento
9. illegal
10. restaurant

TS Inter 1st Year English Grammar Spelling: Missing Letters

Exercise – C

1. Please ……………………….. (wait / weight) for me.
2. I went to market to ……………………….. (buy / bye) a toothbrush.
3. He may not ……………………….. (loose / lose) the match.
4. When Chief Justice came to our state, people from different walks of life went to ……………………….. (meat / meet) him.
5. Ahmad cut the paper into many a ……………………….. (piece / peace).
6. The letters on the board cannot be ……………………….. (scene / seen) clearly.
7. – My friend has a ……………………….. (stationery / stationary) shop.
8. It was a pretty ……………………….. (sight / cite).
Answer:
1. wait
2. buy
3. lose
4. meet
5. piece
6. seen
7. stationery
8. sight

TS Inter 1st Year English Grammar Spelling: Missing Letters

Supply the missing letters in the following words.

Exercise – 1

i) sch _ _ l
ii) enc _ _ raging
iii) app _ _ rance
iv) exce _ _ ent
v) sp _ _ k
vi) a _ _ ention
vii) p _ _ pie
viii) kno _ _ edge
ix) di _ _ ipline
x) a _ _ ord
Answers
i) sch o o l
ii) enc o u raging
iii) app e q rance
iv) exe l l ent
v) sp e a k
vi) a t t ention
vii) p e o ple
viii) kno w l edge
ix) di s c ipline
x) a f f ord

TS Inter 1st Year English Grammar Spelling: Missing Letters

Exercise – 2

i) tea _ _ er
ii) gl _ _ my
iii) le _ _ on
iv) re _ _ect
v) f _ _ thful
vi) infl _ _ nce
vii) le _ _ ers
viii) pl _ _ sant
ix) su _ _ est
x) si _ _ le
Answer:
i) tea c h er
ii) gl o o my
iii) le s s on
iv) re s p ect
v) f a i thful
vi) infl u e nce
vii) le a d ers
viii) pl e a sant
ix) su g g est
x) si m p le

Exercise – 3

i) childh _ _ d
ii) p _ _ ce
iii) frus _ _ ation
iv) ha _ _ en
v) gra _ _ ar
vi) col _ _ r
vii) ang _ _ sh
viii) li _ _ten
ix) obed _ _ nt
x) mu _ _ le
Answer:
i) child o o d
ii) p i e ce
iii) frs t r ation
iv) ha p p en
v) gra m m ar
vi) col o u r
vii) ang u i sh
viii) li g h ten
ix) obed i e nt
x) mu s c le

TS Inter 1st Year English Grammar Spelling: Missing Letters

Exercise – 4

i) g _ _de
ii) ma _ _ er
iii) mar _ _ es
iv) fi _ _ ing
v) ye _ _ow
vi) h _ _ lithly
vii) sq _ _ re
viii) lau _ _ed
ix) su _ _ect
x) hi _ _ly
Answer:
i) g u i de
ii) ma n n er/ ma t t er/ ma d d er/ma p p er
iii) mar b l es / mar c h es
iv) fi b b ing
v) ye l l ow
vi) h e a lthy
vii) sq u a re
viii) lau g h ed
ix) su s p ect
x) hi g h ly

TS Inter 1st Year English Grammar Spelling: Missing Letters

Exercise – 5

i) hi _ _ top
ii) ba _ _ an
iiii) r _ _ tine
iv) conc _ _ ve
v) m _ _ ntain
vi) mi _ _ ion
vii) in _ _ edible
viii) mons _ _ n
ix) ca _ _ y
x) reco _ _ ition
Answer:
i) hi l l top
ii) ba n y an
iii) r o u tine
iv) con e i ve
v) m o u ntain
vi) mi s s ion / mi l l ion
vii) in c r edible
viii) mons o o n
ix) ca r r y
x) reco g n ition

Exercise – 6

i) sa _ _ ling
ii) rup _ _ s
iii) hu _ _ and
iv) res _ _ rces
v) s _ _ rce
vi) su _ _ icient
vii) ma _ _ ive
viii) vi _ _ age
ix) init _ _ tive
x) a _ _ roval
Answer:
i) sa p p ling
ii) rup e e s
iii) hu s b and
iv) res o u rces
v) s o u rce
vi) su f f icient
viii) ma s s ive
ix) init i a tive
x) a p p roval

TS Inter 1st Year English Grammar Spelling: Missing Letters

Exercise – 7

i) pers _ _ de
ii) flu _ _ er
iii) p _ _ nce
iv) ex _ _ ode
v) a _ _ empt
vi) br _ _th
vii) hu _ _ red
viii) pa _ _ ive
ix) co _ _ apse
x) thr _ _ ten
Answer:
i) per u a de
ii) flu t t er
iii) p o u nce
iv) ex p l ode
v) a t t empt
vi) br e a th
vii) hu n d red
viii) pa s s ive
ix) co l l apse
x) thr e a ten

 

Exercise – 8

i) thr _ _ gh
ii) sli _ _ tly
iii) gr _ _ nd
iv) wo _ _ y
v) sp _ _ d
vi) ang _ _ sh
vii) prev _ _ us
viii) mi _ _ t
ix) rec _ _ ve
x) p _ _ ce
Answer:
i) thr o u gh
ii) sli g h tly
iii) gr o u nd
iv) wo r r y
v) sp e e d
vi) ang u i sh
vii) prev i o us
viii) mi g h t
ix) rec e i ve
x) p i e ce / p e a ce

TS Inter 1st Year English Grammar Spelling: Missing Letters

Exercise – 9

i) cro _ _ ed
ii) em _ _ atic
iii) tr _ _ ble
iv) consc _ _ us
v) pl _ _ sant
vi) dr _ _ dful
vii) chi _ _ ey
viii) pu _ _ le
ix) incr _ _ se
x) de _ _ ive / de _ _ ive
Answer:
i) cro p p ed / cro w n ed
ii) em p h atic
iii) tr o u ble
iv) cons i o us
v) pl e a sant
vi) dr e a dful
vii) chi m n ey
viii) pu z z le
ix) incr e a se
x) de p r ive / de c e ive

TS Inter 1st Year English Grammar Spelling: Missing Letters

Exercise – 10

i) app _ _ r
ii) wo _ _ le
iii) tre _ _le
iv) con _ _ ary
v) cr _ _ m
vi) com _ _ ain
vii) f _ _ lt
viii) req _ _ st
ix) enc _ _ nter
x) acq _ _ int
Answer:
i) app e a r
ii) wo b b le
iii) tre m b le
iv) con t r ary
v) cr e a m
vi) com p l ain
vii) f a u lt
viii) req u e st
ix) enc o u nter
x) acq u a int

TS Inter 2nd Year Commerce Study Material Telangana | TS Intermediate 2nd Year Commerce Textbook Solutions Pdf

Here you will find Telangana TSBIE State Board Syllabus TS Inter 2nd Year Commerce Study Material Pdf free download, TS Intermediate 2nd Year Commerce Textbook Solutions Questions and Answers in English Medium and Telugu Medium according to the latest exam curriculum. The chapter-wise TS Inter 2nd Year Study Material will help the students in understanding the concept behind each question in a detailed way.

Students can check the TS Inter 2nd Year Commerce Syllabus & TS Inter 2nd Year Commerce Important Questions for strong academic preparation. Students can use TS Inter 2nd Year Commerce Notes as a quick revision before the exam.

TS Intermediate 2nd Year Commerce Study Material Pdf Download | TS Inter 2nd Year Commerce Textbook Solutions Telangana

TS Inter 2nd Year Commerce Study Material in Telugu Medium

TS Inter 2nd Year Commerce Study Material in English Medium

We hope this TS Intermediate 2nd Year Commerce Study Material Pdf Download in English Medium and Telugu Medium will be useful for students to attain the right approach for precisely answering the textbook questions. If there is any trouble in grasping the concepts related to TS Inter 2nd Year Commerce Textbook Solutions Telangana, drop your questions in the comment and we will get back to you with a solution in time.

TS Inter 2nd Year Accountancy Study Material Chapter 5 Admission of a Partner

Telangana TSBIE TS Inter 2nd Year Accountancy Study Material 5th Lesson Admission of a Partner Textbook Questions and Answers.

TS Inter 2nd Year Accountancy Study Material 5th Lesson Admission of a Partner

Very Short Answer Questions

Question 1.
What are the aspects which require attention when a new partner is admitted?
Answer:
The following Adjustments are to be made in the books of accounts at the time of admission of a new partner. They are:

  1. Calculation of new profit sharing ratio.
  2. Revaluation of assets and liabilities.
  3. Accounting treatment of goodwill.
  4. Distribution of reserves and undistributed profits/losses.
  5. Adjustment of capital in proportion to profit sharing ratio.

Question 2.
What is a Revaluation account?
Answer:
An account prepared with the specific purpose of recording changes in the value of assets and liabilities of a partnership firm. It is called a Revaluation account.

TS Inter 2nd Year Accountancy Study Material Chapter 5 Admission of a Partner

Question 3.
Why Revaluation account is prepared?
Answer:

  1. When the new partner is admitted, it becomes necessary to revalue the assets and liabilities of the firm in order to ascertain and record their true values.
  2. The revaluation account is prepared to see that the new partner should not be benefitted or suffered from any appreciation or depreciation in the value of assets and liabilities.

Question 4.
What is goodwill?
Answer:

  1. Goodwill is the reputation or good name associated with the name of firm.
  2. Goodwill is an intangible asset. It is the force of attracting customers. It helps to earn more profits than the normal profits in feature.
  3. Firm which have goodwill will enjoy continuous patronage of customers.

Question 5.
State the essential features of goodwill.
Answer:
Features of goodwill:

  • It is an intangible asset.
  • It is inseparable from the business. It exists with the business. It cannot be separated and sold like other tangible assets.
  • It helps in generating more profits than normal profits.

Question 6.
What is Ratio of sacrifice?
Answer:

  1. The ratio in which old partners agree to sacrifice their share of profits in favour of the incoming new partner is called Ratio of Sacrifice.
  2. Ratio of sacrifice can be get by deducting new profit-sharing ratio from old profit-sharing ratio.
    Ratio of sacrifice = Old profit sharing Ratio – New profit sharing Ratio.

Question 7.
X and Y are partners sharing profits and losses in the ratio of 3: 2. They decided to admit Mr. Z for 1/5 share in profit. Calculate new profit-sharing ratio of X, Y and Z.
Answer:
Old ratio of X and Y = 3: 2
Assume total profit = 1
Share of Z = 1/5
TS Inter 2nd Year Accountancy Study Material Chapter 5 Admission of a Partner 1
The remaining profit is 1 – 1/5 = 4/5 will be given to X and Y in their old profit-sharing ratio

Question 8.
Ram and Rahim are partners sharing profits and losses in the ratio of 5: 3. They decided to admit Robert by giving him a 2,8th share in the profits. Calculate new profit-sharing ratio.
Answer:
Old ratio of Ram and Rahim 5 : 3
Assume total profit = 1
Share of Robert 2/8 th
TS Inter 2nd Year Accountancy Study Material Chapter 5 Admission of a Partner 2

TS Inter 2nd Year Accountancy Study Material Chapter 5 Admission of a Partner

Question 9.
A and B are partners sharing profits and losses equally. They decided to admit Krishna for 1/5th share of profit in the business. Calculate New profit-sharing ratio of A, B & C.
Answer:
Old ratio of A and B is 1 : 1
Assume total profit = 1
Krishna share (given) = 1/5
TS Inter 2nd Year Accountancy Study Material Chapter 5 Admission of a Partner 3
= 4 : 4 : 2
= 2 : 2 : 1.

Question 10.
Radha and Rani share profits in the ratio of 4: 3. Mamatha admitted into business for l/8th share in the future profits. Calculate new profit-sharing ratio.
Answer:
Old ratio of Radha and Rani = 4 : 3
Give share to Mamatha 1/8 th
Total profits assumed ‘1’
TS Inter 2nd Year Accountancy Study Material Chapter 5 Admission of a Partner 4

Question 11.
X and Y are partners sharing profits & losses in the ratio of 3/5 and 2/5 respectively. They decided to admit Mr. Z for 3/7th share in profits, which he takes 2/7th share from X and 1/7th share from Y. Calculate New profit sharing ratio.
Answer:
Profit sharing ratio of X and Y = 3/5 : 2/5
Give to Z = 3/7th
New Profit shares ratio = Old profit sharing ratio – Share profit given to new partner
TS Inter 2nd Year Accountancy Study Material Chapter 5 Admission of a Partner 5

Question 12.
A and B are partners sharing profits and losses in the ratio of 5: 3 respectively. Mr. C is admitted for 3/8th share of profit, which he takes 2/8th from Mr. A and 1/8th from Mr. B. Calculate new profit sharing ratio.
Answer:
Old ratio of A and B = 5/8 : 3/8
C’s New share 3/8th
New Profit shares ratio = Old profit sharing ratio – Share profit given to new partner
TS Inter 2nd Year Accountancy Study Material Chapter 5 Admission of a Partner 6

Question 13.
Akbar and Anthony are partners sharing profits and losses in the ratio of 3 : 2 respectively. Mr. Amar is admitted into partnership. The new profit sharing ratio of Akbar, Anthony and Amar is 5 : 3 : 2 respectively. Calculate Ratio of sacrifice of old partners.
Answer:
Akbar and Anthony old ratio = 3:2
Akbar and Anthony old ratio = 3:2
Ratio of Akbar, Anthony and Amar is 5: 3: 2
Sacrifice of old partners = Old ratio – New ratio
TS Inter 2nd Year Accountancy Study Material Chapter 5 Admission of a Partner 7
Ratio of sacrifice 1 : 1.

Question 14.
Sitha and Geetha are partners sharing profits and losses in the ratio of 4: 3 respectively. Kavitha joined as new partner. The new profit sharing ratio of Sitha, Geetha and Kavitha is 7: 4: 3. Calculate Ratio of sacrifice of Sitha and Geetha.
Answer:
Sitha and Geetha profit sharing ratio = 4:3
Sitha, Geetha, Kavitha New profit sharing ratio = 7 : 4 : 3
Sacrifies Raju = Old ratio – New ratio
TS Inter 2nd Year Accountancy Study Material Chapter 5 Admission of a Partner 8
Ratio of sacrifice Sitha and Geetha = 1 : 2.

Question 15.
Give journal entry when goodwill is brought in cash.
Answer:
Journal Entry
TS Inter 2nd Year Accountancy Study Material Chapter 5 Admission of a Partner 9

Question 16.
Give journal entry when general reserve is distributed to old partners.
Answer:
Journal Entry
TS Inter 2nd Year Accountancy Study Material Chapter 5 Admission of a Partner 10

Question 17.
Give journal entry for distribution of undistributed profit among old partners.
Answer:
Journal Entry
TS Inter 2nd Year Accountancy Study Material Chapter 5 Admission of a Partner 11

Question 18.
Give journal entry when goodwill is created/raised in the books.
Answer:
Journal Entry
TS Inter 2nd Year Accountancy Study Material Chapter 5 Admission of a Partner 12

Question 19.
Give journal entry when goodwill is written off in the books.
Answer:
Journal Entry
TS Inter 2nd Year Accountancy Study Material Chapter 5 Admission of a Partner 13

Question 20.
X and Y are partners sharing profits and losses in the ratio of 2: 3 respectively. They admitted Mr. Z into partnership for l/4th share. For the purpose of admission of Mr. Z, Goodwill is valued at 3 years purchase of average profits of last 5 years. The profits of last 5 years were X 30,000, Rs. 40,000, Rs. 35,000, Rs. 45,000 and Rs. 50,000 respectively. Calculate the value of Goodwill.
Answer:
TS Inter 2nd Year Accountancy Study Material Chapter 5 Admission of a Partner 14
Goodwill = Average profit x Purchase of 3 years
= 40,000 x 3
Goodwill = Rs. 1,20,000.

TS Inter 2nd Year Accountancy Study Material Chapter 5 Admission of a Partner

Question 21.
A and B are partners sharing profits and losses in the ratio of 5: 3 respectively. They admitted Mr. C into the partnership on 31-3-2020. On that date General Reserve a/c showing a credit balance of Rs. 16,000 and P & L a/c showing a credit balance t 24,000. Give necessary Journal entries.
Answer:
Journal Entries
TS Inter 2nd Year Accountancy Study Material Chapter 5 Admission of a Partner 15
TS Inter 2nd Year Accountancy Study Material Chapter 5 Admission of a Partner 16

Question 22.
Ram and Ravan are in partnership sharing profits and losses in the ratio of 4: 3. They admitted, Vibhishana for 1/4 share in profits, Vibhishana brings Rs. 40,000 for capital and Rs. 28,000 for goodwill in cash. Goodwill is retained in the business. Give necessary journal entries.
Answer:
Journal Entries
TS Inter 2nd Year Accountancy Study Material Chapter 5 Admission of a Partner 17

Question 23.
A and B are partners sharing profits and losses in the ratio of 3: 2 respectively. They admitted Mr. C as new partner. He brings Rs. 40,000 as goodwill in cash. The goodwill is withdrawn by A and B from the business. Give necessary Journal entries.
Answer:
Journal Entries
TS Inter 2nd Year Accountancy Study Material Chapter 5 Admission of a Partner 18
TS Inter 2nd Year Accountancy Study Material Chapter 5 Admission of a Partner 19

Question 24.
Ram and Sitha are in partnership sharing profits and losses in the ratio of 5: 3. They admitted Laxman as new partner for 1/5 share of profit. The Goodwill of the firm is valued at Rs. 80,000. Pass necessary Journal entry to raise goodwill.
Answer:
Journal Entries
TS Inter 2nd Year Accountancy Study Material Chapter 5 Admission of a Partner 20

Question 25.
Saritha and Kavitha are sharing profits and losses equally. They admitted Lalitha as new partner. Their new profit sharing ratio would be 2: 2: 1 respectively. The goodwill of the firm is valued at Rs. 1,00,000. The partners decided to create and write off goodwill completely. Pass necessary Journal entries.
Answer:
Journal Entries
TS Inter 2nd Year Accountancy Study Material Chapter 5 Admission of a Partner 21

Textual Problems

Question 1.
The following was the Waianae sneer oi Jttam ana nanim, who were sharing profits and losses in the ratio of 2: 3. Their balance sheet as on 31 March 2019 was as under.
On 1st April 2019, they agreed to admit Mr. Peter as new partner for l/5th share in profits on the following terms:
(a) Peter should bring Rs. 40,000 for capital and Rs. 20,000 for goodwill in cash.
(b) Depreciates furniture by 5% and stock by 10%.
(c) Appreciate building value by 15%.
(d) Provide for bad debts at 5% on debtors.
Give necessary journal entries and ledger accounts and opening the balance sheet of new firm.
Answer:
Journal Entries
TS Inter 2nd Year Accountancy Study Material Chapter 5 Admission of a Partner 22
TS Inter 2nd Year Accountancy Study Material Chapter 5 Admission of a Partner 23
TS Inter 2nd Year Accountancy Study Material Chapter 5 Admission of a Partner 24
TS Inter 2nd Year Accountancy Study Material Chapter 5 Admission of a Partner 25
TS Inter 2nd Year Accountancy Study Material Chapter 5 Admission of a Partner 26
TS Inter 2nd Year Accountancy Study Material Chapter 5 Admission of a Partner 27

Balance sheet of Ram, Rahim, Peter as on 01-04-2019
TS Inter 2nd Year Accountancy Study Material Chapter 5 Admission of a Partner 28

Question 2.
Amar and Akbar are partners sharing profits and losses in the ratio of 4: 3 respectively. Their balance sheet as on 31 March 2020 was as under.
TS Inter 2nd Year Accountancy Study Material Chapter 5 Admission of a Partner 29
On the above date, Anthony was admitted into partnership for 1/4 share in the future profits on the following conditions:
(a) Anthony should bringRs. 35,000 towards capital andRs. 28,000 towards goodwill in cash.
(b) Land to be valued atRs. 20,000.
(c) Machinery valued atRs. 23,000.
(d) Stock be depreciated by 10%.
(e) Provide for bad debtsRs. 1,300.
Pass necessary journal entries, ledger accounts and give balance sheet of new firm.
Answer:
Journal Entries
TS Inter 2nd Year Accountancy Study Material Chapter 5 Admission of a Partner 30
TS Inter 2nd Year Accountancy Study Material Chapter 5 Admission of a Partner 31
TS Inter 2nd Year Accountancy Study Material Chapter 5 Admission of a Partner 32
TS Inter 2nd Year Accountancy Study Material Chapter 5 Admission of a Partner 33
Amar, Akbar, Anthony Balance Sheet as on 31.03.2020.
TS Inter 2nd Year Accountancy Study Material Chapter 5 Admission of a Partner 34

TS Inter 2nd Year Accountancy Study Material Chapter 5 Admission of a Partner

Question 3.
Naresh and Ramesh are partners in a firm sharing profits and losses in the ratio of 2: 1. Their balance sheet as on 31 March 2019 was as under.
TS Inter 2nd Year Accountancy Study Material Chapter 5 Admission of a Partner 35
On 1st April 2019, Suresh was admitted into partnership for 1/6th share in the profits of the business. The terms of admission are:
(a) Suresh should bring Rs. 30,000 as his capital.
(b) Stock be depreciated by 5%.
(c) Machinery was valued at Rs. 50,000.
(d) Provide for bad debts @ 8% on debtors.
(e) Bill payable need not be paid Rs. 2,000.
(f) Suresh should pay Rs. 15,000 to Naresh and Ramesh as goodwill privately.
Give journal entries, necessary ledger accounts and balance sheet of new firm.
[Hints: Provision for bad debtsRs. 1,680 i.e., 21,000 x 8/100. Provision already existing is Rs. 1,000. So Rs. 680 to be debited to Revaluation a/c for provision. Deduction from debtors in balance sheetRs. 1,680 as provision.]
Answer:
Journal Entries
TS Inter 2nd Year Accountancy Study Material Chapter 5 Admission of a Partner 36
TS Inter 2nd Year Accountancy Study Material Chapter 5 Admission of a Partner 37
TS Inter 2nd Year Accountancy Study Material Chapter 5 Admission of a Partner 38
TS Inter 2nd Year Accountancy Study Material Chapter 5 Admission of a Partner 39
Balance Sheet as on 1-04-2019
TS Inter 2nd Year Accountancy Study Material Chapter 5 Admission of a Partner 40

Question 4.
Raju and Rao are partners sharing profits and losses in the ratio of 3: 2. Their balance sheet as on 31 March 2020 was as under.
TS Inter 2nd Year Accountancy Study Material Chapter 5 Admission of a Partner 41
They decided to admit Mr. Reddy into partnership by giving him l/4th share in future profits of the firm the following conditions:
(a) Reddy is to bring ^ 2,50,000 as capital andRs. 1,00,000 as goodwill in cash.
(b) Stock and Furniture to be depreciated by 10%.
(c) Make a provision of 5% on Sundry debtors.
(d) Land & Buildings are to be appreciated by 20%.
Prepare necessary ledger accounts and show the new balance sheet.
Answer:
TS Inter 2nd Year Accountancy Study Material Chapter 5 Admission of a Partner 42
TS Inter 2nd Year Accountancy Study Material Chapter 5 Admission of a Partner 43
Balance Sheet of Raju, Rao & Reddy as on 31-3-2020
TS Inter 2nd Year Accountancy Study Material Chapter 5 Admission of a Partner 44

Question 5.
Mr. X and Y are partners sharing profits and losses in the ratio of 4: 1. Their balance sheet as on 31 March 2020 was as under.
TS Inter 2nd Year Accountancy Study Material Chapter 5 Admission of a Partner 45
They agreed to take Mr. Z into partnership with effect from 1st April 2020 on the following terms:
(a) Mr. Z brings Rs. 40,000 towards goodwill and Rs. 60,000 as capital.
(b) The assets are revalued as under:
Furniture — Rs. 50,000
Stock — Rs. 78,000
Debtors — Rs. 58,000.
(c) The goodwill will be retained in the business.
Prepare necessary ledger accounts and prepare balance sheet of new firm.
Answer:
TS Inter 2nd Year Accountancy Study Material Chapter 5 Admission of a Partner 46
TS Inter 2nd Year Accountancy Study Material Chapter 5 Admission of a Partner 47
Balance Sheet of X, Y, Z as on 31-3-2020
TS Inter 2nd Year Accountancy Study Material Chapter 5 Admission of a Partner 48

Question 6.
Vasu and Dasu are partners sharing profits and losses equally. Their balance sheet as on 31 March 2020 was as under:
TS Inter 2nd Year Accountancy Study Material Chapter 5 Admission of a Partner 49
They decided to admit Mr. Sonu from 1st April 2020 on the following conditions:
(a) Sonu has to pay Rs. 1,25,000 as capital for 1/4th share in future profits.
(b) Sonu shall pay Rs. 30,000 as Goodwill.
(c) Machinery be depreciated by 10%.
(d) Buildings to be appreciated by 20%.
(e) Provide for bad debts @ 6% on debtors.
Pass necessary journal entries to give effect to the above and give opening balance sheet of Vasu, Dasu and Sonu.
Answer:
Journal Entries
TS Inter 2nd Year Accountancy Study Material Chapter 5 Admission of a Partner 50
TS Inter 2nd Year Accountancy Study Material Chapter 5 Admission of a Partner 51
TS Inter 2nd Year Accountancy Study Material Chapter 5 Admission of a Partner 52
TS Inter 2nd Year Accountancy Study Material Chapter 5 Admission of a Partner 53
Balance Sheet of Vasu, Dasu & Sonu as on 1-04-2020
TS Inter 2nd Year Accountancy Study Material Chapter 5 Admission of a Partner 54

TS Inter 2nd Year Accountancy Study Material Chapter 5 Admission of a Partner

Question 7.
Ganesh and Sankar are the partners sharing profits and losses in the ratio of 3: 2 respectively. Their balance sheet as on 31 March 2020 was as under:
TS Inter 2nd Year Accountancy Study Material Chapter 5 Admission of a Partner 55
On 1st .April 2020, they decided to admit Mr. Balu, for 1/4 share in the future profits. The conditions of admission are:
(a) Balu should bring Rs. 75,000 as capital and Rs. 40,000 as goodwill.
(b) The amount of goodwill is withdrawn from the business by old partners.
(c) Buildings be appreciated by 20%.
(d) Furniture and stock to be depreciated by 5%.
(e) There is an unrecorded liability in respect of workmen compensation Rs. 3,000.
Give journal entries, necessary ledger accounts and balance sheet of new firm.
Answer:
Journal Entries
TS Inter 2nd Year Accountancy Study Material Chapter 5 Admission of a Partner 56
TS Inter 2nd Year Accountancy Study Material Chapter 5 Admission of a Partner 57
TS Inter 2nd Year Accountancy Study Material Chapter 5 Admission of a Partner 58
TS Inter 2nd Year Accountancy Study Material Chapter 5 Admission of a Partner 59
TS Inter 2nd Year Accountancy Study Material Chapter 5 Admission of a Partner 60

Question 8.
Ganga and Yamuna are partners sharing profits and losses in the ratio of 3: 2 respectively. Their balance sheet as on 31st March 2020 was as follows.
TS Inter 2nd Year Accountancy Study Material Chapter 5 Admission of a Partner 61
On the above date they decided to admit Saraswathi for 2/9“ share in profits of business. The conditions of admission are:
(a) Saraswathi should bringRs. 50,000 as capital andRs. 20,000 as goodwill.
(b) Land & Buildings be appreciated by 20%.
(c) Furniture be depreciated by 5% and stock by 10%.
(d) There is an unrecorded Investments valued atRs. 3,000 to be brought into books.
(e) Goodwill be retained in the business. New profit sharing of Ganga, Yamuna and Saraswathi is 4: 3: 2.
Give journal entries, Ledger accounts and Balance sheet of Ganga, Yamuna and Saraswathi.
[Hint: Ratio of sacrifice between Ganga and Yamuna is 7: 3 GoodwillRs. 20,000 distributed accordingly i.e.,Rs. 14,000 andRs. 6,000 Unrecorded InvestmentsRs. 3,000 credited to Revaluation a/c and appear on assets side of New Balance Sheet.]
Answer:
Journal Entries
TS Inter 2nd Year Accountancy Study Material Chapter 5 Admission of a Partner 62
TS Inter 2nd Year Accountancy Study Material Chapter 5 Admission of a Partner 63
TS Inter 2nd Year Accountancy Study Material Chapter 5 Admission of a Partner 64

Working Notes:
Old ratio = 3 : 2,
New ratio = 4 : 3 : 2
Sacrificing ratio:
Ganga = Old ratio – New ratio
TS Inter 2nd Year Accountancy Study Material Chapter 5 Admission of a Partner 65
TS Inter 2nd Year Accountancy Study Material Chapter 5 Admission of a Partner 66
TS Inter 2nd Year Accountancy Study Material Chapter 5 Admission of a Partner 67
Balance Sheet of Ganga, Yamuna, Saraswathi as on 31-03-2020
TS Inter 2nd Year Accountancy Study Material Chapter 5 Admission of a Partner 68

Question 9.
P and Q are partners sharing profits and losses equally. Their balance sheet as on 31 March 2020 was as under.
TS Inter 2nd Year Accountancy Study Material Chapter 5 Admission of a Partner 69
On the above date Mr. R was admitted into partnership for 2/9th share in future profits of the firm. The following are the terms of admission:
(a) R should bring Rs. 40,000 as capital andRs. 16,000 as goodwill.
(b) Half of their share of goodwill will be withdrawn from the business by the old partners.
(c) Provide for bad debts @ 5% on Trade debtors.
(d) Buildings are valued at Rs. 50,000.
(e) The new profit-sharing ratio of P, Q and R would be 4: 3: 2 respectively.
Give journal entries and opening balance sheet of P, Q and R.
[Hints: Ratio of sacrifice between P & Q is 1: 3. Goodwill Rs. 16,000 shared by P & Q i.e., Rs. 4,000 and Rs. 12,000. Goodwill withdrew by Rs. 2,000 and Q Rs. 6,000 in cash]
Answer:
Journal Entries
TS Inter 2nd Year Accountancy Study Material Chapter 5 Admission of a Partner 70
TS Inter 2nd Year Accountancy Study Material Chapter 5 Admission of a Partner 71
Working Note:
Old ratio = 1 : 1,
New ratio = 4 : 3 : 2
Sacrificing ratio = Old ratio – New ratio
TS Inter 2nd Year Accountancy Study Material Chapter 5 Admission of a Partner 72
TS Inter 2nd Year Accountancy Study Material Chapter 5 Admission of a Partner 73
TS Inter 2nd Year Accountancy Study Material Chapter 5 Admission of a Partner 74

Balance Sheet as on 31-03-2020
TS Inter 2nd Year Accountancy Study Material Chapter 5 Admission of a Partner 75

TS Inter 2nd Year Accountancy Study Material Chapter 5 Admission of a Partner

Question 10.
Vani and Rani are partners sharing profits and losses in the ratio of 1: 2 respectively. Their balance sheet as on 31 March 2020 was given below:
TS Inter 2nd Year Accountancy Study Material Chapter 5 Admission of a Partner 76

On 1st April 2020, they admitted Mani as partner for 1/4th share in the profits of the firm. The conditions of admission are as under:
(a) Mani should bring Rs. 30,000 as capital and Rs. 21,000 as goodwill in cash.
(b) The assets are valued as follows:
Machinery Rs. 47,000; Buildings Rs. 25,000 Stock Rs. 38,000.
(c) Goodwill is to be retained in the business.
(d) The new profit-sharing ratio of Vani, Rani and Mani would be 1: 2: 1 respectively. Give necessary ledger accounts and opening balance sheet.
[Hint: Ratio of sacrifice between Vani and Rani is 1: 2 respectively and Goodwill Rs. 21,000 shared accordingly i.e., Rs. 7,000 & Rs. 14,000]
Answer:
Working Note: Old Ratio =1:2,
New Ratio =1:2:1
Sacrificing ratio = Old ratio – New ratio
TS Inter 2nd Year Accountancy Study Material Chapter 5 Admission of a Partner 77
Balance Sheet of Vani, Rani & Mani as on 1-4-2020
TS Inter 2nd Year Accountancy Study Material Chapter 5 Admission of a Partner 78
TS Inter 2nd Year Accountancy Study Material Chapter 5 Admission of a Partner 79
Balance Sheet of Vani and Rani & Mani as on 1-4-2020
TS Inter 2nd Year Accountancy Study Material Chapter 5 Admission of a Partner 80

Problems on Creation of Goodwill

Question 11.
Vani and Sarada are partners sharing profits and losses equally. Their balance sheet was as under as on 31 March 2020.
TS Inter 2nd Year Accountancy Study Material Chapter 5 Admission of a Partner 81
On the above date Neeraja was admitted for 1/4th share in future profits on the following conditions.
(a) Neeraja should bring Rs. 50,000 as capital.
(b) Goodwill of business valued at Rs. 40,000.
(c) Stock revalued at Rs. 58,000 and Building at Rs. 40,000.
(d) Creditors increased by Rs. 3,000.
Give journal entries, necessary ledger accounts and balance sheet of new firm.
Answer:
Journal Entries
TS Inter 2nd Year Accountancy Study Material Chapter 5 Admission of a Partner 82
TS Inter 2nd Year Accountancy Study Material Chapter 5 Admission of a Partner 83
TS Inter 2nd Year Accountancy Study Material Chapter 5 Admission of a Partner 84
TS Inter 2nd Year Accountancy Study Material Chapter 5 Admission of a Partner 85
New Balance Sheet as on 31-3-2020
TS Inter 2nd Year Accountancy Study Material Chapter 5 Admission of a Partner 86

Question 12.
A and B are partners sharing profits and losses in the ratio of 3: 2 respectively. Their balance sheet as on 31 March 2020 was as follows.
TS Inter 2nd Year Accountancy Study Material Chapter 5 Admission of a Partner 87
Mr. C was admitted into business on the above date for 1/5 profit in the business on the following terms.
(a) C should bring Rs. 60,000 as capital.
(b) Goodwill of the firm valued at Rs. 40,000.
(c) Plant and Machinery to be depreciated by 5%.
(d) Create a provision for Bad Debts @ 5% on Debtors.
(e) Buildings valued at Rs. 40,000.
Give journal entries and opening balance sheet of A, B and C.
[Hint: Goodwill to be created is Rs. 30,000, Goodwill already exists in books at Rs. 10,000. Goodwill now appears at Rs. 40,000 in New Balance Sheet]
Answer:
Journal Entries
TS Inter 2nd Year Accountancy Study Material Chapter 5 Admission of a Partner 88
TS Inter 2nd Year Accountancy Study Material Chapter 5 Admission of a Partner 89
Note: Goodwill to be created is 40,000 – 10,000 = 30,000
Goodwill already in the balance sheet 1 10,000. Goodwill now appears atRs. 40,000 in new Balance Sheet.
TS Inter 2nd Year Accountancy Study Material Chapter 5 Admission of a Partner 90
TS Inter 2nd Year Accountancy Study Material Chapter 5 Admission of a Partner 91
TS Inter 2nd Year Accountancy Study Material Chapter 5 Admission of a Partner 92

Question 13.
Praveen and Naveen are partners sharing profits and losses in the ratio of 3: 1 respectively. Their balance sheet as on 31st March 2020 was as follows.
TS Inter 2nd Year Accountancy Study Material Chapter 5 Admission of a Partner 93
They decided to admit Kiran into partnership on the following conditions.
(a) Kiran has to bring Rs. 25,000 as capital for 1/5th share in profits.
(b) Machinery and furniture to be depreciated by 10%.
(c) Buildings to be appreciated by 20% and stock by 10%.
(d) Goodwill of the firm valued at Rs. 20,000.
(e) Create a provision for bad debts at 5% on Trade Debtors.
Show necessary accounts and balance sheet of new firm.
Answer:
TS Inter 2nd Year Accountancy Study Material Chapter 5 Admission of a Partner 94
TS Inter 2nd Year Accountancy Study Material Chapter 5 Admission of a Partner 95
New Balance Sheet as on 1-4-2020
TS Inter 2nd Year Accountancy Study Material Chapter 5 Admission of a Partner 96

TS Inter 2nd Year Accountancy Study Material Chapter 5 Admission of a Partner

Question 14.
X and Y are partners sharing profits and losses in the ratio of their capitals. Their balance sheet as on 31 March 2019 was as under.
TS Inter 2nd Year Accountancy Study Material Chapter 5 Admission of a Partner 97
They admitted Z as new partner for 1/3rd share in the profits. The conditions of admission are:
(a) Z should bring t 20,000 as capital.
(b) Stock valued at t 11,000 and Land at Rs. 30,000.
(c) Depreciate furniture by 5%.
(d) Provide for bad debts @ 5% on debtors.
(e) Goodwill of the firm is valued at 2 years purchase of average profit of last 3 years. The profit for last 3 years was Rs. 5,000,1 11,000 and t 8,000. Prepare necessary ledger accounts and balance sheet of X, Y and Z.
Answer:
X, Y profit sharing Ratio = 30,000: 20,000 = 3:2
TS Inter 2nd Year Accountancy Study Material Chapter 5 Admission of a Partner 98
Working Notes:
TS Inter 2nd Year Accountancy Study Material Chapter 5 Admission of a Partner 99
Goodwill = Average profit x purchase of 2 years
= 8,000 x 2
= 16,000.

Goodwill created and written off:

Question 15.
Naidu and Shekar are partners sharing profits and losses in the ratio of 3: 2. Their balance sheet as on 31 March 2020 was as follows.
TS Inter 2nd Year Accountancy Study Material Chapter 5 Admission of a Partner 100
On the above date, Harish was admitted into partnership for 1/6 share in profits. The terms of admission are:
(a) Harish should bring Rs. 2,00,000 as capital.
(b) Stock appreciate by Rs. 20,000.
(c) Machinery depreciate by Rs. 26,000.
(d) Outstanding expenses Rs. 10,000 not required.
(e) Goodwill of the firm valued at Rs. 60,000. This is to be written off immediately.
(f) New profit sharing ratio of Naidu, Shekar and Harish is 3: 2: 1 respectively. Prepare necessary Ledger accounts and Balance sheet of new firm.
[Hint: Goodwill a/c will not appear in New Balance Sheet as it is written off]
Answer:
TS Inter 2nd Year Accountancy Study Material Chapter 5 Admission of a Partner 101
TS Inter 2nd Year Accountancy Study Material Chapter 5 Admission of a Partner 102
Balance Sheet of Ram, Rahim, Harish as on 31-03-2020
TS Inter 2nd Year Accountancy Study Material Chapter 5 Admission of a Partner 103

Problems on Capital Adjustments:

Question 16.
Rajesh and Ramesh are partners sharing profits and losses in the ratio of 3: 1. Their Balance sheet as on 31 March 2020 was as under.
TS Inter 2nd Year Accountancy Study Material Chapter 5 Admission of a Partner 104
They decided to take Mr. Suresh into partnership for 1/5th share in future profits. The conditions of admission are as follows.
(a) Suresh should bring Rs. 20,000 as his capital in cash.
(b) Depreciate furniture and stock by 10%.
(c) Land & Buildings are to be appreciated by 20%.
(d) Goodwill of the firm valued at Rs. 8,000.
(e) Create a provision for bad debts @ 5% on Debtors.
(f) Capital accounts of the partners to be adjusted in cash on the basis of their new profits sharing ratio.
Answer:
TS Inter 2nd Year Accountancy Study Material Chapter 5 Admission of a Partner 105
TS Inter 2nd Year Accountancy Study Material Chapter 5 Admission of a Partner 106

Working Notes:
Calculation of New profit sharing ratio.
Old ratio = 3:1
TS Inter 2nd Year Accountancy Study Material Chapter 5 Admission of a Partner 107
TS Inter 2nd Year Accountancy Study Material Chapter 5 Admission of a Partner 108

Question 17.
X and Y are partners sharing profits and losses in the ratio of 3: 2 respectively. Their balance sheet as on 31 March 2015 was as under.
TS Inter 2nd Year Accountancy Study Material Chapter 5 Admission of a Partner 109
TS Inter 2nd Year Accountancy Study Material Chapter 5 Admission of a Partner 110
On the above date Mr. Z is admitted into the partnership for 1/5th share in profits. The conditions of admission are as follows.
(a) Z should bring Rs. 40,000 as capital and Rs. 10,000 for goodwill in cash.
(b) Appreciate buildings by Rs. 10,000.
(c) Depreciate machinery by Rs. 8,000 and furniture by Rs. 2,000.
(d) New profit sharing ratio of X, Y and Z is 12: 8: 5 respectively.
(e) Capital accounts of partners to be adjusted in cash on the basis of new profit-sharing ratio. Give necessary ledger accounts and balance sheet of X, Y, Z.
Answer:
Working Notes:
New ratio of X: Y: Z = 12 : 8 : 5
TS Inter 2nd Year Accountancy Study Material Chapter 5 Admission of a Partner 111
TS Inter 2nd Year Accountancy Study Material Chapter 5 Admission of a Partner 112
TS Inter 2nd Year Accountancy Study Material Chapter 5 Admission of a Partner 113
TS Inter 2nd Year Accountancy Study Material Chapter 5 Admission of a Partner 114

Balance Sheet of X, Y, Z as on 31-3-2020
TS Inter 2nd Year Accountancy Study Material Chapter 5 Admission of a Partner 115

TS Inter 2nd Year Accountancy Study Material Chapter 5 Admission of a Partner

Textual Examples

Question 1.
A and B are partners sharing profits and losses in the ratio of 3: 2. They admitted Mr. C. into partnership firm for l/5th share in future profits. Calculate new profit-sharing ratio of A, B and C.
Answer:
Total profit of the business is 1 out of this 1/5 share given to Mr. C. Remaining profit is 4/5 (i.e., 1-1/5). The remaining profit of 4/5th will be given to Mr. A and B in their old profit sharing ratio, i.e., 3: 2 respectively.
New profit sharing ratio of existing partners = Remaining Profit Share x Old Profit Sharing Ratio.
TS Inter 2nd Year Accountancy Study Material Chapter 5 Admission of a Partner 116
So, new profit sharing ratio of A, B and C is 12: 8: 5 respectively, (or) 12/25 : 8/25 : 5/25

(Note: It is to be understood that the 1/5 share given to new partner C is contributed/ sacrificed by A & B in their old profit sharing ratio, i.e., 3: 2. Even we calculate the ratio of sacrifice by A and B it will be same i.e., 3: 2 respectively.
The ratio of sacrifice = Old profit sharing ratio – New profit sharing ratio).

Question 2.
X and Y are partners sharing profits and losses in the ratio of 2 : 3. They agreed to adimit Z into partnership for l/5,h share in profits. Z’s entire share is given by Mr. Y alone. Calculate new profit sharing ratio.
Answer:
X and Ys old profit sharing ratio is 2: 3
Z gets 1/5th share in profit from Mr. Y
X share of profit remain unchanged.

Calculation of new profit sharing ratio:
New profit sharing ratio of Mr. Y = Old profit sharing ratio – Profit given to Z
TS Inter 2nd Year Accountancy Study Material Chapter 5 Admission of a Partner 117
New profit sharing ratio of Mr. X = 2/5
New profit sharing ratio of Mr. Z (given) = 1/5

Thus the new profit sharing ratio of X, Y and Z are 2 : 2 : 1 i.e., 2/5, 2/5, 1/5 respectively.

Question 3.
A and B are partners sharing profits and losses in the ratio of 3: 2. Mr. C is admitted into partnership business for 1/5th share, Mr. C purchases his share as to 2/25 th from A and 3/25 from B. Calculate new profit sharing ratio of A, B and C.
Answer:
New profit sharing ratio = Old profit sharing ratio – Share of profit given to new partner.
TS Inter 2nd Year Accountancy Study Material Chapter 5 Admission of a Partner 118

Question 4.
Ram and Robert are partners sharing profits and losses in the ratio of 7: 3. Rahim admitted as new partner. Ram and Robert decided to surrender in favour of Rahim 1/ 7 and 1/3 of their share respectively.
Calculate New Profit sharing Ratio of the partners.
Answer:
Old profit sharing ratio of Ram and Robert = 7 : 3 (or) 7/10 and 3/10 respectively.
Ram gives/surrenders 1/7th in his share of profit.
Robert surrenders 1/3rd of his share of profit.
Sacrificing ratio to Ram and Robert are
TS Inter 2nd Year Accountancy Study Material Chapter 5 Admission of a Partner 119
New profit sharing ratio or Ram, Robert and Rahim is 6/10 : 2/10 : 2/10 or 6: 2: 2 (or) 3:1:1.

Question 5.
P and Q are partners sharing profits and losses in the ratio of 9: 7. They agreed to admit R into partnership who gets 1/8th share equally from P and Q. Calculate new profit sharing ratio of P, Q and R.
Answer:
TS Inter 2nd Year Accountancy Study Material Chapter 5 Admission of a Partner 120
Now, the new profit sharing ratio of P, Q and R is 8: 6: 2 (or) 8/16: 6/16: 2/16 respectively.

Question 6.
Ganga and Yamuna are partners sharing profits and losses in the ratio of 3: 2. They admitted Saraswathi as new partner. Hereafter, they share profits and losses in the ratio of 4: 3: 2 by Ganga, Yamuna and Saraswathi respectively. Calculate the ratio of sacrifice.
Answer:
The old profit sharing ratio of Ganga and Yamuna is
3:2 (or) 3/5 : 2/5
The new profit sharing ratio of Ganga, Yamuna and Saraswathi is 4: 3: 2 respectively.
Ratio of sacrifice = Old ratio – New ratio
TS Inter 2nd Year Accountancy Study Material Chapter 5 Admission of a Partner 121
The ratio of sacrifice between Ganga and Yamuna is 7: 3 respectively. It means loss to old partners Ganga and Yamuna and is a gain new partner Saraswathi i.e., TS Inter 2nd Year Accountancy Study Material Chapter 5 Admission of a Partner 122
[Note: Ratio of sacrifice is to be calculated, when both old profit sharing ratio and new profit sharing ratio of all the partners, including new partner, are given in the problem. Otherwise, no need to calculate the ratio of sacrifice. Because, it is assumed that old partners sacrifice in their respective old profit sharing ratio.]

Question 7.
A and B are partners sharing profits and losses in the ratio of 7: 3. Following was the balance sheet as on 31 March, 2020.
TS Inter 2nd Year Accountancy Study Material Chapter 5 Admission of a Partner 123
On the above date the assets and liabilities are to be revalued as under:
(a) Depreciate Machinery by 10%.
(b) Stock to be depreciated by 5%.
(c) Create a provision for bad debts at 5% on debtors.
(d) The value of buildings to be appreciated by 20%.
(e) Creditors are to be increased byRs. 1,000.
Give necessary journal entries to record the changes in the value of assets & liabilities and Prepare the Revaluation account and Partners capital accounts.
Answer:
Journal Entries in the Books of A and B
TS Inter 2nd Year Accountancy Study Material Chapter 5 Admission of a Partner 124
TS Inter 2nd Year Accountancy Study Material Chapter 5 Admission of a Partner 125
TS Inter 2nd Year Accountancy Study Material Chapter 5 Admission of a Partner 126
TS Inter 2nd Year Accountancy Study Material Chapter 5 Admission of a Partner 127

Question 8.
Ram and Rahim are partners sharing profits and losses in the ratio of 2: 1 respectively. Their balance sheet as on 31 March 2020 stands as follows.
TS Inter 2nd Year Accountancy Study Material Chapter 5 Admission of a Partner 128
They agreed to admit Joseph into partnership for 1/4th share in the profits on 1st April 2020. Give necessary entries for distribution of Reserves and surpluses and draw new balance sheet.
Answer:
Journal Entries in the Books of Ram and Rahim
TS Inter 2nd Year Accountancy Study Material Chapter 5 Admission of a Partner 129
TS Inter 2nd Year Accountancy Study Material Chapter 5 Admission of a Partner 130
TS Inter 2nd Year Accountancy Study Material Chapter 5 Admission of a Partner 131
Balance Sheet of Ram, Rahim and Joseph as on 01-04-2020
TS Inter 2nd Year Accountancy Study Material Chapter 5 Admission of a Partner 132

Question 9.
The Net profit of a firm for last four years was Rs. 40,000, Rs. 38,000, Rs. 50,000 and Rs. 52,000 respectively. The goodwill is to be taken as 2 years purchase of average profits of last four years. Calculate the value of Goodwill.
Answer:
TS Inter 2nd Year Accountancy Study Material Chapter 5 Admission of a Partner 133
Goodwill = Average profit x 2 years = 45,000 x 2 =Rs. 90,000.

Question 10.
The normal of rate of return on the capital employed (Investment) in the industry is 20%. The investment/or capital employed in the firm isRs. 2,00,000. Actual average profit of the firm isRs. 60,000. Goodwill of the firm is valued at 4 years purchase of super profit. Calculate the value of goodwill.
Answer:
Capital employed = Rs. 2,00,000
Rate of return/profit on capital employed = 20%
Actual average profit = 7 60,000
Normal profit/retum = Capital employed x Return on capital employed.
Normal profit/return =Rs. 2,00,000 x 20/100 = Rs. 40,000
Super profit = Actual average profit – Normal profit on capital employed.
Super profit =Rs. 60,000 -Rs. 40,000
Super profit =Rs. 20,000
Goodwill = Super profit x 4 years purchase of super profit.
Goodwill = Rs. 20,000 x 4 years =Rs. 80,000.

Question 11.
Average profits of a firm areRs. 20,000, the normal rate of return expected on capital from similar business is 10%. The actual capital employed/or net tangible assets of the business isRs. 1,50,000. Calculate the value of goodwill as per capitalisation of average profit method.
Answer:
TS Inter 2nd Year Accountancy Study Material Chapter 5 Admission of a Partner 134
Actual capital employed/Net assets (given) = Rs. 1,50,000
Goodwill = Capitalised value of business – Actual capital employed / or Net tangible assets.
= Rs. 2,00,000 – Rs. 1,50,000
Goodwill = Rs. 50,000.
Notes: To earn a profit of Rs. 20,000 at 10% return on capital, the amount of capital required is Rs. 2,00,000 i.e., 20,000 x 100/10 = Rs. 2,00,000. But, this firm is actually earning a profit of Rs. 20,000 with an investment of Rs. 1,50,000. So, the firm is efficient and has goodwill.

Question 12.
Average profit of a firm is Rs. 18,000. Normal profit is Rs. 12,000. Normal rate of return is 12%. Calculate Goodwill.
Answer:
TS Inter 2nd Year Accountancy Study Material Chapter 5 Admission of a Partner 136
Super profit = Average profit – Normal profit
= Rs. 18,000 – Rs. 12,000 = Rs. 6,000
Goodwill = Rs. 6,000 x 100/2 = Rs. 50,000.

Question 13.
A and B are partners sharing profits and losses in the ratio of 2: 3 respectively. They admitted Mangal as new partner for 1/5th share in profits. He brings in 7 30,000 towards goodwill in cash. The share of profit of Ramu and Somu remains same as earlier. Give Journal Entries.
Answer:
Journal Entries
TS Inter 2nd Year Accountancy Study Material Chapter 5 Admission of a Partner 137

TS Inter 2nd Year Accountancy Study Material Chapter 5 Admission of a Partner

Question 14.
X and Y are partners sharing profits in the ratio of 3: 1 respectively. They decided to admit Mr. Z as new partner for 1/4 share in profits given by X and Y in their old profit sharing ratio. Mr. Z brings inRs. 16,000 towards goodwill. X and Y withdraw their entire share of goodwill from the business. Give Journal entries.
Answer:
Journal Entries
TS Inter 2nd Year Accountancy Study Material Chapter 5 Admission of a Partner 138
Note: The above last two entries may be combined.

Question 15.
A & B are partners sharing profits and losses in the ratio of 3: 2 respectively. They admitted C into partnership for l/4th share in profits foFwhich Mr. C brings inRs. 30,000 towards his share of goodwill. The old partners withdrew half of their share of goodwill from the business. Here after, they share profits and losses in the ratio of 2:1:1 among A, B and C respectively . Give journal entries.
Answer:
Calculation of Ratio of sacrifice.
Ratio of sacrifice = Old profit sharing ratio – New profit sharing ratio.
TS Inter 2nd Year Accountancy Study Material Chapter 5 Admission of a Partner 139

Therefore, goodwill brought in by new partner shared by A and B in their respective share of sacrifice ratio i.e., 2: 3.
Journal Entries
TS Inter 2nd Year Accountancy Study Material Chapter 5 Admission of a Partner 140
TS Inter 2nd Year Accountancy Study Material Chapter 5 Admission of a Partner 141

Question 16.
P and Q are partners sharing profits and losses in the ratio of 2: 1. They admitted Mr. R into partnership for 1/5th share in future profits. For the purpose of admission, the value of goodwill agreed at Rs. 60.000. Give Journal entries.
Answer:
TS Inter 2nd Year Accountancy Study Material Chapter 5 Admission of a Partner 142
Note: When goodwill is created, the value of goodwill appears on assets side of the balance sheet of new firm.

Question 17.
A and B are partners sharing profits and losses in the ratio of 3: 2. They decided to admit Mr. C into partnership for 1/5 share in the profit. Mr. C is unable to bring goodwill in cash, it is decided to create goodwill and writeoff immediately. The new profit sharing ratio of A, B and C is 2: 2: 1 respectively. The value of goodwill is Rs. 60,000. Give necessary Journal entries.
Answer:
Journal Entries
TS Inter 2nd Year Accountancy Study Material Chapter 5 Admission of a Partner 143

Question 18.
Ram and Rahim are partners sharing profits and losses in the ratio of 2: 1 respectively. They admitted Robert as a new partner for 1/4th share in profit. He brings in Rs. 40,000 towards his capital. Give Journal entry.
Answer:
Journal Entry
TS Inter 2nd Year Accountancy Study Material Chapter 5 Admission of a Partner 144

Question 19.
A and B are partners sharing profits and losses in the ratio of 3: 2 respectively. They admitted Mr. C into partnership for 1/5th share in profits, for which he has to contributeRs. 20,000 for his share of capital. The capital accounts of A and B stood atRs. 45,000 andRs. 30,000 respectively on that date. As per the partnership agreement, the partners capital is to be adjusted in accordance with their new profit sharing ratio. The new profit sharing ratio of A, B and C is 2: 2: 1 respectively. Excess or deficiency of capital of old partners be adjusted in cash. Give Journal entries.
Answer:
Calculation of total capital of the firm:
For C’s 1/5 share of profit, the capital is Rs. 20,000
Total capital =Rs. 20,000 x 5/1 =Rs. 1,00,000
This total capitals is to be contributed by all the partners in their new profit sharing ratio. Capital to be contributed by:
TS Inter 2nd Year Accountancy Study Material Chapter 5 Admission of a Partner 145

A’s capital balance is Rs. 45,000, but he has to contribute Rs. 40,000 towards capital. So he is having excess capital of Rs. 5,000. So Rs. 5,000 to be returned to A.
Incase of B capital to be contributed is Rs. 40,000, but his capital a/c balance is Rs. 30,000. He has to bring into business Rs. 10,000 in cash.

The entries are:
Journal Entries
TS Inter 2nd Year Accountancy Study Material Chapter 5 Admission of a Partner 146
Now, the following illustrations help in understanding accounting treatment of all issues/ transactions pertaining to admission of a new partner;

Question 20.
Ravi and Kiran are partners sharing profits and losses in the ratio of 3: 2 respectively. Their balance sheet as on 31 March 2020 was as follows.
TS Inter 2nd Year Accountancy Study Material Chapter 5 Admission of a Partner 147
On 1st April 2020, they decided to admit Mr. Bharath for 1/5th share in profits. The terms of admission are:
(a) He has to bring Rs. 20,000 towards capital and Rs. 10,000 towards goodwill in cash.
(b) Furniture is to be depreciated by Rs. 1,000.
(c) Create a provision on Rs. 1,500 for Bad Debts on Debtors.
(d) Appreciate the value of Buildings by Rs. 5,000.
Give necessary Journal entries, ledger accounts and opening balance sheet of new firm.
Answer:
Journal Entries
TS Inter 2nd Year Accountancy Study Material Chapter 5 Admission of a Partner 148
TS Inter 2nd Year Accountancy Study Material Chapter 5 Admission of a Partner 149
Ledger Accounts:
TS Inter 2nd Year Accountancy Study Material Chapter 5 Admission of a Partner 150
TS Inter 2nd Year Accountancy Study Material Chapter 5 Admission of a Partner 151
TS Inter 2nd Year Accountancy Study Material Chapter 5 Admission of a Partner 152
TS Inter 2nd Year Accountancy Study Material Chapter 5 Admission of a Partner 153
Balance Sheet of Ravi, Kiran and Bharath as on 1st April 2015
TS Inter 2nd Year Accountancy Study Material Chapter 5 Admission of a Partner 154

Note:

  1. We have to prepare all the accounts which are being effected. However, we cannot prepare all the accounts due to time factor, but important ledger accounts are to be prepared.
  2. Accounts showing debit balance will appear on Assets side and showing credit balance appear on Liabilities side.
  3. Provision for Bad Debts shows credit balance, it is a specific provision against debtors. Therefore, it is shown as deduction from Debtors.
  4. When Goodwill is brought in Cash, it is shared by old partners in their ratio of sacrifice.

TS Inter 2nd Year Accountancy Study Material Chapter 5 Admission of a Partner

Question 21.
Phani and Mani are partners sharing profits and losses in the ratio of 3: 2. Their balance sheet as on 31 March 2020 is as under.
TS Inter 2nd Year Accountancy Study Material Chapter 5 Admission of a Partner 155
On 1st April 2020 Mr. Krishna is admitted into the partnership for 1/5th share in profits. The terms and conditions are
(a) Krishna has to bring Rs. 30,000 towards capital andRs. 20,000 for his share of goodwill.
(b) Stock to be depreciated by 5%.
(c) Machinery to be reduced to Rs. 28,000.
(d) Sundry creditors increased by Rs. 2,000.
The new profit-sharing ratio of A, B and C in the new firm is 2: 2: 1 respectively.
Give necessary Journal entries and Ledger accounts and opening Balance sheet.
Answer:
Calculation of Ratio of sacrifice.
Ratio of sacrifice = Old profit sharing ratio – New profit sharing ratio.
TS Inter 2nd Year Accountancy Study Material Chapter 5 Admission of a Partner 156
On admission of Mr. Krishna as a new partner, Phani alone losing/sacrificing, hence the entire amount brought in by Krishna for goodwill to be given to Phani only.

Journal Entries
TS Inter 2nd Year Accountancy Study Material Chapter 5 Admission of a Partner 157
TS Inter 2nd Year Accountancy Study Material Chapter 5 Admission of a Partner 158
Ledger Accounts
TS Inter 2nd Year Accountancy Study Material Chapter 5 Admission of a Partner 159
TS Inter 2nd Year Accountancy Study Material Chapter 5 Admission of a Partner 160
TS Inter 2nd Year Accountancy Study Material Chapter 5 Admission of a Partner 161
TS Inter 2nd Year Accountancy Study Material Chapter 5 Admission of a Partner 162

Balance Sheet of Phani, Mani and Krishna as on 1st April 2020
TS Inter 2nd Year Accountancy Study Material Chapter 5 Admission of a Partner 163

Question 22.
X and Y are partners sharing profits and losses in the ratio of 4: 3. Their balance sheet as on 31 March 2020 stood as follows.
TS Inter 2nd Year Accountancy Study Material Chapter 5 Admission of a Partner 164
On 1st April 2020 Mr. Z is admitted into partnership for 1/5th share in future profits on the following terms.
(a) He has to bring Rs. 40,000 as capital Rs. 21,000 for goodwill.
(b) Stock to be reduced by 10% and machinery by Rs. 1,700.
(c) Create a provision for Bad Debts @ 5% on Debtors.
(d) There is an unrecorded liability in respect of rent due Rs. 1,000 and an unrecorded investments (asset) of Rs. 2,000. Both are to be brought into Books.
(e) Land is valued at Rs. 25,000.
(f) New profit sharing ratio of X, Y and Z will be 2: 2: 1 respectively.
Give necessary Journal entries and Ledger accounts and the opening balance sheet of new firm.
Answer:
Calculation of Ratio of sacrifice:
TS Inter 2nd Year Accountancy Study Material Chapter 5 Admission of a Partner 165
Ratio of sacrifice = Old profit sharing ratio – New profit sharing ratio.
The ratio of sacrifice of X and Y is 6: 1. Goodwill is to be distributed accordingly. Z gets
TS Inter 2nd Year Accountancy Study Material Chapter 5 Admission of a Partner 166
Journal Entries
TS Inter 2nd Year Accountancy Study Material Chapter 5 Admission of a Partner 167
TS Inter 2nd Year Accountancy Study Material Chapter 5 Admission of a Partner 168
TS Inter 2nd Year Accountancy Study Material Chapter 5 Admission of a Partner 169
Ledger Accounts:
TS Inter 2nd Year Accountancy Study Material Chapter 5 Admission of a Partner 170
TS Inter 2nd Year Accountancy Study Material Chapter 5 Admission of a Partner 171
TS Inter 2nd Year Accountancy Study Material Chapter 5 Admission of a Partner 172
Balance Sheet of X, Y and Z as on April 2020
TS Inter 2nd Year Accountancy Study Material Chapter 5 Admission of a Partner 173

Question 23.
Amar and Akbar are partners sharing profits and losses in the ratio of 3:1 respectively. The balance sheet of firm as on 31 March 2020 was as under.
TS Inter 2nd Year Accountancy Study Material Chapter 5 Admission of a Partner 174
On 1st April 2020, they admitted Mr. Anthony into partnership for 1/4th share in profits on the following conditions.
(a) Anthony was to bring Rs. 40,000 towards capital and Rs. 20,000 for goodwill.
(b) Amar and Akbar withdraw from business their share of goodwill.
(c) Stock and machinery to be depreciated by 10%.
(d) Buildings value to be appreciated by 25%.
Give Journal entries and necessary ledger accounts and show balance sheet of the new firm.
Answer:
Journal Entries
TS Inter 2nd Year Accountancy Study Material Chapter 5 Admission of a Partner 175
TS Inter 2nd Year Accountancy Study Material Chapter 5 Admission of a Partner 176
Ledger Accounts
TS Inter 2nd Year Accountancy Study Material Chapter 5 Admission of a Partner 177
TS Inter 2nd Year Accountancy Study Material Chapter 5 Admission of a Partner 178
Balance Sheet of Amar, Akbar and Anthony as on 1-4-2020
TS Inter 2nd Year Accountancy Study Material Chapter 5 Admission of a Partner 179

TS Inter 2nd Year Accountancy Study Material Chapter 5 Admission of a Partner

When Goodwill is created in the Books:

Question 24.
Sitha and Geetha are partners sharing profits and losses in the ratio of 2: 1 respectively. Their balance sheet as on 31st March 2020 was as under.
TS Inter 2nd Year Accountancy Study Material Chapter 5 Admission of a Partner 180
On 1st April 2020, they decided to admit Radha into partnership for 1/4th share in profits on the following terms.
(a) Radha should bring Rs. 20,000 towards capital.
(b) Goodwill account be raised in the books of the new firm at a value of Rs. 15,000.
(c) Trade creditors be reduced by Rs. 2,000.
(d) Buildings to be appreciated by Rs. 10,000.
Give Journal entries and necessary ledger accounts and balance sheet of new firm.
Answer:
Journal Entries
TS Inter 2nd Year Accountancy Study Material Chapter 5 Admission of a Partner 181
TS Inter 2nd Year Accountancy Study Material Chapter 5 Admission of a Partner 182
Ledger Accounts
TS Inter 2nd Year Accountancy Study Material Chapter 5 Admission of a Partner 183
TS Inter 2nd Year Accountancy Study Material Chapter 5 Admission of a Partner 184
Balance Sheet of Sitha, Geetha and Radha as on 1-4-2020
TS Inter 2nd Year Accountancy Study Material Chapter 5 Admission of a Partner 185
When Goodwill account created and writtenoff:

Question 25.
Ram and Shyam are partners sharing profits and losses in the ratio of 2: 3. Their balance sheet as on 31 March 2020 was given below.
TS Inter 2nd Year Accountancy Study Material Chapter 5 Admission of a Partner 186
On 1st April 2020, they admitted Mr. Madhav for 1/4th share in profits on the following conditions.
(a) Madhav should bring Rs. 20,000 towards capital in cash.
(b) Goodwill of the firm is valued atRs. 30,000 and it has been decided to create and write it off completely.
(c) Depreciate furniture by 5% and machinery by 10%.
(d) Appreciate the value of buildings by 20%.
(e) New profit-sharing ratio of Ram, Shyam & Madhav would be 1: 2: 1 respectively. Give Journal entries and necessary ledger accounts and balance sheet of new firm.
Answer:
Journal Entries
TS Inter 2nd Year Accountancy Study Material Chapter 5 Admission of a Partner 187
TS Inter 2nd Year Accountancy Study Material Chapter 5 Admission of a Partner 188
TS Inter 2nd Year Accountancy Study Material Chapter 5 Admission of a Partner 189
Ledger Accounts:
TS Inter 2nd Year Accountancy Study Material Chapter 5 Admission of a Partner 190
TS Inter 2nd Year Accountancy Study Material Chapter 5 Admission of a Partner 191
Balance Sheet of Ram, Shyam and Madhav as on 1-04-2020
TS Inter 2nd Year Accountancy Study Material Chapter 5 Admission of a Partner 192
When Goodwill is already existing in the books:

Question 26.
X and Y are partners sharing profits and losses in the ratio of 2: 1 respectively. Their balance sheet as on 31 March 2019 was given below.
TS Inter 2nd Year Accountancy Study Material Chapter 5 Admission of a Partner 193
On 1st April 2019, they decided to admit Mr. Z into partnership for 1/4th share in future profits on the following conditions.
(a) Z should bring Rs. 30,000 towards his capital.
(b) Goodwill of the firm is valued at Rs. 18,000 and decided to write it off immediately.
(c) Buildings to be appreciated by 10%.
(d) Create a provision for bad debts @ 8% on Debtors.
(e) Depreciate machinery by Rs. 5,000.
(f) New profit sharing ratio of X, Y and Z would be 2: 1: 1 respectively in the new firm. Give Journal entries and necessary ledger accounts and balance sheet of new firm.
Answer:
Journal Entries
TS Inter 2nd Year Accountancy Study Material Chapter 5 Admission of a Partner 194
TS Inter 2nd Year Accountancy Study Material Chapter 5 Admission of a Partner 195
TS Inter 2nd Year Accountancy Study Material Chapter 5 Admission of a Partner 196
Ledger Accounts:
TS Inter 2nd Year Accountancy Study Material Chapter 5 Admission of a Partner 197
TS Inter 2nd Year Accountancy Study Material Chapter 5 Admission of a Partner 198
TS Inter 2nd Year Accountancy Study Material Chapter 5 Admission of a Partner 199
TS Inter 2nd Year Accountancy Study Material Chapter 5 Admission of a Partner 200
Working Notes:
1. Provision for bad debts required isRs. 2,400 ie., 30,000 x 8/100. Provision already existing is Rs. 1,000. It requires additional Rs. 1,400 to make it Rs. 2,400. So additional provision required debited to revaluation a/c is Rs. 1,400.
2. Goodwill value of firm is Rs. 18,000. Goodwill already existing in the books was Rs. 6,000. So, Goodwill is to be created to the extent of Rs. 12,000 in order to make it Rs. 18,000. Hie full value of goodwill Rs. 18,000 writtenoff against all partners capital accounts in their new profit sharing ratio.

Question 27.
Hari and Giri are partners sharing profits and losses in the ratio of 3: 1 respectively. Their balance sheet as on 31-03-2020 was given below.
TS Inter 2nd Year Accountancy Study Material Chapter 5 Admission of a Partner 201
On 1st April 2015 Mr. Siva is admitted for 2/5th share in profits. The terms of admission are:
(a) Siva should bring Rs. 40,000 towards capital.
(b) Fixed assets are valued at Rs. 35,000.
(c) Goodwill of the firm valued at Rs. 25,000.
(d) Provision for bad debts required is Rs. 2,000.
Give Journal entries, Ledger accounts and opening balance sheet.
Answer:
Journal Entries
TS Inter 2nd Year Accountancy Study Material Chapter 5 Admission of a Partner 202
TS Inter 2nd Year Accountancy Study Material Chapter 5 Admission of a Partner 203
TS Inter 2nd Year Accountancy Study Material Chapter 5 Admission of a Partner 204
Ledger Accounts:
TS Inter 2nd Year Accountancy Study Material Chapter 5 Admission of a Partner 205
TS Inter 2nd Year Accountancy Study Material Chapter 5 Admission of a Partner 206
TS Inter 2nd Year Accountancy Study Material Chapter 5 Admission of a Partner 207
Balance Sheet of Hari, Giri and Siva as on 1-04-2020
TS Inter 2nd Year Accountancy Study Material Chapter 5 Admission of a Partner 208
Working Notes:
1. Provision for bad debts required isRs. 2,000, but the provision existing is Rs. 3,000, so, Rs. 1,000 is in excess, credited to revaluation.
2. Goodwill value reduced by Rs. 20,000 (45,000 – 25,000) debited to old partners capital a/cs in their old profits sharing ratio.

TS Inter 2nd Year Accountancy Study Material Chapter 5 Admission of a Partner

Adjustment of capitals based on New Profit sharing Ratio:

Question 28.
P and Q are partners sharing profits and losses in the ratio of 3: 2 respectively. Their balance sheet as on 31 March 2020 was as here under.
TS Inter 2nd Year Accountancy Study Material Chapter 5 Admission of a Partner 209
On 1st April 2020, Mr. R is admitted into partnership 1/3rd share in future profits on the following terms.
(a) R shall bring Rs. 50,000 towards capital andRs. 20,000 towards goodwill in cash.
(b) Depreciate machinery by t 5,000.
(c) Provide for bad debts @ 5% on Debtors.
(d) Appreciate the value of Buildings by 20%.
(e) Creditors to be reduced by Rs. 2,000.
P, Q and R will share the profits and losses equally. P and Q capitals are to be adjusted in cash based on R’s capital.
Give Journal entries and necessary ledger accounts and the balance sheet of new firm.
Answer:
Journal Entries
TS Inter 2nd Year Accountancy Study Material Chapter 5 Admission of a Partner 210
TS Inter 2nd Year Accountancy Study Material Chapter 5 Admission of a Partner 211
TS Inter 2nd Year Accountancy Study Material Chapter 5 Admission of a Partner 212
Ledger Accounts:
TS Inter 2nd Year Accountancy Study Material Chapter 5 Admission of a Partner 213
TS Inter 2nd Year Accountancy Study Material Chapter 5 Admission of a Partner 214
Balance Sheet of P, Q and R as on 1-04-2020
TS Inter 2nd Year Accountancy Study Material Chapter 5 Admission of a Partner 215

Working Notes:
1. Calculation of Ratio of sacrifice:
Ratio of sacrifice = Old Ratio – New Ratio
TS Inter 2nd Year Accountancy Study Material Chapter 5 Admission of a Partner 216
Ratio of sacrifice = 4:1
So, goodwill Rs. 20,000 transferred to P & Q’s capital accounts in their ratio of sacrifice.
TS Inter 2nd Year Accountancy Study Material Chapter 5 Admission of a Partner 217

2. Ascertainment of total capital of the firm:
For 1/3 share of profit capital =Rs. 50,000
TS Inter 2nd Year Accountancy Study Material Chapter 5 Admission of a Partner 218
P’s capital balance is Rs. 83,800 and required to contribute Rs. 50,000. He is having excess capital, so refunded Rs. 33,800 (83,800 – 50,000).
Q’s capital balance after all adjustments is Rs. 49,200 his share of capital for 1/3 share of profit is 7 50,000. There is a shortage Rs. 800 (50,000 – 49,200). So, he brings cash 7 800 to make his capital equal to Rs. 50,000.

TS Inter 1st Year English Grammar Silent Letters

Telangana TSBIE TS Inter 1st Year English Study Material Grammar Silent Letters Exercise Questions and Answers.

TS Inter 1st Year English Grammar Silent Letters

Q.No. 16 (8 × 1/2 = 4 Marks)

Silent letters are a peculiar feature of English spelling. Letters are used in writing but the corresponding sounds are not uttered in pronunciation. This poses problems to learners both in spelling and pronunciation. A study says that 60% of the English words have silent letters !

Careful observation of both the spelling and pronunciation is the only way out to overcome this problem. There are, however, some generalizations about silent letters that will help learners understand this feature to some extent.

In the Intermediate Public Examination, normally, the words that appear in the prescribed selections with a silent consonant letter are set under this question.

TS Inter 1st Year English Grammar Silent Letters

Some Guidelines :

  • ‘b’ before word final ‘t’ is silent – doubt debt.
  • ‘b’ in final ‘mb’ clusters is also silent.
    comb
    womb
    tomb
  • ‘g’ before word final ‘n’ is silent.
    sign
    resign
    foreign
    campaign
    reign
    sovereign
  • ‘g’ in most ‘ough’, ‘augh’ combinations is silent.
    (But in some words with ‘augh’ it may sound as /f/ as in ‘laughter),
    though
    taught
    through
    benign
    thorough
  • ‘h’ in word beginning position (not always) is silent.
    honest
    honour
  • ‘k’ in word beginning followed by ‘n’ is silent.
    knowledge
    know
    knit
    knee
    knave
    knuckle
  • ‘l’ before word final’m’ is silent.
    calm
    palm (but in realm and film – T is not silent)
  • Word final ‘n’ preceded by ‘m’ is silent,
    condemn
    column
    autumn
  • ‘p’ in word beginning position followed by ‘s’ is silent.
    psychology
    psalm
    pseudo
  • ‘p’ in words like receipt is also silent.
  • ‘r’ followed by a consonant letter is silent,
    world
    card
  • ‘f is silent in clusters like ‘astle’, ‘isten’, ‘istle’ as in
    castle
    whistle
    listen
  • ‘W’ is silent in words like
    Write
    wrap
    know
    fawn
    lawn

TS Inter 1st Year English Grammar Silent Letters

(These guiding principles are by no way exhaustive. They help the learner to a great extent in identifying the silent letters. About vowels – the problem is not this simple or unambiguous. So no generalisation is given here.)

TEXTUAL EXAMPLES

Silent letter – Example words

b – lamb, bomb, tomb, climb, dumb, subtle, plumber, womb, crumb, thumb
c – muscle, blackguard, yacht, indict, scene
d – Wednesday, handkerchief, handbag, handsome, adjourn, adjective, judge
g – gnaw, gnome, phlegm, foreign, resign, campaign, align, sovereign
h – honour, heir, ghost, night, rhyme, rhythm, when, where, hour
k – know, knee, knock, knot, kneel, knowledge
t – talk, folk, salmon, colonel, calf, calm, half, walk, baulk
m – mnemonic . . .
n – hymn, solemn, damn, autumn, column
p – recepit, psychic, pneumonia, psyche
q(u) – lacquer
r – girl, bird, card, teacher, leader, curd, world
s – isle, aisle, viscount, island
t – thistle, fasten, mortgage, soften, watch, tsunami
w – whole, sword, two, who, wrist, wrong
y – prayer, mayor
z – rendezvous
gh – sigh, high, daughter, naughty, caught, brought, bought, night, haughty

TS Inter 1st Year English Grammar Silent Letters

Exercise -1

I. Underline the silent letters in the following words.

1) knell
2) consign
3) thorough
4) yellow
5) often
6) delight
7) benign
8) almond
9) yolk
10) limb
11) pseudonym
12) cupboard
13) Indict
14) climb
15) half
16) bouquet
17) wreath
18) dumb
19) depot
20) answer
21) aisle
22) exhibition
23) night
24) condemn
25) pneumonia
26) design
27) christmas
28) reign
29) palm
30) debut

TS Inter 1st Year English Grammar Silent Letters

31) precis
32) whistle
33) poignant
34) knead
35) castle
36) subtle
37) feign
38) debt
39) knight
40) knack
41) debris
42) comb
43) succumb
44) fight
45) deign
46) chalk
47) folk
48) bustle
49) align
50) malign
51) honest
52) lodge
53) pawn
54) doubt
55) bridge
56) coup
57) rapport
58) ghost
59) through
60) listen
Answer:
1) knell
2) consign
3) thorough
4) yellow
5) often
6) delight
7) benign
8) almond
9) yolk
10) limb

TS Inter 1st Year English Grammar Silent Letters

11) pseudonym
12) cupboard
13) Indict
14) climb
15) half
16) bouquet
17) wreath
18) dumb
19) depot
20) answer
21) aisle
22) exhibition
23) night
24) condemn
25) pneumonia
26) design
27) christmas
28) reign
29) palm
30) debut
31) precis
32) whistle
33) poignant
34) knead
35) castle
36) subtle
37) feign
38) debt
39) knight
40) knack
41) debris
42) comb
43) succumb
44) fight
45) deign
46) chalk
47) folk
48) bustle
49) align

TS Inter 1st Year English Grammar Silent Letters

50) malign
51) honest
52) lodge
53) pawn
54) doubt
55) bridge
56) coup
57) rapport
58) ghost
59) through
60) listen

II. Identify the silent consonant letters in the following words.

Exercise – 1

i) bright
ii) scene
iii) hour
iv) neighbour
v) wrong
vi) knell
vii) wreath
viii) palm
ix) limb
x) design
Answer:
i) bright – gh
ii) scene – c
iii) hour – h – r
iv) neighbour – g, h, r
v) wrong – w
vi) knell – k
vii) wreath – w
viii) palm – l
ix) limb – b
x) design – g

TS Inter 1st Year English Grammar Silent Letters

Exercise – 2

i) chalk
ii) knock
iii) depot
iv) teacher
v) often
vi) thought
vii) honest
viii) almond
ix) know
x) talk
Answer:
i) chalk – 1
ii) knock – k
iii) depot – t
iv) teacher – r
v) often – t
vi) thought – gh
vii) honest – h
viii) almond – l
ix) know – k, w
x) talk – l

TS Inter 1st Year English Grammar Silent Letters

Exercise – 3

i) lodge
ii) castle
iii) feign
iv) laugh
v) debut
vi) malign
vii) talk
viii) psyche
ix) lighten
x) muscle
Answer:
i) lodge – d
ii) castle – l
iii) feign – g
iv) laugh – …
v) debut – t
vi) malign – g
vii) talk – l
viii) psyche – p
ix) lighten – gh
x) muscle – c

TS Inter 1st Year English Grammar Silent Letters

Exercise – 4

i) yolk
ii) would
iii) pneumonia
iv) consign
v) drawing
vi) what
vii) knead
viii) doubt
ix) island
x) aisle
Answer:
i) yolk – l
ii) would – l
iii) pneumonia – p
iv) consign – g
v) drawing – w
vi) what – h
vii) knead – k
viii) doubt – b
ix) island – s
x) aisle – s

TS Inter 1st Year English Grammar Silent Letters

Exercise – 5

i) thorough
ii) who
iii) benign
iv) receipt
v) rhythm
vi) diversity
vii) nursery
viii) column
ix) curd
x) kneel
Answer:
i) thorough – gh
ii) who – w
iii) benign – g
iv) receipt – p
v) rhythm – h
vi) diversity – r
vii) nursery – r
viii) column – n
ix) curd – r
x) kneel – k

TS Inter 1st Year English Grammar Silent Letters

Exercise – 6

i) bustle
ii) although
iii) parliament
iv) fight
v) knee
vi) brought
vii) bomb
viii) could
ix) hymn
x) which
Answers
i) bustle – t
ii) although – gh
iii) parliament – r, i
iv) fight – gh
v) knee – k
vi) brought – gh
vii) bomb – b
viii) could – l
ix) hymn – n
x) which – h

Exercise – 7

i) align
ii) ghost
iii) leader
iv) straight
v) calf
vi) plumber
vii) wrap
viii) thistle
ix) attempt
x) burden
Answer:
i) align – g
ii) ghost – h
iii) leader – r
iv) straight – gh
v) calf – l
vi) plumber – b, r
vii) wrap – w
viii) thistle – t
ix) attempt – t
x) burden – r

TS Inter 1st Year English Grammar Silent Letters

Exercise – 8

i) through
ii) sovereign
iii) slightly
iv) tsunami
v) watch
vi) tomb
vii) caught
viii) naughty
ix) half
x) leopard
Answer:
i) through – gh
ii) sovereign – g
iii) slightly – gh
iv) tsunami – t
v) watch – t
vi) tomb – b
vii) caught – gh
viii) naughty – gh
ix) half – l
x) leopard – o, r

Exercise – 9

i) wrist
ii) daughter
iii) receipt
iv) solemn
v) hatter
vi) mnemonic
vii) 4umb
viii) damn
ix) should
x) folk
Answer:
i) wrist – w
ii) daughter – gh
iii) receipt – p
iv) solemn – n
v) hatter – r
vi) mnemonic – m
vii) dumb – b
viii) damn – n
ix) should – l
x) folk – l

TS Inter 1st Year English Grammar Silent Letters

Exercise – 10

i) knock
ii) autumn
iii) cupboard
iv) tight
v) walk
vi) sword
vii) subtle
viii) psalm
ix) handsome
x) gnaw
Answer:
i) knock – k
ii) autumn – n
iii) cupboard – p
iv) tight – gh
v) walk – l
vi) sword – w, r
vii) subtle – b
viii) psalm – p, l
ix) handsome – d
x) gnaw – g, w

TS Inter 1st Year English Grammar Phonetic Transcription

Telangana TSBIE TS Inter 1st Year English Study Material Grammar Phonetic Transcription Exercise Questions and Answers.

TS Inter 1st Year English Grammar Phonetic Transcription

Q.No. 17 (4 × 1 = 4 Marks)

Meaningful speech sounds are the basic raw material for any language. These sounds are represented by symbols in writing. We refer to these symbols as ‘alphabet’.

Most of the Indian languages have a fixed relationship between the sounds and their symbols. In other words, one symbol always stands for one sound and vice versa. Therefore we find absolutely no problem while reading or writing Indian languages once we learn the alphabet of that language.

The same is not the case with English. One letter may stand for many sounds. Example Q as / k / in car, as / s / in century as /t/ in change. One sound is also represented by various letters. Ex : / f / is represented by ‘ph’ in philosophy, by ‘f in fan, by ‘gh’ in rough. This results in a lot of problems for the learners, particularly for foreign learners in writing the spelling and pronouncing the written words.

A way out of this problem is a set of forty four symbols, called phonetic symbols. Each of these symbols stands for one sourid only. Learning these symbols arms us with the necessary weapons to war against the problems in pronounciation and spelling.

Study the following forty four phonetic symbols carefully and learn to identify and use them. Phonetic symbols are always placed between two Slant lines.

Vowels

TS Inter 1st Year English Grammar Phonetic Transcription 1

Consonants

TS Inter 1st Year English Grammar Phonetic Transcription 2

Writing the symbols that represent the sounds in a word is called phonetic transcript. In many examinations phonetic transcription is given and the examinee is asked to write the spelling of those words.

TS Inter 1st Year English Grammar Phonetic Transcription

Exercises

Exercise – A

Read the words and fill in the spaces with the appropriate vowel symbol. The first one is done for you. If necessary, don’t hesitate to use a dictionary.
TS Inter 1st Year English Grammar Phonetic Transcription 3

Exercise – B

Read the words according to the vowel symbols mentioned.

/ɪ/ /i:/ /u/ /u:/ /ɒ/ /ɔ:/
bit beat wood wooed pot port
fit feet look fluke wad ward
rich reach should shoed cod cord
filled field soot suit don dawn

TS Inter 1st Year English Grammar Phonetic Transcription

Exercise – C

Go through the words and identify the sounds the end with. The first one is done for you.

Word /t/ /d/ /id/ Word /s/ /z/ /iz/
rounded /id/ rounds /z/
packed /t/ packs /s/
wished /t/ wishes /iz/
matched /t/ matches /iz/
flogged /d/ flogs /z/
played /d/ plays /z/
planted /id/ plants /s/
worked /t/ works /s/

Exercise-D

Read the following words. You will notice that in some words the letters ‘th’ are pronounced as /θ/ and in some others, as /ð/ and in some others, as 161. Write the sound you noticed. The first one is done for you.
the /ð/ this /ð/ through /θ/ then /ð/
thus /ð/ thought /θ/ thick /θ/ mother /ð/

Exercise – E

We get confused with the sounds /w/ and /v/. The sound /w/ is pronounced with rounded lips. The sound /v/ is pronounced with the articulation of front upper teeth and lower lip and with more force.
Now, pronounce the words aloud.
wheel   ventilator
worst    verse
wet      veto

TS Inter 1st Year English Grammar Phonetic Transcription

Exercise – F

Read the following transcriptions and write the words in ordinary spelling. The first one is done for you.
TS Inter 1st Year English Grammar Phonetic Transcription 4

Exercise – G

Pronounce the following words and transcribe them in the column my transcription Later, consult a dictionary and make necessary corrections.
TS Inter 1st Year English Grammar Phonetic Transcription 5

Exercise – H

Words with short vowels are entirely different from their long counterparts. Understanding the difference is vital for pronunciation. Read the words in the following table and write a few more words from your text.

/ɪ/ /i:/ /ɪ/ /i:/ /ɪ/ /i:/         ‘ /ɪ/ /i:/
knit neat hid heed rim ream bid bead
kill keel rid read lid lead din dean
sit seat kin keen bin bean/been fill feel
grit greet hit heat grid greed chit cheat

TS Inter 1st Year English Grammar Phonetic Transcription

Write the following transcriptions using ordinary English spelling.

Exercise – 1

TS Inter 1st Year English Grammar Phonetic Transcription 6
Answer:
i) purpose
ii) accomplish
iii) beautiful
iv) question
v) faith
vi) miserable

Exercise – 2

TS Inter 1st Year English Grammar Phonetic Transcription 7
Answer:
i) speak
ii) constantly
iii) attention
iv) unfortunate
v) want
vi) individual

Exercise – 3

TS Inter 1st Year English Grammar Phonetic Transcription 8
Answer:
i) transgression
ii) nervy
iii) harbinger
iv) recognize
v) strive
vi) pesticide

TS Inter 1st Year English Grammar Phonetic Transcription

Exercise – 4

TS Inter 1st Year English Grammar Phonetic Transcription 9
Answers
i) provide
ii) literate
iii) frustration
iv) imagination
v) fear
vi) adamant

Exercise – 5

TS Inter 1st Year English Grammar Phonetic Transcription 10
Answer:
i) stretch
ii) incredible
iii) plant
iv) condition
v) hospital
vi) entire

Exercise – 6

TS Inter 1st Year English Grammar Phonetic Transcription 11
Answer:
i) education
ii) husband
iii) pension
iv) recently
v) mountain
vi) close

TS Inter 1st Year English Grammar Phonetic Transcription

Exercise – 7

TS Inter 1st Year English Grammar Phonetic Transcription 12
Answer:
i) desperate
ii) lull
iii) impelled
iv) resistance
v) pride
vi) faint

Exercise – 8

TS Inter 1st Year English Grammar Phonetic Transcription 13
Answer:
i) success
ii) effort
iii) excitement
iv) worry
v) previous
vi) athletic

Exercise – 9

TS Inter 1st Year English Grammar Phonetic Transcription 14
Answer:
i) acquaint
ii) attic
iii) horizontal
iv) gridiron
v) curb
vi) vengeance

TS Inter 1st Year English Grammar Phonetic Transcription

Exercise – 10

TS Inter 1st Year English Grammar Phonetic Transcription 15
Answer:
i) emphatic
ii) appearance
iii) mention
iv) gentleman
v) tremble
vi) sleep