TS Inter 1st Year

Students must practice these Maths 1A Important Questions TS Inter 1st Year Maths 1A Matrices Important Questions Short Answer Type to help strengthen their preparations for exams.

TS Inter 1st Year Maths 1A Matrices Important Questions Short Answer Type

Question 1.
If A = \(\left[\begin{array}{cc}
\cos \theta & \sin \theta \\
-\sin \theta & \cos \theta
\end{array}\right]\), , then show that for all the positive integers n, Aⁿ = \(\left[\begin{array}{cc}
\cos \theta & \sin \theta \\
-\sin \theta & \cos \theta
\end{array}\right]\) [May 98, 91]
Answer:

∴ S(k + 1) is true.
∴ By the principle of mathematical induction, S(n) is true for all n ∈ N.
∴ Aⁿ = \(\left[\begin{array}{cc}
\cos n \theta & \sin n \theta \\
-\sin n \theta & \cos n \theta
\end{array}\right]\), ∀ n ∈ N.

Question 2.
If A = \(\left[\begin{array}{rrr}
1 & -2 & 1 \\
0 & 1 & -1 \\
3 & -1 & 1
\end{array}\right]\), then find A³ – 3A² – A – 3I, where I is unit matrix of order 3. [Mar. 19 (TS); Mar. 11, 98; May 98]
Answer:

Question 3.
If I = \(\left[\begin{array}{ll}
1 & 0 \\
0 & 1
\end{array}\right]\) and E = \(\left[\begin{array}{ll}
0 & 1 \\
0 & 0
\end{array}\right]\), then show that (aI + bE)³ = a³I + 3a²bE, where I is unit matrix of order 2. [Mar. 16 (TS), 15(AP), 10; May 05]
Answer:

Question 4.
If θ – Φ = \(\frac{\pi}{2}\), then show that \(\left[\begin{array}{cc}
\cos ^2 \theta & \cos \theta \sin \theta \\
\cos \theta \sin \theta & \sin ^2 \theta
\end{array}\right]\left[\begin{array}{cc}
\cos ^2 \phi & \cos \phi \sin \phi \\
\cos \phi \sin \phi & \sin ^2 \phi
\end{array}\right]\) = 0 [May 15 (TS); May 11, 09, 96; Mar. 04]
Answer:

Question 5.
If A = \(\left[\begin{array}{ll}
3 & -4 \\
1 & -1
\end{array}\right]\), then show that Aⁿ = \(\left[\begin{array}{cc}
1+2 n & -4 n \\
n & 1-2 n
\end{array}\right]\) for any integer n ≥ 1, by using mathematical induction. [May 08, 02]
Answer:

∴ S(k + 1) is true.
∴ By using the principle of mathematical Induction, S(n) is true for all n ∈ N.
∴ Aⁿ = \(\left[\begin{array}{cc}
1+2 n & -4 n \\
n & 1-2 n
\end{array}\right]\) ∀ n ∈ N.

Question 6.
For any n × n matrix A, prove that A can be uniquely expressed as a sum of a symmetric matrix and a skew symmetric matrix. (Mar. ‘03)
Answer:
Let A be a square matrix.

∴ A can be expressed as a sum of a symmetric matrix and a skew symmetric matrix.

Question 7.
Show that \(\left|\begin{array}{ccc}
\mathbf{1} & \mathbf{a} & \mathbf{a}^2 \\
\mathbf{1} & \mathbf{b} & \mathbf{b}^2 \\
\mathbf{1} & \mathbf{c} & \mathbf{c}^2
\end{array}\right|\) = (a – b) (b – c) (c – a). [Mar. 17 (TS). 05]
Answer:

= (a – b) (b – c) (c – a) [0(c² – c) – 1(0 – 1) + (a + b) (0 – 0)]
= (a – b) (b – c) (c – a) (1) = (a – b) (b – c) (c – a) = RHS

Question 8.
Show that \(\left|\begin{array}{lll}
b c & b+c & 1 \\
c a & c+a & 1 \\
a b & a+b & 1
\end{array}\right|\) = (a – b) (b – c) (c – a). [Board Paper]
Answer:

= (a – b) (c – a) [b (1 – 0) – 1 (c – 0) + 0 (ac + bc – ab)]
= (a – b) (c – a) [b – c] = (a – b) (b – c) (c – a) = R.H.S.

Question 9.
Show that \(\left|\begin{array}{ccc}
b+c & c+a & a+b \\
a+b & b+c & c+a \\
a & b & c
\end{array}\right|\) = a³ + b³ + c³ – 3abc. [May 13, 07; Mar. 08]
Answer:

= (a + b + c) [c² – bc – ac + ab + a² – 2ab + b²]
= (a + b + c) [a² + b² + c² – ab – bc – ca]
= a³ + b³ + c³ – 3abc

Question 10.
If \(\left|\begin{array}{ccc}
a & a^2 & 1+a^3 \\
b & b^2 & 1+b^3 \\
c & c^2 & 1+c^3
\end{array}\right|\) = 0 and \(\left|\begin{array}{lll}
a & a^2 & 1 \\
b & b^2 & 1 \\
c & c^2 & 1
\end{array}\right|\) ≠ 0 then show that abc = – 1. [Mar. 14, 04; May. 98, 95]
Answer:

Question 11.
Show that \(\left|\begin{array}{lll}
a-b & b-c & c-a \\
b-c & c-a & a-b \\
c-a & a-b & b-c
\end{array}\right|\) = 0. [May. 08]
Answer:

Question 12.
Let A and B be invertiable matrices then show that (AB)^-1 = B^-1 A^-1. [May. 03]
Answer:
A is invertible matrix then A^-1 exists and AA^-1 = A^-1 A = I
B is an invertible matrix then B^-1 exists and BB^-1 = B^-1B = I
Now (AB) (B^-1 A^-1) = A(BB^-1)A^-1 = A(T)A^-1 = AA^-1 = I
∴ (AB) (B^-1 A^-1) = I ………………… (1)
(B^-1 A^-1) (AB) = B^-1 (A^-1 A) B = B^-1 (I) B = B^-1 B = 1
∴ (B^-1 A^-1) (AB) = I ………………….. (2)
From (1) & (2)
(AB) (B^-1 A^-1) = (B^-1 A^-1) (AB) = I
AB is invertiable and (AB)^-1 = B^-1 A^-1.

Question 13.
Find the adjoint and the inverse of the matrix A = \(\left[\begin{array}{lll}
1 & 3 & 3 \\
1 & 4 & 3 \\
1 & 3 & 4
\end{array}\right]\) [May 14; Mar. 08]
Answer:
Given A = \(\left[\begin{array}{lll}
1 & 3 & 3 \\
1 & 4 & 3 \\
1 & 3 & 4
\end{array}\right]\)
Cofactor of 1 is A₁₁ = +(16 – 9) = 7
Cofactor of 3 is A₁₂ = – (4 – 3) = – 1
Cofactor of 3 is A₁₃ = (3 – 4) = – 1
Cofactor of 1 is B₁₁ = – (12 – 9) = -3
Cofactor of 4 is B₁₂ = (4 – 3) = 1
Cofactor of 3 is B₁₃ = – (3 – 3) = 0
Cofactor of 1 is C₁₁ = (9 – 12) = – 3
Cofactor of 3 is C₁₂ = – (3 – 3) = 0
Cot actor of 4 is C₁₃ = (4 – 3) = 1
∴ Cofactor matrix,

Now, det A = 1(16 – 9) – 3(4 – 3) + 3 (3 – 4)
= 1(7) – 3(1) + 3(- 1) = 7 – 3 – 3 = 1
Hence A is invertiable.
A^-1

Question 14.
Show that A = \(\left[\begin{array}{lll}
1 & 2 & 1 \\
3 & 2 & 3 \\
1 & 1 & 2
\end{array}\right]\) is non-singular and find A^-1. [Mar. 17 (TS). 12, 98; May 89]
Answer:
Given A = \(\left[\begin{array}{lll}
1 & 2 & 1 \\
3 & 2 & 3 \\
1 & 1 & 2
\end{array}\right]\)
det A = 1 (4 – 3) – 2 (6 – 3) + 1 (3 – 2)
= 1 – 6 + 1 = – 4 ≠ 0
∴ A is a non-singular matrix.
Cofactor of 1 is A₁ = + (4 – 3) = 1
Cofactor of 2 is B₁ = – (6 – 3) = – 3
Cofactor of 1 is C₁ =+(3 – 2) = 1
Cofactor of 3 is A₂ = – (4 – 1) = – 3
Cofactor of 2 is B₂ = + (2 – 1) = 1
Cofactor of 3 is C₂ = – (1 – 2) = + 1
Cofactor of 1 is A₃ = + (6 – 2) = 4
Cofactor of 1 is B₃ = – (3 – 3) = 0
Cofactor of 2 is C₃ = + (2 – 6) = – 4
∴ Cofactor matrix of A is B

Find the adjoint and the inverse of the matrix \(\left[\begin{array}{lll}
1 & 0 & 2 \\
2 & 1 & 0 \\
3 & 2 & 1
\end{array}\right]\). [Mar. 05; May 98]
Answer:

Find the adjoint and the inverse of the matrix \(\left[\begin{array}{lll}
2 & 1 & 2 \\
1 & 0 & 1 \\
2 & 2 & 1
\end{array}\right]\). [Mar. 08, 89]
Answer:
\(\left[\begin{array}{rrr}
-2 & 3 & 1 \\
1 & -2 & 0 \\
2 & -2 & -1
\end{array}\right],\left[\begin{array}{rrr}
-2 & 3 & 1 \\
1 & -2 & 0 \\
2 & -2 & -1
\end{array}\right]\)

Question 15.
If A = \(\left[\begin{array}{rrr}
-1 & -2 & -2 \\
2 & 1 & -2 \\
2 & -2 & 1
\end{array}\right]\), then show that the adjoint of A is 3A’. Find A^-1. [Mar. 19 (AP), May 08]
Answer:
Given A = \(\left[\begin{array}{rrr}
-1 & -2 & -2 \\
2 & 1 & -2 \\
2 & -2 & 1
\end{array}\right]\)

Cofactor of – 1 is A₁ = + (1 – 4) = – 3
Cofactor of – 2 is B₁ = – (2 + 4) = – 6
Cofactor of – 2 is C₁ = + (- 4 – 2) = – 6
Cofactor of 2 is A₂ = – (- 2 – 4) = 6
Cofactor of 1 is B₂ = + (- 1 + 4) = 3
Cofactor of – 2 is C₂ = – (2 + 4) = – 6
Cofactor of 2 is A₃ = + (4 + 2) = 6
Cofactor of – 2 is B₃ = – (2 + 4) = – 6
Cofactor of 1 is C₃ = + (- 1 + 4) = 3
∴ Cofactor matrix of

∴ Adj A = 3A’
det A = – 1 (1 – 4) + 2 (2 + 4) – 2 (- 4 – 2)
= – 1 (- 3) + 2(6) – 2 (- 6) = + 3 + 12 + 12 = 27 ≠ 0
∴ A is invertiable.
A^-1 = \(\frac{{adj} A}{{det} A}=\frac{1}{27}\left[\begin{array}{ccc}
-3 & 6 & 6 \\
-6 & 3 & -6 \\
-6 & -6 & 3
\end{array}\right]\)

Question 16.
If abc ≠ 0, find the inverse of \(\left[\begin{array}{lll}
a & 0 & 0 \\
0 & b & 0 \\
0 & 0 & c
\end{array}\right]\). [Mar. 06; Oct. 96]
Answer:
Let A = \(\left[\begin{array}{lll}
a & 0 & 0 \\
0 & b & 0 \\
0 & 0 & c
\end{array}\right]\)
Cofactor of a is A₁ + (bc – 0) = bc
Cofactor of 0 is B₁ = – (0 – 0) = 0
Cofactor of 0 is C₁ = + (0 – 0) = 0
Cofactor of 0 is A₂ = – (0 – 0) = 0
Cofactor of b is B₂ = + (ac – 0) = ac
Cofactor of 0 is C₂ = – (0 – 0) = 0
Cofactor of 0 is A₃ = + (0 – 0) = 0
Cofactor of 0 is B₃ = – (0 – 0) = 0
Cofactor of c is C₃ = + (ab – 0) = ab
∴ Cofactor matrix of

Question 17.
If 3A = \(\left[\begin{array}{rrr}
1 & 2 & 2 \\
2 & 1 & -2 \\
-2 & 2 & -1
\end{array}\right]\), then show that A^-1 = A’. [Mar. 14, 09; May. 12]
Answer:

Question 18.
If A = \(\left[\begin{array}{ccc}
1 & -2 & 3 \\
0 & -1 & 4 \\
-2 & 2 & 1
\end{array}\right]\), then find (A’)^-1. [Board Paper]
Answer:
Given A = \(\left[\begin{array}{ccc}
1 & -2 & 3 \\
0 & -1 & 4 \\
-2 & 2 & 1
\end{array}\right]\)
Cofactor of 1 is A₁ = + (- 1 – 8) = – 9
Cofactor of 0 is A₂ = – (- 2 – 6) = 8
Cofactor of – 2 is A₃ = (- 8 + 3) = – 5
Cofactor of – 2 is B₁ = – (0 + 8) = – 8
Cot actor of – 1 is B₂ = + (1 + 6) = 7
Cofactor of 2 is B₃ = – (4 – 0) = – 4
Cofactor of 3 is C₁ = + (0 – 2) = – 2
Cofactor of 4 is C₂ = – (2 – 4) = 2
Cofactor of 1 is C₃ = (- 1 + 0) = – 1

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

TS Inter 1st Year English Grammar Syllables

Q.No. 19 (4 × 1 = 4 Marks)

A syllable is the next higher unit to a speech sound and forms a word or part of a word. It contains one (and only one) vowel sound (not letter). The number of consonant sounds in a syllable may be ‘Zero to Seven’.

A word may have one syllable or more.

• Words with one syllable each are called monosyllabic words.
• Words with two syllables each are called disyllabic words.
• Words with three syllables each are called trisyllabic words.
• Words with more than three syllables each are called polysyllabic words.

The, number of vowel sounds in a word gives us the number of syllables in that word. By noticing the vowel symbols in the phonetic transcript of a given word, we can arrive at the number of syllables in that word. Look at the following examples :

pen / pen only one vowel sound – one syllable – monosyllabic paper / peips (r) / two vowel sounds – two syllables – disyllabic gravity / graeviti / three vowel sounds – three syllables – trisyllabic.

discovery / dɪˈskʌvɚɹi / four vowel sounds – four syllables – poly (tetra) syllabic, organization / ˌɔːrɡənəˈzeɪʃən / five vowel sounds – five syllables – poly (penta) syllabic.

There are, however, certain words in which the number of vowel sounds is not equal to the number of syllables. Look at the following examples :
brittle / ˈbɹɪtl̩ / only ong vowel sound – but two syllables
prism / pnzm / only one vowel sound – but two syllables
mutton / mAtn / only one vowel sound – but two syllables

The reason for this variation is that the consonant sounds / l /, / m / and / n / help form a syllable. These sounds in such words are, therefore, called syllabic consonants.
Examine some more examples of this kind :

Careful observation of phonetic transcription or correct pronunciation of words will help students find out the number of syllables in a given word.

Exercise – A

In the following table four categories of words are given. Read them aloud paying attention to the syllabic division.

S.No.	Words with one syllable	Words with two syllables	Words with three syllables	Words with four or more syllables
1.	life	en-gage	te-le-phone	in-sti-tu-tion
2.	pen	suf-fer	po-ta-to	clas-si-fi-cation
3.	two	teach-er	ba-che-lor	e-du-ca-tion
4.	try	mat-ter	am-bu-lance	com-pe-ti-tion
5.	hat	spi-der	in-va-lid	math-e-ma-tics
6.	quite	to-day	com-pu-ter	con-gra-tu-late
7.	light	an-swer	con-tem-plate	in-tel-li-gence
8.	fly	eng-lish	de-scrip-tive	ci-vi-li-za-tion
9.	few	fa-ther	re-pre-sent	he-li-co-pter
10.	bet	don-key	re-mem-ber	ob-serv-a-to-ry

Exercise – B

Read the words in the table and write the number of syllables in the columns. Look up the words in a dictionary to check your answers. The first one has been done for you.

Word	Number of Syllables	Word	Number of Syllables	Word	Number of Syllables
Sunday	2	apology	4	examine	3
question	2	history	3	bun	1
fixation	3	manager	3	student	2
college	2	paper	2	instrumental	4
grammar	2	but	1	monday	2
immoral	3	glass	1	doctor	2
time	1	policy	3	intelligent	4
feather	2	food	1	example	3
near	1	present	2	bright	1
go	1	phone	1	syllabus	3
ugly	2	property	3	agitation	4
create	2	persistent	3	criticism	3
application	4	ant	1	resolution	4
complain	2	particular	4	mother	2
cricketer	3	bachelor	3	beautiful	3
sorry	2	anaesthesia	5	discussion	3
fate	1	honour	2	fan	1
employee	3	amplification	5	fight	1

Mention the number of syllables in the following words.

Exercise – 1

i) misery
ii) direction
iii) remember
iv) information
v) encourage
vi) excellent
Answer:
i) 3 trisyllabic
ii) 3 – trisyllabic
iii) 3 – trisyllabic
iv) 4 – polysyllabic
v) 3 – trisyllabic
vi) 3 – trisyllabic

Exercise – 2

i) person
ii) weakness
iii) dark
iv) thought
v) fact
vi) discipline
Answer:
i) 2 – disyllabic
ii) 2 – disyllabic
iii) 1 – monosyllabic
iv) 1 – monosyllabic
v) 1 – monosyllabic
vi) 3 – trisyllabic

Exercise – 3

i) lawyer
ii) literacy
iii) square
iv) harbinger
v) adamant
vi) muse
Answer:
i) 2 – disyllabic
ii) 4 – polysyllabic
iii) 1 – monosyllabic
iv) 3 – trisyllabic
v) 3 – trisyllabic
vi) 1 – monosyllabic

Exercise – 4

i) before
ii) doctor
iii) mother
iv) imagination
v) essence
vi) quarter
Answer:
i) 2 – disyllabic
ii) 2 – disyllabic
iii) 2 – disyllabic
iv) 5 – polysyllabic
v) 2 – disyllabic
vi) 2 – disyllabic

Exercise – 5

i) glance
ii) propel
iii) silence
iv) realize
v) excitement
vi) climax
Answers:
i) 1 – monosyllabic
ii) 2 – dissyllabic
iii) 2 – disyllabic
iv) 2 – disyllabic / 3 – tnsyllabic
v) 3 – trisyllabic
vi) 2 – disyllabic

Exercise – 6

i) understand
ii) decision
iii) shout
iv) supremely
v) encouragement
vi) flashlight
Answer:
i) 3 – trisyllabic
ii) 3 – trisyllabic
iii) 1 – monosyllabic
iv) 3 – trisyllabic
v) 4 – polysyllabic
vi) 2 – disyllabic

Exercise – 7

i) pension
ii) source
iii) confer
iv) captivate
v) modest
vi) contribution
Answer:
i) 2 – disyllabic
ii) 1 – monosyllabic
iii) 2 – disyllabic
iv) 3 – trisyllabic
v) 2 – disyllabic
vi) 4 – polysyllabic

Exercise – 8

1) popular
ii) today
iii) side
iv) plant
v) rainwater
vi) condition
Answer:
i) 3 – trisyllabic
ii) 2 – disyllabic
iii) 1 – monosyllabic
iv) 1 – monosyllabic
v) 3 – trisyllabic
vi) 3- trisyllabic

Exercise – 9

i) punctual
ii) increase
iii) room
iv) mantelpiece
v) breakfast
vi) gracious
Answer:
i) 2 – disyllabic
ii) 2 – disyllabic
iii) 1 – monosyllabic
iv) 3 – trisyllabic
v) 2 – disyllabic
vi) 2 – disyllabic

Exercise – 10

i) particular
ii) handful
iii) apearance
iv) often
v) apartment
vi) idea
Answer:
i) 4 – polysyllabic
ii) 2 – disyllabic
iii) 3 – trisyllabic
iv) 2 – disyllabic
v) 3 – trisyllabic
vi) 2 – disyllabic

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

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

Question 1.
Prove that angle in a semi-circle is a right angle by using vector method. [MAR ’13, ’08, ’99]
Answer:
Let AB be a diameter of a circle with centre O.
Let OA = a, then OB = -a
Let P be a point on the circle and OP = r
OA = OB = OP


∠APB = 90°
∴ Angle in a semicircle is 90°.

Question 2.
If P, Q, R and S are points whose position vectors are i̅ – k̅, -i̅ + 2j̅, 2i̅ – 3k̅ and 3i̅ – 2j̅ – k̅ respectively, then find the component of RS on PQ. [Mar. ’98]
Answer:
The position vectors of the points P, Q, R and S with respect to the origin ‘O’ are
\(\overline{\mathrm{OP}}\) = i̅ – k̅,
\(\overline{\mathrm{OQ}}\) = -i̅ + 2j̅,
\(\overline{\mathrm{OR}}\) = 2i̅ – 3k̅,
\(\overline{\mathrm{OS}}\) = 3i̅ – 2j̅ – k̅
Now \(\overline{\mathrm{PQ}}=\overline{\mathrm{OQ}}-\overline{\mathrm{OP}}\) = -i̅ + 2j̅ -i̅ + k̅ = -2i̅ + 2j̅ + k̅
\(\overline{\mathrm{RS}}=\overline{\mathrm{OS}}-\overline{\mathrm{OR}}\) = 3i̅ – 2j̅ – k̅ – 2i̅ + 3k̅ = i̅ – 2j̅ + 2k̅

Question 3.
Prove that the angle ‘θ’ between any two diagonals of cube is given by cos θ = \(\frac{1}{3}\). [Mar ’12, ’11, ’10; Mar. ’10]
Answer:
Let \(\overline{\mathrm{OA}}\) = i̅, \(\overline{\mathrm{Ob}}\) = j̅ ,\(\overline{\mathrm{Oc}}\) = k̅
Let OA = OB = OC = 1 unit
In a cube, diagonals are OF, CD, BG, AE

Question 4.
Show that the points (5, – 1, 1), (7, – 4, 7), (1, – 6, 10) and (- 1, – 3, 4) are the vertices of a rhombus by vectors. [Mar. ’13]
Answer:
Let A(5, – 1, 1), B(7, – 4, 7), C(1, – 6, 10) and D(- 1, – 3, 4) are the given points.

∴ AB = BC = CD = DA = 7 units and AC ≠ BD.
∴ A, B, C, D are the points which are the vertices of a rhombus.

Question 5.
Find the area of the triangle whose vertices are A(1, 2, 3), B(2,3, 1) and C(3,1, 2). [Mar. ’14, ’06]
Answer:
Let the position vectors of A, B, C with respect to the origin are
\(\overline{\mathrm{OA}}\) = i̅ + 2j̅ + 3k̅, \(\overline{\mathrm{OB}}\) = 2i̅ + 3j̅ + k̅, \(\overline{\mathrm{OC}}\) = 3i̅ + j̅ + 2k̅
\(\overline{\mathrm{AB}}=\overline{\mathrm{OB}}-\overline{\mathrm{OA}}\) = 2i̅ + 3j̅ + k̅ – i̅ – 2j̅ – 3k̅ = i̅ + j̅ – 2k̅
\(\overline{\mathrm{AC}}=\overline{\mathrm{OC}}-\overline{\mathrm{OA}}\) = 3i̅ + j̅ + 2k̅ – i̅ – 2j̅ – 3k̅ = 2i̅ – j̅ – k̅

\(\overline{\mathrm{AB}} \times \overline{\mathrm{AC}}\) = \(\left|\begin{array}{ccc}
\overline{\mathbf{i}} & \overline{\mathrm{j}} & \overline{\mathrm{k}} \\
1 & 1 & -2 \\
2 & -1 & -1
\end{array}\right|\)
= i̅(-1 -2) – j̅(-1 + 4) + k̅(-1-2) = -3i̅ -3j̅ – 3k̅

∴ The area of triangle whose vertices are A, B, C is \(\frac{1}{2}|\overline{\mathrm{AB}} \times \overline{\mathrm{AC}}|\) = \(\frac{3 \sqrt{3}}{2}\)

Question 6.
If a̅ + b̅ + c̅ = 0, then prove that a̅ × b̅ = b̅ × c̅ = c̅ × a̅. [Mar. ’03; May ’98]
Answer:
Given a̅ + b̅ + c̅ = 0
⇒ a̅ = -b̅ – c̅
⇒ a̅ × b̅ = (-b̅ – c̅) × b̅
= -(b̅ × b̅) – (c̅ × c̅)
= -0 + b̅ × c̅

= a̅ × b̅ = b̅ × c̅ ………………(1)
⇒ a̅ + b̅ + c̅ = 0
b̅ = -a̅ – c̅

⇒ b̅ × c̅ = (-a̅ – c̅) × c̅ =-(a̅ × c̅) – (c̅ × b̅) = c̅ × a̅ – 0
b̅ × c̅ = c̅ × a̅ ……………………..(2)
From (1) & (2) ⇒ a̅ × b̅ = b̅ × c̅ = c̅ × a̅

Question 7.
Find the unit vector perpendicular to the plane passing through the points (1, 2, 3), (2,-1,1) and (1,2,-4). [Mar. ’17(AP) ’05; May ’10]
Answer:
Let the position vectors of the points A, B, C with respect to the origin ‘O’ are
\(\overline{\mathrm{OA}}\) = i̅ + 2 j̅ + 3k̅; \(\overline{\mathrm{OB}}\) = 2 i̅ – j̅ + k̅; \(\overline{\mathrm{OC}}\) = i̅ + 2 j̅ – 4k̅
\(\overline{\mathrm{AB}}=\overline{\mathrm{OB}}-\overline{\mathrm{OA}}\) = 2i̅ – j̅ + k̅ – i̅ – 2j̅ – 3k̅ = i̅ – 3 j̅ – 2k̅
\(\overline{\mathrm{AB}}=\overline{\mathrm{OB}}-\overline{\mathrm{OA}}\) = i̅ + 2j̅ – 4k̅ – i̅ – 2j̅ – 3k̅

The unit vector perpendicular to the plane passing through the points A, B and C is
\(\pm \frac{(\overline{\mathrm{AB}} \times \overline{\mathrm{AC}})}{|\overline{\mathrm{AB}} \times \overline{\mathrm{AC}}|}=\pm \frac{(21 \overline{\mathrm{i}}+7 \overline{\mathrm{j}})}{7 \sqrt{10}}=\pm \frac{(3 \overline{\mathrm{i}}+\overline{\mathrm{j}})}{\sqrt{10}}\)

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:
±\(\frac{1}{\sqrt{6}}\)(2i̅ + j̅ + k̅)

Question 8.
If a̅ = 2i̅ + 3j̅ + 4k̅, b̅ = i̅ + j̅ – k̅ and c̅ = i̅ – j̅ + k̅, then compute a̅ × (b̅ × c̅) and verify that it is perpendicular to a̅. [Mar. ’19(TS); May ’06; May ’03]
Answer:
Given vectors are a̅ = 2i̅ + 3j̅ + 4k̅, b̅ = i̅ + j̅ – k̅, c̅ = i̅ – j̅ + k̅
b̅ × c̅ = \(\left|\begin{array}{ccc}
\overline{\mathrm{i}} & \overline{\mathrm{j}} & \overline{\mathrm{k}} \\
1 & 1 & -1 \\
1 & -1 & 1
\end{array}\right|\)
= i̅(1 – 1) -j̅(1 + 1) + k̅(-1- 1) = 2i̅ – 2k̅

a̅ × (b̅ × c̅) = \(\left|\begin{array}{ccc}
\overline{\mathrm{i}} & \overline{\mathrm{j}} & \overline{\mathrm{k}} \\
2 & 3 & 4 \\
0 & -2 & -2
\end{array}\right|\)
= i̅(-6 + 8) – j̅(-4 – 0) + k̅(-4-0)
= 2i̅ + 4j̅ – 4k̅

Now [a̅ × (b̅ × c̅)].a̅ = (2i̅ + 4j̅ – 4k̅).(2i̅ + 3j̅ + 4k̅) = 4 + 12 – 16 = 0
a̅ × (b̅ × c̅) is perpendicular to a̅.

Question 9.
For any four vectors a, b, c and d show that (a̅ × b̅) . (c̅ × d̅) = \(\left|\begin{array}{cc}
\bar{a} \cdot \bar{c} & \bar{a} \cdot \bar{d} \\
\bar{b} \cdot \bar{c} & \bar{b} \cdot \bar{d}
\end{array}\right|\) and in particular \((\overline{\mathrm{a}} \times \overline{\mathrm{b}})^2=\overline{\mathrm{a}^2} \overline{\mathrm{b}^2}-(\overline{\mathrm{a}} \cdot \overline{\mathrm{b}})^2\). [Mar. ’02, ’00]
Answer:
LHS = (a̅ × b̅). (c̅ × d̅) = a̅. (b̅ × (c̅ × d̅)) = a̅. [(b̅. d̅) c̅ – (b̅. c̅) d̅]
= (a̅ . c̅)(b̅ . d̅) – (a̅ . d̅)(b̅ . c̅) = \(\left|\begin{array}{cc}
\bar{a} \cdot \bar{c} & \bar{a} \cdot \bar{d} \\
\bar{b} \cdot \bar{c} & \bar{b} \cdot \bar{d}
\end{array}\right|\)

In the above formula if c̅ = a̅ and d̅ = b̅, then
(a̅ × b̅) . (c̅ × d̅) = \(\left|\begin{array}{cc}
\bar{a} \cdot \bar{c} & \bar{a} \cdot \bar{d} \\
\bar{b} \cdot \bar{c} & \bar{b} \cdot \bar{d}
\end{array}\right|\) = (a̅.a̅)(b̅.b̅) – (a̅.b̅)(a̅.b̅) = \(\overline{\mathrm{a}^2} \overline{\mathrm{b}^2}-(\overline{\mathrm{a}} \cdot \overline{\mathrm{b}})^2\)

Question 10.
Let a̅, b̅ and c̅ be unit vectors such that b is not parallel to c and a̅ × (b̅ × c) = \(\frac{1}{2}\) b̅. Find the angles made by a̅ with each of b̅ and c̅. [May ’01]
Answer:
Since a̅, b̅ and c̅ be unit vectors then |a̅| = 1, |b̅| = 1, |c̅| = 1
Given a̅ × (b̅ × c̅) = -b̅
⇒ (a̅.c̅)b̅ – (a̅.b̅)c = \(\frac{1}{2}\)b̅
Since b̅ and c̅ are non-collinear vectors equating corresponding coefficients on both sides.
a̅.c̅ = \(\frac{1}{2}\)

|a||c| cos (a, c) = \(\frac{1}{2}\), -(a̅.b̅) = 0
1.1.cos(a̅, c̅) = \(\frac{1}{2}\), a̅.b̅ = 0
cos(a̅,c̅) = \(\frac{1}{2}\), a̅ ⊥ b̅
(a̅, c̅) = 60°, (a̅, b̅) = 90°

Question 11.
Let a̅ = i̅ + j̅ + k̅, b̅ = 2i̅ – j̅ + 3k̅, c = i̅ – j̅ and d̅ = 6i̅ + 2j̅ + 3k̅ . Express d̅ in terms of b̅ × c̅, c̅ × a̅ and a̅ × b̅. [May ’12]
Answer:
Given a̅ = i̅ + j̅ + k̅, b̅ = 2i̅ – j̅ + 3k̅, c̅ = i̅ – j̅, d̅ = 6i̅ + 2j̅ + 3k̅
= 1 (0 + 3) – 1 (0 – 3) + 1(-2 + 1) = 3 + 3 – 1 = 5
Now, d̅. a̅ = (6 i̅ + 2 j̅ + 3k̅). (i̅ + j̅ + k̅) = 11
d̅.b̅ = (6i̅ + 2j̅ + 3k̅).(2i̅ – j̅ + 3k̅) =19
d̅.c̅ = (6i̅ + 2j̅ + 3k̅).(i̅ – j̅) = 4
Take d̅ = x(b̅ x c̅) + y(c̅ x a̅) + z(a̅ x b̅), then we have x = \(\frac{\overline{\mathrm{d}} \cdot \overline{\mathrm{a}}}{\left[\begin{array}{lll}
\overline{\mathrm{a}} & \overline{\mathrm{b}} & \overline{\mathrm{c}}
\end{array}\right]}\), y = \(\frac{\overline{\mathrm{d}} \cdot \overline{\mathrm{b}}}{\left[\begin{array}{lll}
\overline{\mathrm{a}} & \overline{\mathrm{b}} & \overline{\mathrm{c}}
\end{array}\right]}\), z = \(\frac{\overline{\mathrm{d}} \cdot \overline{\mathrm{c}}}{\left[\begin{array}{lll}
\overline{\mathrm{a}} & \overline{\mathrm{b}} & \overline{\mathrm{c}}
\end{array}\right]}\)
∴ x = \(\frac{11}{5}\), y = \(\frac{19}{5}\), z = \(\frac{4}{5}\)
d̅ = \(\frac{11}{5}\) (3i̅ + 3j̅ – k̅) + \(\frac{19}{5}\)(-i̅ – j̅ + 2k̅) + \(\frac{4}{5}\)(4i̅ – j̅ – 3k̅)

Question 12.
For any four vectors a̅, b̅, c̅ and d̅, show that
(i) (a̅ × b̅) × (c̅ × d̅) = [a̅ c̅ d̅] b̅ – [b̅ c̅ d̅] a̅ and
(ii) (a̅ × b̅) × (c̅ × d̅) = [a̅ b̅ d̅]c̅ – [a̅ b̅ c̅]d̅. [Mar. ’18(AP); May ’99]
Answer:
(i) (a̅ × b̅) × (c̅ × d̅) = [(c̅ × d̅).a̅]b̅ – [(c̅ × d̅).b̅]a̅ = [a̅.(c̅ × d̅)]b̅ – [b̅.(c̅ × d̅)]a̅ = [a̅ c̅ d̅] b̅ – [b̅ c̅ d̅] a̅
(ii) (a̅ × b̅) × (c̅ × d̅) = [(a̅ × b̅). d̅]c̅ – [(a̅ × b̅). c̅]d̅ = [a̅ b̅ d̅]c̅ – [a̅ b̅ c̅]d̅

Question 13.
a, b, c are non-zero vectors and a is perpendicular to both b̅ and c̅. If |a̅| = 2, |b̅| = 3, |c̅| = 4 and (b̅, c̅) = \(\frac{2 \pi}{3}\), then find |[a̅ b̅ c̅]|. [May ’08]
Answer:
Given |a̅| = 2, |b̅| = 3, |c̅| = 4 and (b̅, c̅) = \(\frac{2 \pi}{3}\)
a is perpendicular to both b̅ and c̅.
Now b̅ × c̅ is a vector perpendicular to both b̅ & c̅.
a̅ is parallel to b̅ × c̅ (a̅, b̅ × c̅) = 0° or 180°

Now [a̅ b̅ c̅] = a̅. (b̅ × c̅) = |a̅| |b̅ × c̅| cos (a̅, b̅ × c̅) = |a̅| |b̅| |c̅| sin (b̅, c̅). cos (a̅, b̅ × c̅)
= 2.3.4.sin \(\frac{2 \pi}{3}\) . cos(0° or 180°) = 24. \(\frac{\sqrt{3}}{2}\)(±1) = 12√3 = |[a b c]| = 12√3

Question 14.
If [b̅ c̅ d̅] + [c̅ a̅ d̅] + [a̅ b̅ d̅] = [a̅ b̅ c̅], then show that the points with position vectors a̅, b̅, c̅ and d̅ are coplanar. [Mar ’14; Mar. ’00]
Answer:
Let the position vectors of the points A, B, C and D with respect to the origin O’ are \(\overline{\mathrm{OA}}\) = a, \(\overline{\mathrm{OB}}\) = b, \(\overline{\mathrm{OC}}\) = c, \(\overline{\mathrm{OD}}\) = d.
Given [b̅ c̅ d̅] + [c̅ a̅ d̅] + [a̅ b̅ d̅] = [a̅ b̅ c̅] ……………………(1)
Now \([\overline{\mathrm{AB}}  \overline{\mathrm{AC}}  \overline{\mathrm{AD}}]=[\overline{\mathrm{OB}}-\overline{\mathrm{OA}}  \overline{\mathrm{OC}}-\overline{\mathrm{OA}}  \overline{\mathrm{OD}}-\overline{\mathrm{OA}}]\)
= [b̅ – a̅ c̅ – a̅ d̅ – a̅]
= (b̅ – a̅). [(c̅ – a̅) × (d̅ – a̅)] (b̅ – a̅).[c̅ × d̅ – c̅ × a̅ – a̅ × d̅ + a̅ × a̅]
= (b̅ – a̅).[c̅ × d̅ + a̅ × c̅ + d̅ × a̅ + 0]
= b̅. (c̅ × d̅) + b̅. (a̅ × c̅) + b̅. (d̅ × a̅) – a̅ . (c̅ × d̅) – a̅. (a̅ × c̅) – a̅. (d̅ × a̅)
= [b̅ c̅ d̅] + [b̅ a̅ c̅] + [b̅ d̅ a̅] – [a̅ c̅ d̅] – [a̅ a̅ c̅] – [a̅ d̅ a̅]
= [b̅ c̅ d̅] – [a̅ b̅ c̅] – [b̅ a̅ d̅] + [c̅ a̅ d̅] – 0 – 0
= [b̅ c̅ d̅] – [a̅ b̅ c̅] + [a̅ b̅ d̅] + [c̅ a̅ d̅]
= [b̅ c̅ d̅] + [c̅ a̅ d̅] + [a̅ b̅ d̅] – [a̅ b̅ c̅]
= [a̅ b̅ c̅] – [a̅ b̅ c̅] = 0 (from (1))
∴ The vectors AB, AC, AD are coplanar.
∴ The four points A, B, C and D are coplanar.

Question 15.
Find the volume of the tetrahedron whose vertices are (1, 2, 1), (3, 2, 5), (2, – 1, 0) and (- 1, 0, 1). [Mar. ’15(TS); May ’07; Mar. ’04]
Answer:
Let the position vectors of the points A, B, C and D with respect to the origin ‘O’ are
\(\overline{\mathrm{OA}}\)= i̅ + 2j̅ + k̅, \(\overline{\mathrm{OB}}\) = 3i̅ +2j̅ +5k̅, \(\overline{\mathrm{OC}}\) = 2i̅ – j̅, \(\overline{\mathrm{OD}}\) = -i̅ + k̅
Now \(\overline{\mathrm{AB}}=\overline{\mathrm{OB}}-\overline{\mathrm{OA}}\)A
= 3i̅ + 2j̅ + 5k̅ – i̅ – 2j̅ – k̅
= 2i̅ + 4k̅

\(\overline{\mathrm{AC}}=\overline{\mathrm{OC}}-\overline{\mathrm{OA}}\)
=2i̅ – j̅ – i̅ – 2j̅ – k̅
= i̅ – 3j̅ – k̅

\(\overline{\mathrm{AD}}=\overline{\mathrm{OD}}-\overline{\mathrm{OA}}\)
= -i̅ + k̅ – i̅ – 2j̅ – k̅
= -2i̅ – 2j̅

The volume of the tetrahedron whose vertices are A, B, C and D is \(\frac{1}{6}\left[\begin{array}{lll}
\overline{\mathrm{AB}} & \overline{\mathrm{AC}} & \overline{\mathrm{AD}}
\end{array}\right]\)
\(\frac{1}{6}\left|\begin{array}{ccc}
2 & 0 & 4 \\
1 & -3 & -1 \\
-2 & -2 & 0
\end{array}\right|\)
= \(\frac{1}{6}\)|2(0 – 2) – 0(0 – 2) + 4(-2 – 6)|
= \(\frac{1}{6}\)|-4-32|
= \(\frac{36}{6}\) = 6
∴ Volume = 6 cubic units.

Question 16.
Prove that the four points 4i̅ + 5j̅ + k̅,-(j̅ + k̅), 3i̅ + 9j̅ + 4k̅ and -4i̅ + 4j̅ + 4k̅ are coplanar. [Mar. ’99]
Answer:
Let the position vectors of the points A, B, C and D with respect to the origin ‘O’ are \(\overline{\mathrm{OA}}\) = 4i̅ + 5j̅ + k̅,\(\overline{\mathrm{OB}}\) = -(j̅ + k̅), \(\overline{\mathrm{OC}}\) = 3i̅ + 9j̅ + 4k̅,\(\overline{\mathrm{OD}}\) = -4i̅ + 4j̅ + 4k̅
\(\overline{\mathrm{AB}}=\overline{\mathrm{OB}}-\overline{\mathrm{OA}}\) = -j̅ – k̅ – 4 i̅ – 5j̅ – k̅ = -4i̅ – 6j̅ – 2k̅
\(\overline{\mathrm{AC}}=\overline{\mathrm{OC}}-\overline{\mathrm{OA}}\) = 3i̅ + 9j̅ + 4k̅ – 4i̅ – 5j̅ – k̅ = -i̅ + 4j̅ + 3k̅
\(\overline{\mathrm{AD}}=\overline{\mathrm{OD}}-\overline{\mathrm{OA}}\) = – 4i̅ + 4j̅ + 4k̅ – 4i̅ – 5j̅ – k̅ = -8i̅ – j̅ + 3k̅

Now \([\overline{\mathrm{AB}} \overline{\mathrm{AC}} \overline{\mathrm{AD}}]=\left|\begin{array}{ccc}
-4 & -6 & -2 \\
-1 & 4 & 3 \\
-8 & -1 & 3
\end{array}\right|\)
= -4(15) + 6(21) – 2(33)
= -60 + 126 – 66
= 126 – 126
= 0
∴ The vectors AB, AC, AD are coplanar.
∴ The four points A, B, C and D are coplanar.

Question 17.
If a̅ = 2i̅ + j̅ – k̅, b̅ = – i̅ + 2j̅ – 4k̅ and c̅ = i̅ + j̅ + k̅, then find (a̅ × b̅).(b̅ × c̅). [Mar. ’19(AP); Mar. ’17(TS)]
Answer:
Given a̅ = 2 i̅ + j̅ – k̅; b̅ = – i̅ + 2j̅ – 4k̅; c̅ = i̅ + j̅ + k̅
Now a̅ × b̅ = \(\left|\begin{array}{ccc}
\overline{\mathrm{i}} & \overline{\mathrm{j}} & \overline{\mathrm{k}} \\
2 & 1 & -1 \\
-1 & 2 & -4
\end{array}\right|\)
= i̅ (-4 + 2) – j̅ (-8 – 1) + k̅ (4 + 1)
= -2i̅ + 9j̅ + 5k̅

b̅ × c̅ = \(\left|\begin{array}{ccc}
\overline{\mathrm{i}} & \overline{\mathrm{j}} & \overline{\mathrm{k}} \\
-1 & 2 & -4 \\
1 & 1 & 1
\end{array}\right|\)
= 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

Telangana TSBIE TS Inter 1st Year English Study Material Grammar Odd Sound Out Exercise Questions and Answers.

TS Inter 1st Year English Grammar Odd Sound Out

Q.No. 18 (4 × 1 = 4 Marks)

A set of three words are given. One or two letters which are common in all the three words are underlined. The underlined letter stands for one sound in two of the given words and for a different sound in the other word. The word with a different sound is to be written as the response.

The pronunciation of English words is quite tricky and confusing. Some vowels and consonants are pronounced differently in different places. Learning all these varieties is necessary to master pronunciation. It is possible only with practice.

Look at the following words. Circle the word that sounds different with regards to the sound of the bold letters.

Circle the words that sound different with regard to the sound of the bold letters.

Exercise -1

Exercise – 2

Exercise – 3

Exercise – 4

Exercise – 5

Exercise – 6

Exercise – 7

Exercise – 8

Exercise – 9

Exercise – 10

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

TS Inter 1st Year English Grammar Information Transfer

Q.No. 20 (1 × 4 = 4 Marks)

Information can be expressed through verbal (description) and non verbal (diagrams) modes. Some of the non-verbal modes are :

1. Pie-charts,
2. Bar graphs,
3. Tree diagrams,
4. Flow charts and
5. Tables.

The process of changing a text from Verbal to Non-verbal mode or vice versa is called Information Transfer. This is a very useful and important skill for students. Acquiring this skill enables the students make notes quickly, understand various texts effectively and present ideas clearly and briefly.

Non-verbal expressions are remarkable for their brevity, clarity, simplicity, accessibility and provision for comparative, contrastive and analytical studies.

1. PIE-CHARTS

A pie-chart is a circle divided into parts. Each part represents a particular thing. And eah part is in proportion to the ratio of that thing to its total. Studying the given pie chart slowly helps one understand the information given there. Then the information can be presented in verbal mode. Once the mode of representing the given information in the form of a pie-chart is understood, verbal text can be transferred into a pie-chart.

In a pie charl; the information is presented in the form of a circle. The circle is divided into sections called sectors. The contribution of each unit in the chart is represented in percentages.

Example 1 :
The following pie chart depicts the results of a survey regarding distribution of different Blood Groups in a college.
Blood Groups in a College

From the figure we can see that 35% of the students of a college have 0 Group of Blood and these students form the largest group. The next largest group comprises students with B Group of Blood. 30% of students belong to this category. 25% of students have AB Group of Blood. Finally, we see that only 10% of students have A Group of Blood. Thus, from the piechart we can conclude that while many students have O Group of Blood. Very few have A Group.

Example 2 :
The following piechart depicts the favourite subject of students in a class. We can see from the figure that five subjects have been taken into consideration – Economics, Civics, Commerce, English and 2^nd Language. Students who like Economics form the largest group. A quarter of the students of the class i.e 25% expressed preference for this subject. 20% of the students like English and the same percentage i.e 20% of the students like Commerce. Next in popularity is Civics, liked by 18% of the class. Finally, trailing closely behind Civics, comes 2^nd Language, which is the favourite subject of 17% of the students.
Favourite Subjects of Students

Exercises and Activities

Question 1.
The following paragraph gives the information about the most widely spoken languages in India. Convert the passage into a pie chart.

Hindi is the most widely spoken language in India. The fact that 44% of Indians speak Hindi across India justifies its title as our National Language. 9% of Indians speak Bengali followed by Marathi which is spoken by 8%. Telugu comes next in the list with 7%, Tamil and Gujarati account for 6% and 5% respectively. All other languages together share the remaining percentage.
Answer:
Pie chart showing languages spoken in India

Hindi – 44%
Bengali – 9%
Marathi – 8%
Telugu – 7%
Tamil – 6%
Gujarathi – 5%
All other
languages – 21%

Question 2.
Read the following paragraph and convert the information into a pie chart.

There are seven continents in the world. Asia is the largest continent with an area of 30% followed by Antarctica with 28%. North America occupies 17% of the land on the earth. South America stands fourth in the list with 12% of land. Africa and Australia are the fifth and sixth largest ones with their respective shares of 6% and 5%. Europe is the last in the list which occupies 2% of the land only.
Answer:
Areas of Continents

Continents
Asia – 30%
Antarctica – 28%
North America – 17%
South America – 12%
Africa – 6%
Australia – 5%
Europe – 2%

Question 3.
Observe the pie chart given below. It contains information about the mode of transport used by students of a certain junior college. Write a small paragraph.
Mode of Transport of Students

Answer:
Mode of Transport of Students
The given pie chart presents the mode of transport used by students of a particular junior college. A major part of them 40% – use the public transport, i.e. bus. A half of the share of bus, that is 20% of them travel by autorickshaws. Two wheelers and cars carry 15% each of the students. Just 10% of them use the cleanest and the healthiest mode – walking.

Question 4.
The pie chart given below shows how people spend their time on smart phones. Convert the information into a paragraph.
Time spent on Smart. Phones

Answer:
Time spent on Smart Phones
Time spent on smart phones is presented in the given pie chart. The lion’s share, i.e. 35% of the time goes to games. Social networking follows games with its share of 29% of the time. Utilities Consume 20% time. The share of music and videos is 8%. Others take 5% time. News comes last with just 3% time.

2. BAR BRAPHS

A bar graph is a diagram in which values of variables are shown by the length of rectangular columns with equal width. It is another visual representation of data. It helps to compare the values presented in a group. The bars can be plotted vertically or horizontally. A vertical bar chart is sometimes called a column bar chart.

Example 1 :
Given below is the iar graph that shows the cost of certain vegetables over a period of 4 months. Let us now make a detailed analysis.

The bar graph given below shows the cost of carrots and potatoes over a period of four months – January, February, March and April. Carrots were more costly than potatoes during all the months. In January carrots cost Rs. 35 a kilo, while potatoes cost a little less, at Rs. 30 a kilo. The cost of carrots increased to Rs. 40 in February, while there was a sharp fall in the cost of potatoes.

There was a sharp rise in the cost of both the vegetables after that and in March the cost of carrots was Rs. 50 per kilo while that of potatoes was Rs. 40. In April once again there was a steep increase in the cost of carrots but the cost of potatoes remained the same as in March. Thus we observe that the cost of carrots kept increasing over the months but that of potatoes fluctuating.
COST OF VEGETABLES (in Rs per kg)

Example 2 :
The following bar graph represents the favourite sports of various group of students studying in a college. Students of four sections HEC, CEC, BPC and MPC were asked about their preferences in sports. The number of students in each section varied. Three sports were considered – football, cricket and kabaddi. HEC students expressed great interest in cricket. 50 out of 85 students, i.e. more than half liked cricket. Very few in that section, just 5, were fond , of football. 30 liked kabaddi.

In the CEC section, consisting of 100 students, an equal number of students, i.e. 40 liked kabaddi and cricket. 20 liked football. With regard to the science sections, cricket was more popular among BPC students. An equal number in both the sections, 30, were fond of football. The figures for kabaddi too were more or less the same. The BPC section consisted of 88 students while MPC students were 75 in number. On the whole, one can conclude that cricket is the most popular sport in the college, followed by kabaddi.
FAVOURITE SPORTS OF STUDENTS

Exercises And Activities

Question 1.
The passage below represents the data of improvement of English language skills due to Internet usage. Present it in a bar graph.

Internet plays an important role in improving Reading skills. 94% participants in this study agreed that they improved their Reading skills by using Internet while 91% opined that they improved Translation skills. Internet usage helped 87% of participants in enhancing their vocabulary skills. 80% of participants unanimously agreed that they improved their Writing skills, Speaking skills and Grammar.
Answer:
Bar Graph Showing Skills due to Internet Usage

Question 2.
The following passage shows the favourite sports of the students of a school. Represent the data in a bar graph.

Cricket is the most favourite sport of the students which is liked by 80 students. Tennis falls behind Cricket with a slight difference. It is the favourite of 75 students. Swimming and Football are liked by 40 and 45 students respectively while Badminton is the favourite of 30 students. Hockey is the least favouring sport of the students which is liked by 20 students only.
Answer:
Bar Graph Showing Favourite Sport of Students

Question 3.
Analyse the bar graph given below and write about it in a paragraph.
MARKS OF STUDENTS

Answer:
The bar chart presents marks of three students in three subjects. Meena scored 70 in Telugu, 65 in Maths and in English just 50. Mala scored 65 in Maths, 50 in Telugu and only 40 in English. Megha secured 70 each in English and Maths but scored 60 in Telugu.

Question 4.
The given below bar graph shows how much dietary fibre is found in certain fruits. Convert the information into a paragraph.

Answer:
Fibre Content in Fruits
The given bar graph presents the details of fibre content in various fruits. The guava stands tall with six (6) grams of dietary fibre per a serving of one cup. Next comes the pear with five (5) grams per unit. The third in the order is the apple with four (4) grams per a cup. The banana and the orange have almost the same quantity of dietary fibre – three (3) grams per cup.

3. TREE DIAGRAMS

A tree diagram is another way of representing information. It has a branching tree-like structure. It shows how its components are related to one another. It helps us understand the relevant information in a short time.

Example 1 :
There are three types of muscle in the human body. They are smooth, cardiac and skeletal muscles. Smooth muscles are controlled by involuntary responses. Examples of smooth muscles are muscles in the digestive tract and blood vessels. The second type of muscle is cardiac muscle. It is also an involuntary muscle. Muscles that cover the heart are examples of cardiac muscles. The third type of muscle is the skeletal muscle. It is controlled by voluntary response. All the muscles attached to the bones such as biceps, deltoid are examples of skeletal muscles.

The above paragraph can be depicted in the form of a tree diagram as follows.

Example 2 :
A man who managed a popular hotel was asked the secret of his success. He said that only when customers were happy with the dining experience would they keep returning to the hotel. Dining would be a pleasant experience only if the food served was of a high standard. Good service too was equally important. He elaborated that food should be tasty and fresh. Service should be prompt and courteous.
Given below is a tree diagram representing the man’s views.

Exercises And Activities

Question 1.
Read the following paragraph and transfer the information into a tree diagram.

The oldest musical instrument in the world is the drum, made initially in one of the three ways. First, frame drums were made by stretching the skin over bowl-shaped frames. Next, rattle drums were made by filling gourds or skins with dried grains, shells, or rocks. Finally, tubular drums were made from hollowed logs or bones covered with skins. Both frame and tubular drums were struck with the hand or with beaters to produce sounds. In contrast, rattle drums were shaken or scraped to make rhythmic sounds. For thousands of years, drums have been used to transmit messages to call soldiers to battle and make music.
Answer:
Tree Diagram showing Types of Drums

Question 2.
Read the following paragraph and transfer the information into a tree diagram.

There are so many species of animals that we find living on the earth. Scientists grouped these animals into different classes based on certain similarities they share. Animals are divided into vertebrates, ones with backbones and invertebrates, those without backbones. The vertebrates are basically divided into five classes. They are commonly known as mammals, birds, fish, reptiles and amphibians. Arachnids and insects are the two commonly known classes in the invertebrates group.
Answer:
Tree Diagram showing Species of Animals

Question 3.
The following tree diagram depicts the classification of Vitamins. Present the information in a paragraph.

Answer:
Classification of Vitamins
The given tree diagram presents the classification of vitamins. Vitamins are broadly of two types. They are : 1) Soluble vitamins in water and 2) Soluble in fats. Vitamin B and Vitamin C fall in the category of ‘Soluble in water’. Vitamins A, D, E and K (four) belong to the group of vitamins soluble in fat and Vitamin B is sub-divided into Bl, B2, B3, B6 and B12 (five) types.

Question 4.
Study the following tree diagram and write it in a paragraph.

Answer:
Types of Oils
The given tree diagram explains the types of oils. Based on the source, oils are of three categories. They are : 1) Oils from nuts, 2) Oils from vegetation (plants / flowers) and 3) Oils from minerals. Examples are 1) groundnut oil, 2) oils from flowers and 3) oils from the crust of the earth. Groundnut oil is used in cooking. Oils from flowers go into the making of soap, medicines and perfumes (scents). Mineral oil fuels machines and automobiles.

4. FLOW CHARTS

We draw flow charts when we present information in the form of a process. For instance, we construct flow charts to put the information of the industrial production from raw product to finished product in a logical order in successive steps. Flow charts are simple to construct and easy to understand. Each step in the sequence is written in a diagram shape. These successive stages or steps are linked by connecting directional arrows. They guide readers to understand flow charts logically and follow the process from beginning to end. In these flow charts we find elongated circles, rectangles and diamond shaped diagrams.

Example 1 :
Describe how the following passage is presented in a flow chart. The passage shows the time table for children in a boarding school. You are supposed to wake up at 5 am every day and lights – out time is 9.30 pm. Siesta time is between 1 and 2 in the afternoon. Assembly begins at 8 am sharp in the school hall. You have to report to your House Prefect by 7.30 am on all school days. You may play any game between 4 and 6 pm. You must not be late for study time which is between 6 and 8 in the evening. School timings are from 8.30 am to 3.30 pm with an hour-long lunch break at 1 pm. These details are shown in a flow chart.

Time table of children in a boarding school

Example 2 :
Read the following paragraph and transfer the information into a flow chart.

Rayon is a man-made fiber. It is a reconstituted natural fiber – cellulose. Rayon is made by dissolving cellulose in a solution of sodium hydroxide or caustic soda. The cellulose is obtained from shredded wood pulp. The dissolved cellulose is formed into threads by forcing it through a spinneret in a dilute sulphuric acid setting bath. The threads are drawn from the setting bath, wound on a reel, washed, dried on a heated roller, and finally wound onto a bobbin.

Process of Making Rayon

Exercises And Activities

Question 1.
The following paragraph describes how clothes are washed.

Draw a flow chart based on the information given. First, fill a bucket half full with water. Then, add a spoonful of washing powder. Stir vigorously till the power mixes with water and forms foam. Put the unwashed clothes into it. Wait for fifteen minutes. Take out clothes and scrub with a brush to remove stains. Now, rinse the clothes with clean water.

Wring out the clothes gently by twisting and compressing them. This removes excess water from the clothes. This saves the time of drying. Now dry the washed clothes by putting them on the clothes line. Collect the washed and dried clothes later.
Answer:
How to wash clothes ?

Question 2.
Convert the following paragraph into a flow chart.

Silver occurs in the ores of several metals. The frothing process of extracting silver accounts for about 75% of all silver recovered. Here the ore is ground to a powder, placed in large vats containing a water suspension of frothing agents, and thoroughly agitated by air jets. Depending on the agents used, either the silver-bearing ore or the gangue adhering to the bubbles of the foam is skimmed off and washed. The final refining is done using electrolysis.
Answer:
Flow Chart depicting Frothing Process of Extracting Silver

Question 3.
The following flow chart describes how paper is manufactured in a paper mill. Write the details in a paragraph.
Manufacture of paper

Answer:
The given flow chart describes the process of manufacturing paper. First, the raw materials like wood, grass, bamboo and rags are procured. Secondly they are cut into pieces, immersed in water and made into pulp. Then the pulp is mixed with lime for whitening. Later, the pulp is boiled and passed through wire meshes. At this stage, we obtain wet paper. Finally, it is passed over heated rollers. Then we get the end product, in the form of thin sheets of paper.

Question 4.
Draw a flow chart based on the information given below.

The following process is the description of how a post office transfers a letter from a sender to a receiver. First, the sender posts the letter in a post box. Next, the box is opened. Then the contents in it are sorted out. Then they are kept in a bag and the bag is tied. The destination is written on the bag. The bags are sent to the district post office. The district post office sends the bags to the destination village / town post offices. The destination post office receives the letters. The received letters are arranged and sorted out. The post man delivers the letters to the addressees.
Answer:
Flow Chart depicting the Process of Delivering Letters

5. TABLES

We can also represent information in the form of a table.
Example 1 :
Given below are the marks secured by Aravind, Akash and Ramesh in their half-yearly examinations of class X.

Name of the Subject	Aravind	Akash	Ramesh
Telugu	81	80	81
Hindi	97	97	97
English	60	88	99
Mathematics	99	97	100
Science	68	91	98
Social Studies	95	98	93

After reading the information given in the table we can write a paragraph like this.

In this table, the marks secured by 3 students are compared. While all the three students scored equal marks in Hindi, there is a slight variation of marks in Mathematics and Social Studies. However, there is a great variation of marks in English. From the table it can be concluded that Aravind needs to concentrate more on English and Science, whereas Akash needs to focus on Telugu and English. Ramesh, who scored the highest marks among the three, needs to focus on Telugu.

Example 2 :
The following table shows the number of gold medals won by 8 participating countries in the XII South Asian games 2016. First read the data given in the table.

Rank	Nation	No. of gold medals won
1	India	188
2	Sri Lanka	25
3	Pakistan	12
4	Afghanistan	7
5	Bangladesh	4
6	Nepal	3
7	Maldives	0
8	Bhutan	0

 

Now read the paragraph given below.

The above table gives the information of the number of gold medals won by 8 participating countries in the XII South Asian games 2016. India secured the first rank with 188 gold metals. It was far ahead of the other countries. Sri Lanka was ranked 2, securing only 25 gold medals. Pakistan got only 12 gold medals and was ranked 3. With 7 golds, Afghanistan is in the 4th place. Bangladesh won 4 golds while Nepal secured just 3 golds. Maldives and Bhutan which stood at the bottom of the table got no gold medals. This table shows the commendable performance of India in the XII South Asian Games.

Exercises And Activities

Question 1.
Read the following paragraph and transfer the information into a table.

A reading test assesses reading comprehension by employing multiple testing techniques, represented by eight main types of questions. Question types, such as Multiple-Choice, Matching, Diagram Labelling, Summary Completion, Sentence Completion, Short Answer Questions with percentage, i.e., 37.50%, 18.13%, 16.25%, 10%, 9.36%, and 8.76%, take place respectively. The number of questions for each of these questions types is variable. Basic English grammar, cloze summary, percentages are although with lower portions and are also considered in the reading test.
Answer:
Table Showing Types of Questions in Reading & Tests

S.No.	Type of Questions	Percentage
1.	Multiple-Choice	37.50
2.	Matching	18.13
3.	Diagram Labelling	16.25
4.	Summary Completion	10.00
5.	Sentence Completion	09.36
6.	Short Answer Questions	08.76
7.	Basic English Grammar	Negligible
8.	Cloze Summary	Negligible

Question 2.
Convert the following paragraph into a table.

There are many elements in the earth’s crust. Oxygen occupies 46%; Silicon 28%; Aluminum 8%; Iron 5%; Calcium 3.6%; Sodium 2.8%; Potassium 2.6%; Magnesium 2%; certain other elements occupy 2% of the earth’s crust. This is what we mean by the abundance of elements in the earth’s crust.
Answer:
Table Showing Elements in Earth’s Crust

Sl.No.	Name of the Element	Percentage
1.	Oxygen	46
2.	Silicon	28
3.	Aluminum	08
4.	Iron	05
5.	Calcium	3.6
6.	Sodium	2.8
7.	Potassium	2.6
8.	Magnesium	02
9.	Other elements	02

Question 3.
Study the table below showing a few Asian countries with their capitals and currencies. Write a paragraph containing all the information in the table.

Country	Capital	Currency
Afghanistan	Kabul	Afgani
China       ‘	Beijing	Yuan
Japan	Tokyo	Yen
Saudi Arabia	Riyadh	Riyal
Singapore	Singapore	Singapore dollar

Answer:
The table presents the capitals and their currencies of 5 Asian countries. Kabul is the capital of Afghanistan and their currency is Afgani. China’s capital is Beijing and their currency is Yuan. With Yen as their currency Japan administers the country from Tokyo, the capital city. Saudi Arabia’s capital is Riyadh and their currency is Riyal. Finally Singapore has as its capital Singapore city and their currency is Singapore dollar.

Question 4.
Look at the following table. It gives information about nutrients (in gms) present in 100 ml. of milk. Present the information in the form of a paragraph.

Nutrition information about Milk	Per 100 ml approximately
Energy (kcal)	78.0
Fat (g)	5.0
Carbohydrates (g)	4.4
As sugar (g)	0.0
Protein (g)	2.3
Calcium (mg)	8.9
Minerals (g)	0.8

Note : k stands for thousand; g stands grammes.
Answer:
The given table provides us information about tire nutrition value of milk. 100 ml of milk gives us 78 kcals of energy. Fat is 5.0 gms. Carbohydrates are 4.4 gms. Sugar Nil. Proteins 2.3 gms. Calcium 8.9 mg. and Minerals 0.8 grams.

Telangana TSBIE TS Inter 1st Year Physics Study Material 12th Lesson Thermal Properties of Matter Textbook Questions and Answers.

TS Inter 1st Year Physics Study Material 12th Lesson Thermal Properties of Matter

Very Short Answer Type Questions

Question 1.
Distinguish between heat and temperature. [TS Mar. ’15]
Answer:
Differences between heat and temperature :

Heat	Temperature
1. Heat is a form of energy.	1. It represents relative degree of hotness (or) Coldness of a body.
2. Unit: joule (or) calorie	2. Unit: °C or °F
3. It is cause	3. It is effect.
4. Heat is measured by calorimeter	4. It is measured by thermometer.
5. Quantity of heat supplied Q = m st	5. Change in temperature of a body ∆ t = \(\frac{Q}{ms}\)

Question 2.
Explain triple point of water.
Answer:
The temperature of a substance remains constant during its change of state.

A graph plotted between temperature (T) and pressure (P) of a substance during change of state is called “phase diagram”.

In phase diagram of water, the P – T plane is divided into three regions.

The line ‘AO’ is called fusion curve. It gives equilibrium temperature and pressure between solid and liquid states.

The line ‘CO’ is called vaporisation curve. It gives equilibrium temperature and pressure between liquid and vapour states.

The line ‘BO’ is called sublimation curve. It gives the relation between of temperature and pressure between solid and vapour states.

Triple Point:
At point ‘O’ the curves AO, BO and CO will intersect.

It gives the temperature and pressure at which solid, liquid and vapour states of water are in equilibrium.

Coordinate of triple point of water a temperature = 273.16 K, pressure = 0.006 atmos (or) 611 pascals.

Question 3.
What are the lower and upper fixing points in Celsius and Fahrenheit scales? [TS Mar. ’16; AP Mar. ’19, ’18 ’16, May ’14]
Answer:
Centigrade (Celsius) scale of temperature:
In centigrade scale of temperature lower fixed point is freezing point of water at one atmosphere pressure, as 0°C. The upper limit is boiling point of water at 1 atm pressure, as 100°C.

Fahrenheit scale of temperature :
In Fahrenheit scale, the lower fixed point is freezing point of water at one atmosphere pressure, as 32°F. The upper fixed point is boiling point of water at 1 atm pressure, as 212°F.

Question 4.
Do the values of coefficients of expansion differ, when the temperatures are measured on Centigrade scale or on Fahrenheit scale?
Answer:
Yes. Coefficients of expansion α, α_a and α_v are not same in Celsius scale and in Fahrenheit scale. In Fahrenheit scale values of α, α_a and α_v are less than those in Celsius scale.

Since magnitude of 1°C > magnitude of 1°F this change takes place. The values of Celsius scale are 1.8 times more than the values in Fahrenheit scale.
α_F = 5/9 α_c

Question 5.
Can a substance contact on heating? Give an example. [AP Mar. ’18, ’16, May ’16; TS May, ’18, ’16]
Answer:
Yes. Some substances will contact on heating. Ex: Leather, rubber, cast Iron type metal.

Question 6.
Why gaps are left between rails on a railway track? [TS Mar. ’19; AP Mar. ’19, ’17, ’16, ’09; May ’16; June ’15]
Answer:
To allow the linear expansion rails.

In summer temperature of atmosphere increases so rails will expand. If no gap is given between rails then the rails will bend it leads to accidents. If gap is given the rails will expand into that gap and that track is safe.

Question 7.
Why do liquids have no linear and areal expansions? [TS Mar. ’19]
Answer:
Liquids have only volume expansion. No linear expansion or areal expansion. Because liquids does not have any independent shape they must be taken in a container. So we will consider only volume of liquid.

Question 8.
What is latent heat of fusion? [AP & TS May ’17]
Answer:
Latent heat of fusion (melting):
It is defined as the amount of heat energy absorbed or rejected by unit mass of substance while converting from solid to liquid or from liquid to solid.

Question 9.
What is latent heat of vapourisation? [AP Mar. ’13]
Answer:
Latent heat of vapourisation :
It is defined as the amount of heat energy absorbed or rejected by unit mass of substance while converting from liquid to vapour or from vapour to liquid state.

Question 10.
Why are utensils coated black? Why is the bottom of the utensils made of copper? [AP May ’18; TS Mar. ’18]
Answer:
Lower portion of the utensils is in contact with fire. Black bodies are good heat absorbers. So, a black bottom will absorb more heat.

Copper is a good conductor of heat. So, copper is used at the bottom of cooking utensils.

Question 11.
What is triple point of Water? Mention the values of temperature and pressure at triple point of water. [TS June ’15]
Answer:
Triple point:
The temperature and pressure where a substance can coexist in all its three states is called the “triple point”.

i.e., The substance will exist as a solid, as liquid and as vapour at that particular temperature and pressure.

For water the triple point is at a temperature of 273.16 K and at a pressure of 6.11 × 10^-3 atmospheres or nearly 610 pascals.

Question 12.
State Boyle’s law and Charles law. [AP June 15; TS Mar. 15]
Answer:
Boyle’s Law :
At constant temperature, the volume (V) of a given mass of a gas is inversely proportional to its pressure (P).
∴ V ∝ \(\frac{1}{P}\) ⇒ PV = constant = K.

Charles Law:
At constant pressure, the volume (V) of a given mass of a gas is directly proportional to its absolute temperature (T).
∴ V ∝ T ⇒ \(\frac{V}{T}\) = K (constant)

Question 13.
State Wein’s displacement law. [AP Mar. ’17]
Answer:
Wein’s Displacement Law :
The wavelength (Ain) of maximum intensity of emission of black body radiation is inversely proportional to absolute temperature (T) of the black body.
i.e., λ_m ∝ \(\frac{1}{T}\) (or) λ_m = \(\frac{b}{P}\)
where ‘b’ is called ‘Wein’s constant”.

Question 14.
Ventilators are provided in rooms just below the roof. Why?
Answer:
Density of hot air is less. So in a room hot air goes to top layers i.e., nearer to the roof.

When ventilators are provided nearer to the roof hot air will escape easily from room. So we feel that the room is cool and circulation of air will become easy.

Question 15.
Does a body radiate heat at 0 K? Does it radiate heat at 0°C?
Answer:
According to Precost’s theory, every body above zero Kelvin will radiate heat energy to the surroundings.
So, i) A body at O’ Kelvin does not radiate heat energy.
ii) A body at 0°C i.e., at 273Kwill radiate heat energy.

Question 16.
State the different modes of transmission of heat. Which of these modes require medium? [TS May ’18]
Answer:
Transmission of heat is of three types.
1) Conduction 2) Convection 3) Radiation

For propagation of heat energy medium is required in case of conduction and convection.

Question 17.
Define coefficient of thermal conductivity and temperature gradient.
Answer:
“The coefficient of thermal conductivity”
(K) it is the quantity of heat flowing normally per second through unit area of the substance per unit temperature gradient.

‘Temperature gradient” is defined as the change in temperature along the conductor per unit length.

Temperature gradient
Change in temperature

Question 18.
Define emissive power and emissivity.
Answer:
Emissive power:
The emissive power of a body is defined as the energy radiated by the body per second per unit area at a given temperature and wavelength.

Emissivity:
Emissivity is defined as the ratio of the emissive power of a body to that of a black body at the same temperature.

Question 19.
Is there any substance available in nature that contracts on heating? If so, give an example. [TS May ’16]
Answer:
Yes. Some substances will contact on heating.
Ex: Leather, rubber, cast Iron type metal.

Question 20.
What is greenhouse effect? Explain global warming. [AP Mar. ’15, ’13; TS Mar. & May ’16]
Answer:
Green house effect: Earth will absorb heat radiation and reradiate heat energy of longer wavelength. This longer wave length heat radiation is reflected back to earth due to green house gases such as Carbon dioxide [CO₂], Methane (CH₄) Chloroflurocarbons, Ozone (O₃), etc. As a result temperature of earth’s atmosphere is gradually increasing. This is known as “green house effect.”

Global warming:
Earth receives heat energy during day time from sun. It reradiates heat energy in the form of longer electromagnetic waves.

But due to presence of green house gases the longer electromagnetic waves were reflected back to earth. As a result temperature of earth’s atmosphere is gradually increasing.

This process will increase with the increased content of green house gases in atmosphere. As a result temperature of earth’s atmosphere increases gradually.

Question 21.
Define absorptive power of a body. What is the absorptive power of a perfect black body?
Answer:
Absorptive power of a body is defined as the ratio of energy absorbed by the body within the wave length range of A and A + dA to the total energy flux following on the body.
Absorptive power,

Question 22.
State Newton’s law of cooling. [AP Mar. ’18, ’16, May ’18, ’17, June ’15; TS Mar. ’18, TS May ’16]
Answer:
Newton’s Law of cooling states that the rate of loss of heat of a hot body is directly pro-portional to the difference in temperature between the body and its surroundings pro-vided the difference in temperatures is small and the nature of the radiating surface remains same.

Where k is the proportionality constant

Question 23.
State the conditions under which Newton’s law of cooling is applicable. [AP May ’16; TS June ’15]
Answer:
Newton’s law of cooling is applicable

1. loss of heat is negligible by conduction and only when it is due to convection.
2. loss of heat occurs in a streamlined flow of air i.e., forced convection.
3. temperature of the body is uniformly distributed over it.
4. temperature difference between the body and surroundings is moderate i.e., upto 30 K.

Question 24.
The roofs of buildings are often painted white during summer. Why? [TS Mar. ’17, ’15; AP May ’16]
Answer:
When roofs of buildings are coated white we will feel relatively cold during summer.

Absorptive power of white surface is less. So roofs coated white will absorb less heat energy. So less quantity of heat is transmitted into the house. So we feel less hot or cold inside the house.

Question 25.
What is thermal expansion? [TS Mar. ’16]
Answer:
The increase in interatomic distance due to thermal energy is called “thermal expansion”.

As a result the length solids or volume of liquids or pressure of gases will increase.

Question 26.
Why is it easier to perform the skating on the snow? [TS Mar. ’16]
Answer:
Due to increase of pressure melting point decreases, So it is easier to perform the skating on the snow.

Short Answer Questions

Question 1.
Explain Celsius and Fahrenheit scales of temperature. Obtain the relation between Celsius and Fahrenheit scales of temperature.
Answer:
Celsius (Centigrade) scale of temperature :
In centigrade scale of temperature lower fixed point is freezing point of water at one atmosphere pressure, as 0°C. The upper limit is boiling point of water at 1 atm pressure, as 100°C.

The interval between lower limit and upper limit [100 – 0 = 100] is divided into 100 equal parts and each part is called 1°C.

Fahrenheit scale of temperature :
In Fahrenheit scale, the lower fixed point is freezing point of water at one atmosphere pressure, as 32°F. The upper fixed point is boiling point of water at 1 atm pressure, as 212°F.

The interval between upper fixed point and lower fixed point (212 -32 = 180) is divided into 180 equal parts and each part is called 1°F.

Relation between Fahrenheit and Celsius scale of temperatures:
In both scales, lower limit and upper limit are same. The only change is in numerical values of lower and upper limits.

In Fahrenheit lower limit = 32, upper limit = 212, difference of limits = 180

In Celsius scale lower limit = 0, upper limit = 100, difference of limits = 100

C = Temperature in Celsius scale.
F = Temperature in Fahrenheit scale.

Question 2.
Two identical rectangular strips one of copper and the other of steel, are riveted together to form a compound bar. What will happen on heating?
Answer:
When two dissimilar metals say copper and steel are riveted together that arrangement is called “bimetallic strip”.

When a bimetallic strip is heated copper strip will expand more than steel due to more expansion coefficient.

Since they are riveted they must expand as a common piece. As a result bimetallic strip will bend in the form of an arc. For the metallic strip with high a its length is more so it is on the outer side. For the strip with less a its length is less. It will be at the inner side of the arc.

Question 3.
Pendulum clocks generally go fast in winter and slow in summer. Why? [TS Mar. ’19, ’17]
Answer:
In summer due to increase in temperature of atmosphere length of pendulum will increase.

Time period of pendulum T = 2π\(\sqrt{\frac{l}{g}}\)

T ∝ √l. So it will make less number of oscillations per day. So clock will run slowly in summer.

In winter temperature of atmosphere decreases. So length of pendulum decreases.

Hence time period of oscillation will also decrease. As a result, pendulum will make more oscillations per day so clocks will run fast in winter.

Question 4.
In what way is the anomalous behaviour of water advantageous to aquatic animals? [AP Mar. ’18, 17, 14; May 18. 17, 14; TS May ’18]
Answer:
In cold countries and at polar region temperature falls below 0°C at winter. So surface of water will be frozen. Due to anomalous expansion of water even though the surface of lakes, and sea are frozen water will exist at bottom layers at 4°C.

Different layers in between ice and bottom will have different temperatures like 1°C, 2°C or 3°C. In these layers, aquatic animals are able to survive even in winter.

Anomalous expansion of water helps for the survival of aquatic life at polar region and in cold countries.

Question 5.
Explain conduction, convection and radiation with examples. [TS Mar. ’18, ’16, ’15, June ’15; AP Mar. ’19, ’15, May, ’16]
Answer:
Conduction :
It is a mode of transfer of heat from one part of the body to another, from particle to particle in the direction of fall of temperature without any actual movement of the heated particles.
Ex: When one end of a metal rod is heated, its other end becomes hot. Here, the heat goes from hot end of the metal rod towards cold end, by conduction.

Convection :
It is a mode of transfer of heat from one part of the medium to another part by the actual movement of the heated particles of the medium.
Ex : Seabreeze, Tradewind, etc.

Radiation :
It is a mode of transfer of heat from the source to the receiver without any actual movement of source or receiver and also without heating the intervening medium.
Ex : Heat from sun comes to us through radiation. On standing near fire, we feel hot as heat comes to us through radiation.

Long Answer Questions

Question 1.
Explain thermal conductivity and coefficient of thermal conductivity.
A copper bar of thermal conductivity 401 W (mK) has one end at 104°C and the other end at 24°C. The length of the bar is 0.10 m and the cross-sectional area is 1.0 × 10^-6 m^-2. What is the rate of heat conduction along the bar?
Answer:
The ability to conduct heat in solids is called ‘Thermal conductivity.”

Consider a bar with rectangular cross-section as shown in the figure. The faces ABCD and EFGH are maintained at θ₁ and θ₂ respectively (θ₁ > θ₂). Heat passes from one end to the other.

The amount of heat conducted (Q) depends on,

1. Amount of heat conducted Q is proportional to area of cross-section A perpendicular to flow.
   ∴ Q ∝ A ………. (1)
2. is proportional to temperature difference between the two ends.
   ∴ Q ∝ (θ₂ – θ₁) …………. (2)
3. is proportional to the time of flow.
   Q ∝ t ………. (3) and
4. is inversely proportional to the length of the conductor.
   Q ∝ \(\frac{1}{l}\) …………. (4)

where k = constant called coefficient of thermal conductivity.

Coefficient of thermal conductivity (k) :
It is defined as the amount of heat conducted normally per sec per unit area of cross-section per unit temperature gradient.
S.I. Unit w m k^-1
Dimensional formula = [ M¹L¹T^-3θ^-1]

Problem:
Thermal conductivity of copper,
K_c = 401 W/m-k
Temperature at one end, θ₂ = 104°C
Temperature of 2nd end, θ₁ = 24°C
Length of copper bar, l = 0.1 m; Area,
A = 1.0 × 10^-6 m^-2
Rate of conduction,

Question 2.
State the explain Newton’s law of cooling. State the conditions under which Newton’s law of cooling is applicable.
A body cools down from 60°C to 50°C in 5 minutes and to 40°C in another 8 minutes. Find the temperature of the surroundings. [TS May ’17, ’16; AP May ’13]
Answer:
Newtons’ Law of cooling :
The rate of loss of heat of the body is directly proportional to the difference of temperature of the body and the surroundings.

Explanation :
The law holds good only for small difference of temperature. Also, the loss of heat by radiation depends upon the nature of the surface of the body and the area of the exposed surface. We can write
– \(\frac{dQ}{dt}\) = k (T₂ – T₁) (sign indicates loss) …….. (1)

where k is a positive constant depending upon the area and nature of the surface of the body. Suppose a body of mass ‘m’ and specific heat capacity ‘s’ is at temperature T₂. Let T₁ be the temperature of the surroundings. If the temperature falls by a small amount dT₂ in time dt, then the amount of heat lost is
dQ = ms dT₂
∴ Rate of loss of hfeat is given by

where K = k/ms

Conditions (under which Newton’s law of cooling is applicable):
Newton’s law of cooling is applicable

1. loss of heat is negligible by conduction and only when it is due to convection.
2. loss of heat occurs in a streamlined flow of air i.e., forced convection.
3. temperature of the body is uniformly distributed over it.
4. temperature difference between the body and surroundings is moderate i.e., upto 30 K.

PROBLEM :
Let ‘θ_o‘ be the temperature of the surroundings.

In first case :
Initial temperature, θ₁ = 60°C
Final temperature, θ₂ = 50°C
Time of cooling, t = 5 minutes = 5 × 60 = 300s
From Newton’s law of cooling we can write,

In secoend case :
Initial temperature, θ₁ = 60°C
Final temperature, θ₂ = 40°C
Time of cooling, t = 13 minutes = 13 × 60 = 780s
Again from Newton’s law of cooling we can write,

On solving equations (1) and (2) we get, θ_o = 33.33°C

Problems

Question 1.
What is the temperature for which the readings on Kelvin Fahrenheit scales are same?
Solution:
On the Kelvin and Fahrenheit scales

Question 2.
Find the increase in temperature of aluminium rod if it’s length is to be increased by 1%. (α for aluminium = 25 × 10^-6/°C) [AP Mar. ’15; June ’15]
Solution:
Coefficient of linear expansion of aluminium, α = 25 × 10^-6/°C
We know that percentage increase in length

Question 3.
How much steam at 100°C is to be passed into water of mass 100g at 20°C to raise its temperature by 5°C? (Latent heat of steam is 540 cal / g and specific heat of water is 1 cal / g°C)
Solution:
Latent heat of steam, L_s = 540 cal/g
Specific heat of water, L_w = 1 cal / g°C
Mass of water, m_w = 100g

According to method of mixture or from the principle of calorimetry we can write, Heat lost by steam = heat gained by water
i.e., m_sL_s + m_sS_w(100 – t) = m_wS_w (t – 20)
∴ m_s × 540 + m_s × 1(100 – 25)
⇒ 100 × 1 × (25 – 20)
⇒ 615m_s = 500(or)m_s = \(\frac{500}{615}\) = 0.813 g

Question 4.
2 kg of air is heated at constant volume. The temperature of air is increased from 293 K to 313 K. If the specific heat of air at constant volume is 0.718 kJ/kg K, find the amount of heat absorbed in kJ and kcal. (J = 4.2 kJ/kcal.)
Solution:
Mass of air, m = 2 kg
Change in temperature, ∆T = 313 – 293 = 20K.
Specific heat at constant volume, C_v = 0.718 k.J/kg – K.
Heat mechanical equivalent, J = 4.2 kJ/k.cal.

∴ Heat energy absorbed,
Q = 2 × 0.718 × 10³ × 20. = 28.72 kJ
= 6.838 k calories.

Question 5.
A clock, with a brass pendulum, keeps correct time at 20°C, but loses 8.212 s per day, when the temperature rises to 30°C. Calculate the coefficient of linear expansion of brass.
Solution:
Temperature of correct time, t₁ = 20°C
Loss or gain of time in seconds per day = 8.212 sec.
Final temperature, t₂ = 30°C
∴ ∆t = 30 – 20 = 10
α of pendulum material = ?

In pendulum loss or gain of time in seconds per day = 43,200. α ∆t

Question 6.
A body cools from 60°C to 40°C in 7 minutes. What will be its temperature after next 7 minutes if the temperature of its surroundings is 10°C? [AP May ’13]
Solution:
In first case :
Initial temperature, θ₁ = 60°C
Final temperature, θ₂ = 40°C
Time of cooling, t₁ = 7 minutes
= 7 × 60 = 420s
Temperature of surroundings, θ₀ =10°C
From. Newton’s law of cooling, we can write,

In second case:
Initial temperature, θ₁ = 40°C
Time of cooling, t₂ = 7 minutes = 420s
Again, from Newton’s law of cooling we can write,

on solving equations (1) & (2) we get, 0 = 28°C

Question 7.
If the maximum intensity of radiation for a black body is found at 2.65 µ m, what is the temperature of the radiating body? (Wein’s constant = 2.9 × 10^-3 mK)
Solution:
Wavelength corresponding to maximum intensity, λ_max = 2.65 µm = 2.65 × 10^-6 m.
Wein’s constant, b = 2.90 × 10^-3 mK.
From Wein s Law, T = \(\frac{\mathrm{b}}{\lambda_{\mathrm{m}}}=\frac{2.90 \times 10^{-3}}{2.65 \times 10^{-6}}\)
= 1094 K.

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

TS Inter 1st Year English Grammar Tenses

Q.No. 12 (4 × 1 = 4 Marks)

VERB :

A verb is a word that tells about an action, a state of being or existence, possession, or a change in state.
ఒక పనిని గురించి గాని, ఒక స్థితి గురించి గాని యాజమాన్యం గురించి గాని, స్థితిలో మార్పు గురించి గాని తెలిపేది verb.
e.g. : The boy cried, (action)
I have a watch, (possession)
She is a nurse, (a state of being)
He became weak, (change in state)
పై వాక్యాలలోని cried, have, is, became అను పదాలు పనిని గాని స్థితిని గాని తెలుపుతున్నాయి. అందుచే అవి verbs.

TENSE

Tense : Tense is the form of the verb. It shows the time of the action or event. There are three tenses. They are :

1. Present Tense
2. Past Tense
3. Future Tense

Tense	Indefinite Simple form	Continuous form	Perfect	Perfect Continuous
Present Tense : Active Passive	I call. I am called.	I am calling. I am being called.	I have called. I have been called.	I have been calling. (No form)
Past Tense : Active Passive	I called. I was called.	I was calling. I was being called.	I had called. I had been called.	I had been calling. (No form)
Future Tense : Active passive	I shall call. I shall be called.	I shall be calling. (No form)	I shall have called. I shall have been called.	I shall have been calling. (No form)

THE USE OF THE TENSES

1. SIMPLE PRESENT OR PRESENT INDEFINITE TENSE :

1. It is used to express what actually happens at the time of speaking,
   e.g. :
   • Here comes John.
   • Children do not sit quietly in one place.
2. It is used to express habitual action :
   e.g. : I get up early in the morning.
3. It is used to express general or universal truths :
   e.g. : The earth is round.
   Stars twinkle
   We grow paddy.
   Speed thrills but kills.
4. It is used to express future action that has already been planned :
   e.g. : Our college reopens on 16th June.
   He sails for England next Monday.
5. It is used to express historic present:
   e.g. :
   • Sivaji now sees the danger and immediately kills Afzul Khan with his lion-claws,
   • Birbal now seizes the chance and cracks a joke on his rivals.

2. PRESENT CONTINUOUS TENSE :

1. It is used to express an action that is going on at the time of speaking :
   e.g. :She is dancing. They are writing.
2. It is used to express an action that will happen in the future.
   e.g. : 1) I am going to Mysore tomorrow.
3. It is used to show that some action is in the middle though it is not being done at that time.
   e.g. : I am reading a novel.

Note : The following verbs are not generally used in the Continuous Tense : (ఈ క్రింది verbs ను సామాన్యంగా continuous Tense లో ఉపయోగించరాదు )

Verbs of sense of perception :
hear, see, smell, notice, recognise, taste, feel.
Verbs of appearing : look, seem, appear.
Verbs of thinking :
Suppose, think, believe, realise, understand, know, imagine, mean, agree, consider, trust, remember, forget, expect, recall.
Verbs of emotions :
want, wish, desire, feel, like, love, hate, prefer, hope, refuse.
Miscellaneous :
own, possess, keep, concern, matter, owe etc.
e.g. : He is looking fine. (Wrong)
He looks fine. (Correct)
I am believing you. (Wrong)
I believe you. (Correct)
She is understanding me. (Wrong)
She understands me. (Correct)
I am hating you. (Wrong)
I hate you. (Correct)

3. PRESENT PERFECT TENSE :

i) It is used to denote an action that has just been completed.
e.g. : The train has arrived.
They have finished the work.

ii) It is used to express a past action the result of which continues :
e.g. : I have not seen Ravi for many months.
He has been ill since Monday.

iii) It is used to refer to a past action in a more general way :
e.g. : Have you ever been to Simla ?

iv) A few adverbs or adverbial phrases are used with the Present Perfect Tense :
just, never, ever, so far, till, yet, already, since, today, this week etc.
e.g. : I have just posted the letter.
So far he has not come.
He has not received the money yet.
This week there have been no rains.

4. PRESENT PERFECT CONTINUOUS TENSE :

It is used to refer to an action that begins in the past and continuous through a given period of time up to the present moment.
e.g. : I have been waiting here for Ramu for two hours.
I have been waiting here for Ramu since 3 p.m.

Note : ‘For’ denotes period of time.
‘Since’ denotes point of time.

Observe the following sentences :

1. He has been painting the door for 2 p.m. (Wrong)
   He has been painting the door since 2 p.m. (Correct)
2. The workers have been demanding more wages since ten days. (Wrong)
   The workers have been demanding more wages for ten days. (Correct)

5. SIMPLE PAST OR PAST INDEFINITE TENSE :

i) It is used to express the action completed in the past. Adverbs and adverbial phrases expressing Past time are often used with this tense.
(భూతకాలంలో పని పూర్తయినట్లయితే దానిని తెలుపుటకు Simple Past లేక Past Indefinite Tense ను వాడెదరు. భూతకాలాన్ని తెలిపే క్రియ విశేషణ పదాలు యీ tense లో ప్రయోగింపబడతాయి.)
e.g. : She met me yesterday.
The clerk did his work hurriedly.

ii) It is used to express a habitual action in the past.
(భూతకాలంలో అలవాటుగా చేసే పనులను విశదపరచుటకు Simple Past Tense వాడెదరు.)
e.g. : People performed child marriages in olden days. While I was in Chennai, I spoke to others in Tamil.

6. THE PAST CONTINUOUS TENSE :

It is used to express an action that was still going on in the past time.
(భూతకాలంలో పని కొనసాగింపును Past Continuous Tense తెలుపును.)
e.g. : I met Raghu while he was standing at the college gate.
We noticed some birds which were flying.

7. PAST PERFECT TENSE :

It is used to express an action which had been completed at some point in the past time before another action in the past. We use Past Perfect to refer to the earlier action and Simple Past to refer to the later action.
(భూతకాలంలో ముందు జరిగిన పనిని Past Perfect Tense లోను రెండవ పనిని Simple Past Tense లోను చెప్పాలి.)
e.g. : The train had left before they reached the station.
I had finished my work when Alfred came in.
పై వాక్యాలలోని మొదటి దానిని ఉదాహరణగా తీసుకుందాం. ఇందులో గతంలో జరిగిన రెండు పనులు సూచింపబడ్డాయి. The train left. They reached the station. ఇందులో ముందు జరిగినది The train left. దీనిని Past Perfect Tense లో చెప్పాలి. అప్పుడు వాక్యం The train had left before they reached the station. అయింది.)

8. PAST PERFECT CONTINUOUS TENSE :

It is used to show an action that had begun in the past and continued till some point of time in the past.
(భూతకాలంలో ఒక పని ఎప్పుడో ప్రారంభమై, అదే పని కొంత కాలము వరకు కొనసాగుతున్నదని Past Perfect Continuous Tense లో తెలపాలి. )
e.g. : I had been watching TV for an hour when my uncle came to see me.
We had been playing hockey for three hours when it started to rain.
She had been passing the information to the rivals for a long time before she was caught.

9. SIMPLE FUTURE (OR) FUTURE INDEFINITE TENSE :

It is used to express an action that will take place in the future.
(భవిష్యత్తు కాలంలో జరగబోయే పనిని Simple Future తెలుపును. )
e.g.: I shall meet you tomorrow.

10. FUTURE CONTINUOUS TENSE :
It is used to express an action going on at some point in future.
(భవిష్యత్తు కాలంలో జరగబోయే పనిని Future Continuous తెలుపును.)
e.g. : She will be sleeping then.
We will be playing the match at this time tomorrow.
I shall be writing a letter at this time on Monday.

11. FUTURE PERFECT TENSE :
It is used to express an action that will be completed at some point in the future :
(భవిష్యత్తులో ఒక నిర్ణీతకాలానికి పని పూర్తగునని Future Perfect Tense విశదపరచును.)
e.g. : I shall have done my work before you come.

12. FUTURE PERFECT CONTINUOUS TENSE :
It is used to refer to an action that will be in progress at a point in Future after continuing for a given period.
e.g. : I shall have been completing thirty years of service by next March.
I shall have been writing the examination for two hours by this time on Monday.

TENSES IN CONDITIONAL CLAUSES :

Clauses that show conditions are called conditional clauses. Sentences with conditional clauses use fixed patterns of Tenses.
Conditions are of four types :

1. Real conditions
2. Unreal or improbable conditions
3. Past unfulfilled conditions and
4. Zero conditions.

The tense forms used in a sentence are determined by the type of the condition in that sentence.

Look at the following examples :

1. If it rains, I will not come to your home.
   (Real condition-Simple present in the conditional clause and Simple Future in the main clause)
2. If I were a bird, I would fly high in the sky. (Unreal condition – Simple Past (were-even with I) in the conditional clause and ‘would+V’ in the main clause)
3. If he had worked hard, he would have passed the examination.
   (Past unfulfilled condition-Past Perfect in the conditional clause and would + have + Past Participle of verb in the main clause).
4. If you heat metals, they expand.
   (Zero conditions : The action certainly leads to the second action. Simple present is used in both the clauses).

The information may easily be noted in the table form.

s. No.	Type of condition	Tense in conditional clause	Tense in main clause
1	Real	Simple Present Ex : If you come early.	Simple Future we will go to our friends house.
2	Ureal	Simple Past If I were you	would + V I wouldn’t do that.
3	Past Unfulfilled	Past Perfect If she had started early	would + have + pp of verb she would have
4	Zero condition	Simple Present If you go higher	caught the train. Simple Present you see better.

ADDITIONAL EXAMPLES

1. SIMPLE PRESENT TENSE :

1. Indians love cricket.
2. He looks awful.
3. My father works in the USA.
4. South Indians eat a lot of rice.
5. We play in the field every week.
6. The train leaves at 5 pm.
7. The sun rises in the east.
8. Water boils at 100 degrees Celsius.
9. He practises yoga daily in the morning.
10. Heat evaporates water.
11. What goes up must come down.
12. Do you go for a walk every day ?
13. A cobra hisses when it is disturbed.
14. Cocks crow every morning.
15. He doesn’t wake up early in the morning.

Look at the following examples.

Which do you like more ? Tea or coffee ?
I like coffee.
What channel does your mother, watch usually ?
My mother watches ETV, mostly serials.
Do you read any English newspaper ?
Yes, I do / No, I don’t.
Does your father allow you to use a mobile ?
Yes, he does / No, he doesn’t.
Do your parents check your studies ?
Yes, they do / No, they don’t.

2. PRESENT CONTINUOUS TENSE :

1. I am reading an interesting novel.
2. I am also learning English.
3. We are going home late this week.
4. Ravi : Why are you mewing like a cat ?
   Sonu : I am trying to learn mimicry.
   Ravi : Are you undergoing training in mimicry ?
   Sonu : No, I am learning on my own with the help of my brother. In fact he is going to an institute.
5. Notice the difference.
   Where do you come from ? refers to your home town.
   Where’ are you coming from ? refers to the immediate place from where you are coming.
6. • It is raining heavily. (Now actually happening) _
   • She is going to the market.
   • They are doing business.
   • He is trying for a job.

Unacceptable	Acceptable
1. I am knowing the address.	I know the address.
2. She is resembling her mother.	She resembles her mother.
3. Is anyone here having a flat ?	Does anyone here have a flat ?
4. They are belonging to Kerala.	They belong to Kerala.
5. I am hating loud noise.	I hate loud noise.

3. PRESENT PERFECT TENSE :

i) He has just entered the room.
ii) I have seen the movie.
iii) Pussy cat, pussy cat where have you been ?
iv) I have been to London to see the queen.
v) I have been to Kashmir four times.
vi) The shop has been open for a month.
vii) He has just finished his homework.
viii) They have just gone out.
ix) He has painted die door. (It is still wet) 5
x) She has received the mail. (She is yet to read and respond)
xi) They have learnt dance for two weeks.
xii) My niece has lived in Delhi for two years.
(over this two year period extends till the present moment)
xiii) It has rained heavily this morning. (It is morning still)
xiv) My parents have been to the USA ten times.
xv) Have you ever met a film star or a sports star?
xvi) Has your teacher ever praised you ?
xvii) Have you ever seen a horse flying ?
xviii) When have you met a famous person ? (wrong)
When did you meet a famous person ? (right)
xix) 1 have met him last year, (wrong)
I met him last year, (right)
xx) We have lived in Warangal for years.
xxi) The players have arrived.
xxii) The beauty parloUr has been closed.
xxiii) They have noticed some printing mistakes in the book.
xxiv) I haye repaired the bike, (activity completed)

xxv) Some expressions used with the present perfect tense :
just, recently, lately, already, before, so far, still, ever / never, today, this morning, for weeks / years, since 2000, etc.

xxvi) Husband : Have you packed die luggage ?
Wife : Yes. I have.
Husband : Have you informed the neighbours about our trip ?
Wife : Yes. I have.
Husband : Have you phoned our daughter about our visit ?
Wife : No, I haven’t. Let’s give her a surprise.
Husband : Have you locked the door properly ?
Wife : Yes, 1 have.
Husband : Have you checked all the doors ?
Wife : Oh ! God ! I have forgotten to bolt the back door.
Husband : What!

4. PRESENT PERFECT CONTINUOUS TENSE

1. Harika has been reading a novel since morning.
2. The ladies have been playing Holi for two hours.
3. I have been repairing the bike for the last two hours.
   (the continuation of an activity is stressed)
4. I have been repairing the bike for two hours. (How long have you been repairing it ?)
5. We have been preparing seriously for the examination since 1st January.
6. We have been living in Hyderabad since 2000/ for over twenty years.
7. Keerthi : Hai Shravya ! So late ? I have been waiting here for an hour.
   Shravya : Oh ! Sorry Keerthi. But it has been raining for over an hour and my brother has been quarrelling with me for this umbrella. That’s why I am late.

Note :
Since refers to a point of time – since yesterday, since morning For refers to a period of time – for two days, for four weeks

5. SIMPLE PAST TENSE :

1. We lived in Hyderabad for thirty years.
2. Yesterday an accident took place near the railway station.
3. I walked a lot when I lived on campus.
4. They settled in Hyderabad ten years ago.
5. They didn’t eat anything yesterday.
6. Where did you go last week ?
7. Did he participate in the last week’s meeting ?
8. My brother completed degree last year.
9. India had a glorious past.
10. The player relaxed for ten minutes.
    (over that period in the past)
11. I contacted the secretary this morning.
    (It is afternoon or evening)
12. I attended all classes last week.
13. They lived here for a long time.
14. We went to school every day.

6. PAST CONTINUOUS TENSE :

1. It was raining at that time.
2. People were running all over the platform; they were pushing each other.
3. Two women were walking when the bus came from the opposite direction.
4. When I reached my home at eight, my daughter was playing the guitar and my parrot was singing the tunes. My son was eating a chocolate and my wife was relaxing in a chair.
5. You were doing home work at 6 p.m. yesterday, (a past point of time)
6. The children were playing cricket all the day yesterday.
   (over a period of time in the past)
7. I was making tea when her friend came, (at the time of another past event)
8. What were you doing when your father returned home ?
9. What was your sister doing why your mother was reading a novel ?

7. PAST PERFECT TENSE :

1. My friend had completed the homework by the time I went to his room.
2. The bus had left before we reached the bus station.
3. I had typed the letter before the officer came.
   (= First I typed the letter and then the officer came.)
4. The chain snatcher had escaped before the police arrived.
   (= First the chain snatcher escaped and then the police arrived)
5. We had already consulted a doctor before my father had an attack.
6. He rushed to the station but the train had left.
7. I realized that my pocket had been picked.
8. I recognized the man as I had met him last week.
9. Our trip was comfortable as we had made arrangements earlier.
10. Reshma felt sleepy as she had stayed Up through the night.
11. The student was punished as he had not done his homework.
12. Srikanth had never seen skyscrapers before he went to New York.
13. She did not see me till I had seen her.
    (= First I saw her and then she saw me)
14. I had received your letter yesterday. (NOT acceptable)
    I received your letter yesterday. (When we talk about only ONE past action in a sentence, simple past is acceptable, Not past perfect.) (acceptable)

8. PAST PERFECT CONTINUOUS TENSE :

1. He had been playing cricket since he was a boy but gave it up later when he took up a job.
2. I had been singing a song for five minutes when my friend came.
3. Sureshan had been doing research for two years when his sister joined the university.
4. The murderer had been holding the knife for five minutes when the police entered the room. (Both activities happened in the past.)

9. SIMPLE FUTURE TENSE :

1. Srihan and Srihith will come from the US next August.
   They will stay here for three weeks.
2. I will conduct a quiz competition on spelling tomorrow.
3. The President will stay in Hyderabad for a month.
4. The Chief Minister will conduct a press meet.
5. They will not start the road-work tomorrow.
6. Will they plant the saplings ?
7. When will you inform them ?
8. Shall we have some coffee ?
9. Shall we sit here ?

10. FUTURE CONTINUOUS TENSE :

1. We will be spending our holidays in Shimla this summer.
2. She will be sleeping when I reach home.
3. Dinesh : Vijay, What’s your tomorrow’s programme ?
   Vijay : I will be washing my car at this time tomorrow.
   Dinesh : Don’t you have a driver ?
   Vijay : No, I myself do it every Sunday. What about you ?
   Dinesh : I will be spending my time in the library.
   Vijay, : Good. I like it.
4. As tomorrow is a holiday they will be playing at this time.
5. He will be meeting Venkat next week. (Perhaps, they are colleagues.)

11. FUTURE PERFECT TENSE :

1. We will have cleared the entire loan amount in four years from now.
2. She will have recovered from her illness by next week.
3. Sloka : When are you going to start your medical practice ?
   Sneha : My medical course is not yet over.
   Sloka : Is it so ?
   Sneha : Yes, I will have completed the M.B.B.S. course by 2022.
   Sloka : Oh ! I will have put jn two years of experience in a software job by then.
   Sneha : Of course, but I want to serve the rural poor as a doctor.
   Sloka : Great! You are right. There are very few committed people like you.
   Sneha : In fact, my uncle serves as a doctor in a village in Karimnagar District. He will have served there for ten years by next year.
   Sloka : Great! A family of committed doctors !!
4. We save Rs. 1000/- a month. We started saving in January last. We shall have saved Rs. 12,000/- by the end of the year.
5. They boarded the train at 6 o’ clock in the evening. They will have reached Delhi tomorrow morning by 7.
6. The teachers will have completed the lessons by the end of the acedemic year.

12. FUTURE PERFECT CONTINUOUS TENSE :

1. They will have been travelling for 26 hours in the train when they reach Varanasi.
2. I will have been teaching them grammar for five years when they leave school next year.
3. He will have been staying in the USA for three years when I go there next month.

FUTURE TIME REPRESENTATION :
a) Using simple present tense :
The President visits Hyderabad tomorrow.
My examinations begin next week.
(These are events that are scheduled and are sure to happen. In such cases we use simple present to express a future action.)

b) Using present progressive tense : (Present continuous tense) We are planning an exhibition of paintings in December this year.
You are visiting Bali on your trip to Indonesia next month. (These are events that have been planned. Very likely these events will take place in the future, but there is a likelihood of these events being rescheduled. However, they are yet to happen.)

c) Using going to
I am going to buy a new car on the 1st of next month.
I am going to be a doctor in five years from now.
(The phrase going to is used to of talk actions that we intend to do or plan to achieve. To express a future possibility, this structure is used.)

d) Use of modal will / should :
I will buy a gift when you pass the examination.
You will join a good engineering college if you get a first class.
You should join the army if you choose to serve the country.
We shall be in touch and discuss this matter.
(Will and Shall are modal verbs that help us to express our desire or propositions.

Exercises

I. Fill in the blanks with the present simple or the present continuous of the verbs given in brackets.

1. Custard apple ………………….. (be) a tasty and healthy fruit.
2. The moon ………………….. (appear) at night.
3. I ………………….. (rain) now. We can’t go now.
4. A ray of the sun ………………….. (not, pass) through a wall.
5. Hyderabad ………………….. (be) the Capital of Telangana state.
6. All banks ………………….. (open) on the first and the third Saturday of the month.
7. People ………………….. (speak) Telugu all over AP and Telangana.
8. My English teacher usually ………………….. (speak) English in the classroom, but surprisingly she ………………….. (speak) Telugu now.
9. ………………….. North Indians ………………….. (eat) chapatis daily ?
10. ………………….. he ………………….. (do) any job at present ?
11. Usually I ………………….. (close) all doors before going to bed.
12. ………………….. you………………….. (believe) in ghosts ?
13. My father ………………….. (watch) a serial at the moment.
14. Water ………………….. (freeze) during winter in some parts of the Atlantic Ocean.
Answer:
1) is
2) appears
3) is raining
4) does not pass
5) is
6) open
7) speak
8) speaks, is speaking
9) Do, eat
10) Does do / is doing
11) close
12) Do, believe
13) is watching
14) freezes

II. Fill in the blanks with the present perfect or the present perfect continuous of the verbs given in brackets.

1. Aarthi ………………….. (act) in films since her marriage with Raghu, a film director.
2. She ………………….. (appear) in about twenty films so far.
3. I ………………….. just ………………….. (receive) a call.
4. She ………………….. (not, pay) the exam fee yet.
5. How ………………….. you ………………….. (watch) this TV programme.
Answer:
1) has been acting
2) has appeared
3) have, received
4) has not paid
5) have, watched

III. Fill in the blanks with the Simple Past, the Past Continuous, the Past Perfect or Past Perfect Continuous forms of the verbs given in brackets.

1. The tsunami ………………….. (break) while the sailors ………………….. (row) the boats.
2. How ………………….. you ………………….. (spend) your childhood ?
3. I ………………….. (browse) the internet when he came to our house.
4. The audience ………………….. (occupy) their seats before the cinema began.
5. The farmers ………………….. (sow) seeds for two hours when the sun set.
6. There was a stampede when the pilgrims suddenly ………………….. (rush) into the temple.
7. I wish I ………………….. (have) a car.
8. When ………………….. (be) you born ?
9. How long ………………….. your brother ………………….. (stay) in the US when you went there for MS ?
10. Gandhi ………………….. (pass away) in 1948.
Answer:
1) broke, were rowing
2) did, spend
3) was browsing
4) had occupied
5) had been sowing
6) rushed
7) had
8) were
9) had, been staying
10) passed away

IV. Fill in the blanks with the Simple Future, the Future Continuous, the Future Perfect or Future Perfect Continuous forms of the verbs given in brackets.

1. Telangana ………………….. (become) a developed state in two years.
2. The umpire ………………….. (resolve) the controversy within a few minutes.
3. At this point of time tomorrow the children ………………….. (watch) a cartoon film.
4 ………………….. you ………………….. (solve) all these problems by next week ?
5. If we follow A.RJ. Kalam’s advice, India ………………….. soon ………………….. (become) a superpower.
6. He ………………….. (do) the job for two years by next year.
Answer:
1) will become
2) will resolve
3) will be watching
4) will, have solved
5) will, become
6) will have been doing

V. Fill in the blanks with appropriate forms of the verbs given in brackets.

1. Surya Namaskar ………………….. (consist) of twelve postures.
2. Gandhi ………………….. (influence) by the writings of Tolstoy.
3. Bandla Sirisha ………………….. (be) the first Telugu woman (third Indian origin woman) to go into the space on July 11, 2021.
4. Rohit Sharma ………………….. (bat) for two hours when rain interrupted the match.
5. The meeting ………………….. (start) by 10.00 a.m. tomorrow.
6. Usually my father ………………….. (take) rice for lunch, But now he ………………….. (take) chapatis.
7. People ………………….. (speak) Telugu in Telangana and Andhra Pradesh.
8. Mary ………………….. (eat) her supper by 7.00 p.m.
9. Don’t disturb ! The child ………………….. (sleep)
10. If I ………………….. (be) a bird, 1 would fly high in the sky to have a beautiful view of the earth.
11. It is time we ………………….. (start) working hard.
12. If I were you, I ………………….. (construct) an independent house.
13. Don’t get off the train till it ………………….. (stop).
14. Listen ! Somebody ………………….. (scream).
15. A parrot ………………….. (repeat) our voice as soon as it listens to it.
16. Vinay ………………….. (lose) the job last year because of his misbehaviour.
17. Dhirubai Ambani ………………….. (not, live) in a costly house even when he was a famous industrialist.
18. ………………….. he ………………….. (play) tennis dally ?
19. While I ………………….. (teach) grammar, a student raised a doubt.
20. A philanthropist ………………….. (think) about the welfare of others.
21. My nephew ………………….. (do) business in Hyderabad for the last ten years.
22. The moon ………………….. (wax) and ………………….. (wane) during the cycle of a month.
23. I ………………….. (know, not) the right answer right now.
24. We ………………….. (have) hot coffee one hour ago.
25. The birds ………………….. just ………………….. (fly) away.
Answer:
1) consists
2) was influnced
3) is
4) had been batting
5) will have started
6) takes … is taking
7) speak
8) will have eaten
9) is sleeping
10) were
11) started
12) would construct
13) stops
14) is screaming
15) repeats
16) lost
17) did not live
18) Does … play
19) was teaching
20) thinks
21) has been doing
22) waxes … wanes
23) do not know
24) had
25) have … flown

VI. Rewrite the following sentences correcting the underlined parts :

1. He is doing homework since 8 o’ clock.
2. If they are going out, we will follow them.
3. If you will depend on others for everything, you will not learn anything.
4. If you have helped your mother, she would have felt happy.
5. He is trying for a job since last year.
6. Mukesh Ambani has constructed the world’s costliest house for his wife in Mumbai four years ago.
7. He has returned from Dubai a month ago.
8. He is not having any cash.
9. I am knowing them for the last many years.
10. Is he remembering our help ?
11. He has borrowed a thousand rupees from me yesterday.
12. Don’t disturb him. He reads.
13. Did you left for Hyderabad last year ?
14. Sangeetha joins us tomorrow.
15. Are you smelling anything bad ?
Answer:
1. He has been doing homework since 8 o’ clock.
2. If they go out, we will follow them.
3. If you depend on others for everything, you will not learn anything.
4. If you had helped your mother, she would have felt happy.
5. He has been trying for a job since last year.
6. Mukesh Ambani constructed the world’s costliest house for his wife in Mumbai four years ago.
7. He returned from Dubai a month ago.
8. He doesn’t have any cash.
9. I have known them for the last many years.
10. Does he remember our help ?
11. He borrowed a thousand rupees from me yesterday.
12. Don’t disturb him. He is reading.
13. Did you leave for Hyderabad last year ?
14. Sangeetha will join us tomorrow. (Sangetha is joining us tomorrow)
15. Do you smell anything bad ?

VII. Fill in the blanks with suitable forms of the verbs given in brackets.

Two Sides of Life

Question 1.
There …………………… (be) quite a number of divisions into which life …………………… (be + divide).
Answer:
are ……………………. can be divided

Question 2.
You …………………… …………………… (sometimes / find) two persons who …………………… (get up) in the morning, perhaps a morning that …………………… (be) overcast with shadows.
Answer:
will sometimes find … get up … is

Question 3.
A good teacher …………………… (say) frankly and dearly, “I …………………… (not know). I …………………… (not answer). that question.”
Answer:
will say; don’t know, cannot answer

Question 4.
I …………………… (hear) those tales so manytimes that I …………………… (not want) to get into the atmosphere of the people who …………………… (tell) them.
Answer:
had heard; didn’t want; told

Question 5.
In nine cases out of ten, the person who …………………… (cultivate) the habit of looking on the dark side of life …………………… (be) the little person, the miserable person, the one who …………………… (be) weak in mind, heart and purpose.
Answer:
cultivates; is; is

Question 6.
No teacher …………………… (know) everything about every subject.
Answer:
knows

Question 7.
They …………………… (be) the people who never …………………… (go) forward.
Answer:
are; go

Question 8.
You …………………… (not, accomplish) the task we expect of you if you go with a moody, discouraged,
fault-finding disposition.
Answer:
will not accomplish

Father, Dear Father

Question 9.
This …………………… (be) in answer to your letter about my transgression.
Answer:
is

Question 10.
The operating word ‘think’ …………………… (make) me muse.
Answer:
did make

Question 11.
Father, we’ve never really been close, and I can’t rightly say you …………………… ……………………(be) my friend, philosopher, guide etc.
Answer:
have been

Question 12.
…………………… you …………………… (apply) Pythagoras Theorem or Newton’s law of Gravity ?
Answer:
Do apply

Question 13.
My grandfather …………………… (speak) of a carefree and beautiful childhood.
Answer:
speaks

Question 14.
Father, …………………… he …………………… (fib) ?
Answer:
is… fibbing

Question 15.
She …………………… (be) at peace with her pots, pans and Bhagavad Geeta.
Answer:
is

Question 16.
…………………… it Adam arid Eve …………………… (eat) the Tree of knowledge, all over again ?
Answer:
is … eating

Question 17.
Last week my rose plant …………………… (die).
Answer:
died

Question 18.
I …………………… (ask) my Biology teacher what I …………………… (do) to save it.
Answer:
asked; should do

Question 19.
If I …………………… (be) to meet Newton face to face, I …………………… (fail) to recognise him, so busy am I learning about him !
Answer:
were; would fail

Question 20.
If he …………………… (say) George Bush is the president of India, it (have) to be so.
Answer:
says; will have

The Green Champion – Thimmakka

Question 21.
Every year, the count of these trees …………………… (keep) increasing.
Answer:
kept

Question 22.
Thimmakka (She) not only …………………… (plant) those trees but also …………………… (fence), …………………… (water) and …………………… (guard) them.
Answer:
planted; fenced; watered; guarded

Question 23.
Although Thimmakka …………………… (not receive) a formal education, her work …………………… (honour) with the National Citizen’s Award of India.
Answer:
did not receive; has been honoured

Question 24.
Saalumarada Thimmakka …………………… (be) an individual who …………………… (bring) worldwide recognition to the state of Karnataka through her incredible and massive environmental services.
Answer:
is … has brought

The First Four Minutes

Question 25.
If I …………………… (falter), there …………………… (be) no arms to hold me and the world …………………… (be) a cold, forbidding place, because I …………………… (be) so close.
Answer:
faltered; would be; would be; had been

Question 26.
Blood …………………… (surge) from my muscles and …………………… (seem) to fell me.
Answer:
surged; seemed

Question 27.
I …………………… (know) it would be some time before I …………………… (catch) up with myself.
Answer:
knew; caught

Question 28.
I felt that the moment of a lifetime …………………… (come).
Answer:
had come

Question 29.
The air I breathed …………………… (fill) me with the spirit of the track where I had run my first race.
Answer:
filled

Question 30.
I felt suddenly and gloriously free of the burden of athletic ambition that I …………………… (carry) for years.
Answer:
had been carrying

Box and Cox

Question 31.
At present I …………………… (be) entirely of your opinion because I …………………… (have) not the most distant particle of an idea what you …………………… (mean).
Answer:
am; have; mean

Question 32.
The gentleman who …………………… (get) the attic …………………… (be) hardly ever without a pipe in his mouth and there he …………………… (sit) with his feet upon the mantelpiece.
Answer:
has got; is; sits

Question 33.
I …………………… (be) so dreadfully puzzled to know what to say when Mr. Cox …………………… (speak) about it.
Answer:
was; spoke

Question 34.
Why …………………… (not) you …………………… (keep) your own side of the staircase, sir ?
Answer:
don’t; keep

Question 35.
She …………………… (think) to cook her breakfast while I …………………… (be) asleep with my coals.
Answer:
thought; was

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

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

Question 1.
Find the angle between the vectors i̅ + 2j̅ + 3k̅ and 3i̅ – j̅ + 2k̅. [Mar. ’17(TS), ’14, ’10] [Mar. ’18(AP)]
Answer:
Let a̅ = i̅ + 2 j̅ + 3k̅ and b̅ = 3i̅ – j̅ + 2k̅

Let θ be the angle between the vectors a and b then cos θ = \(\frac{\bar{a} \cdot \bar{b}}{|\bar{a}||\bar{b}|}\)

∴ θ = 60°

If a̅ = 6i̅ + 2j̅ + 3k̅ and b̅ = 2i̅ – 9j̅ + 6k̅ then find a̅. b̅ and the angle between a̅ and b̅. [Mar ’98]
Answer:
12, cos^-1\(\left(\frac{12}{77}\right)\)

Question 2.
If a̅ = i̅ + 2j̅ – 3k̅ and b̅ = 3i̅ – j̅ + 2k̅, then show that a̅ + b̅ and a̅ – b̅ are perpendicular to each other. [Mar. ’15(AP); Mar ’11; Mar. ’10, ’08; B.P]
Answer:
Given vectors are a̅ = i̅ + 2j̅ – 3k̅ and b̅ = 3i̅ – j̅ + 2k̅
Now a̅ + b̅ = i̅ + 2j̅ – 3k̅ + 3i̅ – j̅ + 2k̅ = 4i̅ + j̅ – k̅
a̅ – b̅ = i̅ + 2j̅ – 3k̅ – 3i̅ + j̅ – 2k̅ = -2i̅ + 3j̅ – 5k̅
Now, (a̅ + b̅) . (a̅ – b̅) = (4i̅ + j̅ – k̅) . (-2i̅ + 3 j̅ – 5k̅)
= -8 + 3 + 5 = -8 + 8 = 0
∴ a̅ + b̅ and a̅ – b̅ are perpendicular to each other.

Question 3.
Let a̅ and b̅ be non – zero, non-collinear vectors. If |a̅ + b̅| = |a̅ – b̅| then find the angle between a̅ and b̅. [Mar. ’94]
Answer:
Given |a̅ + b̅| = |a̅ – b̅|
Squaring on both sides ⇒ |a̅ + b̅|² = |a̅ – b̅|²
⇒ a̅² + b̅² + 2a̅. b̅ = a̅² + b̅² – 2a̅.b̅
⇒ 4a̅.b̅ = 0
⇒ a̅.b̅ = 0
∴ Angle between a̅ and b̅ is 90°.

Question 4.
If the vectors 2i̅ + λj̅ – k̅ and 4i̅ – 2j̅ + 2k̅ are perpendicular to each other, then find λ. [Mar ’15(TS); May ’05; Mar. ’05]
Answer:
Let a̅ = 2i̅ + λj̅ – k̅; b̅ = 4i̅ – 2j̅ + 2k̅
Since the vectors a and b are perpendicular, then a̅ . b̅ = 0
(2i̅ + λj̅ – k̅) . (4i̅ – 2j̅ + 2k̅) = 0
8 – 2λ – 2 = 0
6 – 2λ = 0
⇒ 2λ = 6
⇒ λ = 3

For what values of λ, the vectors i̅ – λj̅ + 2k̅ and 8i̅ + 6 j̅ – k̅ are at right angles ?
Answer:
1

If the vectors λi̅ – 3j̅ + 5k̅ and 2λi̅ – λj̅ – k̅ are perpendicular to each other then find λ. [Mar. ’19(AP); Mar ’16(TS); May ’14]
Answer:
\(\frac{-5}{2}\) or 1.

Question 5.
Let a̅ = i̅ + j̅ + k̅ and b̅ = 2i̅ + 3j̅ + k̅, find projection vector of b̅ on a̅ and its magnitude.
Answer:
Orthogonal projection of vector b̅ on a̅ is
= \(\frac{(\bar{a} \cdot \bar{b}) \bar{a}}{|\bar{a}|^2}=\frac{[(\bar{i}+\bar{j}+\bar{k}) \cdot(2 \bar{i}+3 \bar{j}+\bar{k})]}{|\bar{i}+\bar{j}+\bar{k}|^2}\)
= \(\frac{(2+3+1)}{(\sqrt{3})^2}\)(i̅ + j̅ + k̅) = 2(i̅ + j̅ + k̅)
Magnitude = |2(i̅ + j̅ + k̅)| = 2\(\sqrt{1+1+1}\) = 2√3

If a̅ = i̅ – j̅ – k̅ and b̅ = 2i̅ – 3j̅ + k̅, then find the projection vector of b̅ on a̅ and its magnitude. [Mar ’17(AP), ’91]
Answer:
\(\frac{4}{3}\)(i̅ – j̅ – k̅); \(\frac{4}{\sqrt{3}}\)

Question 6.
If a̅ = 2i̅ + 2j̅ – 3k̅, b̅ = 3i̅ – j̅ + 2k̅, then find the angle between the vectors 2a̅ + b̅ and a̅ + 2b̅. [Mar ’02; Mar. ’02]
Answer:
Given that a̅ = 2i̅ + 2j̅ – 3k̅, b̅ = 3i̅ – j̅ + 2k̅
Now, 2a̅ + b̅ = 2(2i̅ + 2 j̅ – 3k̅) + 3i̅ – j̅ + 2k̅
= 7i̅ + 3 j̅ – 4k̅
a̅ + 2b̅ = 2i̅ + 2j̅ – 3k̅ + 2(3i̅ – j̅ + 2k̅)
= 8i̅ + k̅
If θ is the angle between 2a̅ + b̅ and a̅ + 2b̅ then

Question 7.
If a̅ = 2i – j̅ + k̅ and b̅ = i̅ – 3j̅ – 5k̅, then find a̅ × b̅. [Mar. ’13]
Answer:
a̅ = 2 i̅ – j̅ + k̅ and b̅ = i̅ – 3j̅ – 5k̅

a̅ × b̅ = \(\left|\begin{array}{rrr}
\overline{\mathrm{i}} & \overline{\mathrm{j}} & \overline{\mathrm{k}} \\
2 & -1 & 1 \\
1 & -3 & -5
\end{array}\right|\) = i̅ (5 + 3) – j̅ (-10 -1) + k̅ (- 6 +1) = 8i̅ +11j̅ – 5k̅
∴ |a̅ × b̅| = \(\sqrt{64+121+25}=\sqrt{210}\)

Question 8.
If 4i̅ + \(\frac{2p}{3}\) j̅ + pk̅ is parallel to vector i̅ + 2j̅ + 3k̅, find p.
Answer:
Let a̅ = 4i̅ + \(\frac{2p}{3}\) j̅ + pk̅, b̅ = i̅ + 2j̅ + 3k̅
Since the vector a̅ and b̅ are parallel then
⇒ \(\frac{4}{1}=\frac{2 p / 3}{2}=\frac{p}{3}\)
⇒ 4 = \(\frac{\mathrm{p}}{3}=\frac{\mathrm{p}}{3} \Rightarrow \frac{\mathrm{p}}{3}\) = 4
⇒ p = 12

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

Find the area of the parallelogram for which the vectors a̅ = 2i̅ – 3j̅ and b̅ = 3i̅ – k̅ are adjacent sides. [Mar. ’12, ’08, ’07; Mar. ’08]
Answer:
\(\sqrt{94}\) sq. units.

Question 10.
Find the area of the parallelogram whose diagonals are 3i̅ + j̅ – 2k̅ and i̅ – 3j̅ + 4k̅. [May ’02]
Answer:
Let a̅ = 3i̅ + j̅ – 2k̅ & b̅ = i̅ – 3j̅ + 4k̅
a̅ × b̅ = \(\left|\begin{array}{ccc}
\bar{i} & \bar{j} & \bar{k} \\
3 & 1 & -2 \\
1 & -3 & 4
\end{array}\right|\)
= i̅(4 – 6) – j̅(12 + 2) + k̅(-9 – 1) = -2i̅ – 14j̅ – 10k̅
|a̅ × b̅| = \(\sqrt{(-2)^2+(-14)^2+(-10)^2}\)
= \(\sqrt{4+196+100}\)
= \(\sqrt{300}\) = 10√3

The area of the parallelogram whose diagonals a̅ and b̅ is
\(\frac{1}{2}\)|a̅ × b̅| = \(\frac{1}{2}\) × 10√3 = 5√3 sq.units

Question 11.
W Find unit vector perpendicular to the plane determined by the vectors a̅ = 4i̅ + 3j̅ – k̅ and b̅ = 2i̅ – 6j̅ – 3k̅.
Answer:
Given vectors are a̅ = 4i̅ + 3j̅ – k̅ and b̅ = 2i̅ – 6j̅ – 3k̅
a̅ × b̅ = \(\left|\begin{array}{ccc}
\overline{\mathrm{i}} & \overline{\mathrm{j}} & \overline{\mathrm{k}} \\
4 & 3 & -1 \\
2 & -6 & -3
\end{array}\right|\)
= i̅(-9 – 6) – j̅(-12 + 2) + k̅(-24 – 6) = -15i̅ + 10j̅ – 30k̅

|a̅ × b̅| = \(\sqrt{(-15)^2+(10)^2+(-30)^2}\)
= \(\sqrt{225+100+900}=\sqrt{1225}\) = 35
∴ The unit vector perpendicular to the plane determined by the vector a̅ and b̅ = \(\pm \frac{(\bar{a} \times \bar{b})}{|\bar{a} \times \bar{b}|}\)
= \(\pm \frac{(-15 \overline{\mathrm{i}}+10 \overline{\mathrm{j}}-30 \overline{\mathrm{k}})}{35}=\pm \frac{(-3 \overline{\mathrm{i}}+2 \overline{\mathrm{j}}-6 \overline{\mathrm{k}})}{7}\)

If a̅ = 2i̅ – 3j̅ + 5k̅, b̅ = -i̅+ 4j̅ + 2k̅ then find a̅ x b̅ and unit vector perpendicular to both a̅ and b̅.
Answer:
\(\pm\left(\frac{1}{\sqrt{782}}\right)\)(-26i̅ – 9j̅ + 5k̅)

Find unit vector perpendicular to both i̅ + j̅ + k̅ and 2i̅ + j̅ + 3k̅.
Answer:
\(\pm \frac{1}{\sqrt{6}}\)(2i̅ – j̅ – k̅)

Question 12.
Let a̅ = 2i̅ – j̅ + k̅ and b̅ = 3i̅ + 4j̅ – k̅. If θ is the angle between a̅ and b̅, then find sin θ.
Answer:
Given a̅ = 2i̅ – j̅ + k̅ and b̅ = 3i̅ + 4j̅ – k̅

Question 13.
Compute [i̅ – j̅ j̅ – k̅ k̅ – i̅] [Mar ;’96; Mar. ’95]
Answer:
[i̅ – j̅ j̅ – k̅ k̅ – i̅] = \(\left|\begin{array}{rrr}
1 & -1 & 0 \\
0 & 1 & -1 \\
-1 & 0 & 1
\end{array}\right|\) = 1(1 – 0) + 1(0 – 1) + 0(0 + 1)
= 1(1) + 1(-1) + 0(1) = 1 – 1 = 0

Question 14.
If a̅ = i̅ – 2j̅ – 3k̅, b̅ = 2i̅ + j̅ – k̅, c̅ = i̅ + 3j̅ – 2k̅ then compute a̅.(b̅ × c̅). [May ’08]
Answer:
Given a̅ = i̅ – 2j̅ – 3k̅, b̅ = 2i̅ + j̅ – k̅, c̅ = i̅ + 3j̅ – 2k̅ then
a̅.(b̅ × c̅) = [a̅ b̅ c̅] = \(\left|\begin{array}{ccc}
1 & -2 & -3 \\
2 & 1 & -1 \\
1 & 3 & -2
\end{array}\right|\)
= 1(-2 + 3) + 2(-4 – 1) – 3(6 – 1) = 1 – 6 – 13 = -20

If a̅ = (1, -1, -6), b̅ = (1, -3, 4) and c̅ = (2, -5, 3), then compute a̅.(b̅ × c̅).
Answer:
0

Question 15.
Find the volume of the parallelopiped having coterminus edges i̅ + j̅ + k̅, i̅ – j̅ and i̅ + 2j̅ – k̅. [May ‘09; Mar. ‘03]
Answer:
Let a̅ = i̅ + j̅ + k̅,
b̅ = i̅ – j̅
and c̅ = i̅ + 2j̅ – k̅
The volume of parallelopiped having coterminus edges a̅, b̅, c̅ is = [a̅ b̅ c̅]
= \(\left|\begin{array}{rrr}
1 & 1 & 1 \\
1 & -1 & 0 \\
1 & 2 & -1
\end{array}\right|\)
= 1(1 – 0) – 1(-1 – 0) + 1(2 + 1)
= 1(1) – 1(-1) + 1(3)
= 1 + 1 + 3
= 5 cubic units.

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:
14 cubic units.

Question 16.
For non coplanar vectors a̅, b̅ and c̅, determine p for which the vectors a̅ + b̅ + c̅, a̅ + pb̅ + 2c̅ and -a̅ + b̅ + c̅ are coplanar. [May ’01]
Answer:
Given a̅, b̅, c̅ are non coplanar vector we have [a̅ b̅ c̅] ≠ 0
If the vectors a̅ + b̅ + c̅, a̅ + pb̅ + 2c̅ and -a̅ + b̅ + c̅ are coplanar
Then [a̅ b̅ c̅]\(\left|\begin{array}{ccc}
1 & 1 & 1 \\
1 & p & 2 \\
-1 & 1 & 1
\end{array}\right|\) = 0
\(\left|\begin{array}{ccc}
1 & 1 & 1 \\
1 & p & 2 \\
-1 & 1 & 1
\end{array}\right|\) = 0 (∵ [a̅ b̅ c̅] ≠ 0)
⇒ 1(p – 2) – 1(1 + 2) + 1(1 + p) = 0
⇒ p – 2 – 3 + 1 + p = 0
⇒ 2p – 4 = 0
⇒ 2p = 4
⇒ p = 2

Find ‘t’ for which the vectors 2i̅ – 3j̅ + k̅, i̅ + 2j̅ – 3k̅ and j̅ – tk̅ are coplanar.
Answer:
1

If the vector a̅ = 2i̅ – j̅ + k̅, b̅ = i̅ + 2j̅ – 3k̅ and c̅ = 3i̅ + pj̅ + 5k̅ are coplanar then find p.
Answer:
-4.

Question 17.
Determine λ for which the volume of the parallelopiped having coterminus edge; i̅ + j̅, 3i̅ – j̅ and 3j̅+ λk̅ is 16 cubic units. [May
Answer:
Let a̅ = i̅ + j̅, b̅ = 3i̅ – j̅ and c̅ = 3j̅+ λk̅
The volume of the parallelopiped having coterminus edges a̅, b̅, c̅ is [a̅ b̅ c̅]
Given that the volume of the parallelopiped = ± 6
[a̅ b̅ c̅] = ±6 = \(\left|\begin{array}{rrr}
1 & 1 & 0 \\
3 & -1 & 0 \\
0 & 3 & \lambda
\end{array}\right|\) =±16
⇒ 1(-λ -0) -1(3λ – 0) + 0(9 – 0) = ± 16
⇒ -λ – 3λ + 0 = ± 16
⇒ -4λ =± 16
⇒ λ = ±4

Question 18.
Show that i̅ × (a̅ × i̅) + j̅ × (a̅ × j̅) + k̅ × (a̅ × k̅) = 2a̅ for any vector a̅. [Mar. ’03; May ’98]
Answer:
Let a = xi̅ + yj̅ + zk̅
Now i̅ × (a̅ × i̅) = (i̅.i̅)a̅ – (i̅.a̅)i̅ = a̅ – (i̅.a̅)i̅;
j̅ × (a̅ × j̅) = a̅ – (j̅.a̅)j̅;
k̅ ×(a̅ × k̅) = a̅ – (k̅.a̅)k̅

LHS = i̅ x (a̅ x i̅) + j̅ x (a̅ x j̅) + k̅ x (a̅ x k̅)
= a̅ – (i̅.a̅)i̅ + a̅ – (j̅ . a̅)j̅ + a̅ – (k̅ . a̅)k̅
= 3a̅ – [(i̅.a̅)i̅ +(j̅.a̅)j̅ + (k̅.a̅)k̅]
= 3a̅ – [(x)i̅ + (y)j̅ (z)k̅]
= 3a̅ – a̅ = 2a̅
= RHS

Question 19.
For any three vectors a̅, b̅, c̅ , prove that [b̅ + c̅ c̅ + a̅ a̅ + b̅] = 2[a̅ b̅ c̅]. [Mar. ’00, ’99]
Answer:
LHS = [b̅ + c̅ c̅ + a̅ a̅ + b̅]
= [a̅ b̅ c̅]\(\left|\begin{array}{lll}
0 & 1 & 1 \\
1 & 0 & 1 \\
1 & 1 & 0
\end{array}\right|\) = [a̅ b̅ c̅][0(0 – 1) – 1(0 – 1) + 1 (1 – 0)]
= [a̅ b̅ c̅][0 + 1 + 1] = 2[a̅ b̅ c̅] = R.H.S

Question 20.
For any three vectors a̅, b̅, c̅, prove that [b̅ × c̅ c̅ × a̅ a̅ × b̅] = [a̅ b̅ c̅]². [May ’02, ’98]
Answer:
LHS = [b̅ × c̅ c̅ × a̅ a̅ × b̅] = (b̅ × c̅).[(c̅ × a̅) × (a̅ × b̅)]
= (b̅ × c̅).[{(c̅ × a̅).b̅}a̅ – {(c̅ × a̅). a̅}b̅]
= (b̅ × c̅).a̅[c̅ a̅ b̅] = [a̅ b̅ c̅][a̅ b̅ c̅] = [a̅ b̅ c̅]² = RHS

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

TS Inter 1st Year English Grammar Prepositions

Q.No. 11 (8 × 1/2 = 4Marks)

PREPOSITION :
A preposition is placed before nouns, pronouns, noun equivalents, noun-phrases or noun clauses. It shows its relation to some other word or words in the sentence.

ఒక నామవాచకము, సర్వనామము, నామవాచక సమానాలు, నామవాచక పదసముదాయం లేక నామవాచక ఉపవాక్యాల ముందు విభక్తి ప్రత్యయం (preposition) ఉంచబడుతుంది. ఇది వాక్యంలోని ఇతర పదము లేక పదాలతో ఆ నామవాచకము యొక్క సంబంధాన్ని తెలుపుతుంది.

e.g. :

1. She is fond of sweets.
2. He jumped into the river.

USING PREPOSITIONS :

A) In :

1) To denote place : in Canada; in a village.
2) To indicate time : in the morning.
3] To indicate position : in intensive care, in a jovial mood.
4) To indicate dress : in blue frock, in uniform.
5) To indicate surroundings : in open space, in prison.

B) At :

1) To denote state : India and Pakistan were at war in the early sixties.
2) To indicate a point of time : I shall meet you at 5 p.m.
3) To denote degree or price : We bought these apples at forty rupees a dozen.
4) To denote a place : She was at school then.
5) To tell the sense of beingengaged : All the students are at play.
6) To denote aim : The hunter fired his gun at the bird.
7) With the names of small villages and towns : She lives at Kolanupaka.

C) By :

1) To show nearness : There is a house by the stream.
2) To mean ‘during’ . : By night or by day, he is a nuisance.
3) To mean ‘measure’ : He is taller by an inch.
4) To mean in the name of : I swore in the court by God.
5) To mean instrument : The Inspector caught the thief by the collar.
6) To mean ‘past’ : He goes by my house every morning.
7) To mean the cause : The house was destroyed by fire.

D) On :

1) Place : My pen is on the table.
2) Time : I was on time to the examination.
3) Position : Sarala is on probation.
4) Concern : This is a book on law.
5) Objective : I am bent on visiting Mysore this summer.

E) Of :

1) Relationship : The results of S.S.C. are published today.
2) Phrases : a man of principles, a story of adventure.
3) Division : He took one metre of this cloth.
4) Subjective relation : The love of mother can never be repaid.
5) Cause : He died of sunstroke.
6) Source : She comes of a rich family.
7) Quality : Shyiock was a man of cruel character.
8) Contents : I received a bag full of gifts.
9) Peculiar constructions : How nice of you !

F) For :

1) In place of : Dalda is used for ghee.
2) On account of : We entered slowly for the fear of disturbing the baby.
3) Purpose : Let us pray for peace.
4) Destination : I am leaving for Chennai.
5) Period of time : They have been working for the last three hours.

G) After :

1) Resemblance : Sivaji takes after his mother.
2) Next : The dog ran after the hare.
3) Time : I usually return home after 5 p.m.

DIFFERENCES IN USING PREPOSITIONS

1. At, in : a) At …. small villages She lives at Masaipet. b) At … inside or outside. She is at the station.	In … cities and countries. She lives in Warangai. She lives in the U.K.In … inside only. She is in the Cafeteria.
2. On, upon : On denotes things at rest. He sat on a chair.	Upon denotes things in motion. The tiger jumped upon the deer.
3. Between; among : a) Between refers to two : Choose between these two pens. b)  The two thieves divided the money between themselves.	Among refers to “more than two” Choose one among these ribbons. The four thieves divided the money among themselves.
4. Beside; beside : Beside means next to, at the side of, near to a) My house is beside the post office. b) Ravikant sits beside me.	Besides means “in addition to” I take bread besides biscuits. She speaks Germar besides French.
5. For, since : ‘For‘ denotes period of time. a) We have been working for four hours. b) She has been staying here for six months.	‘Since‘ denotes point of time. We have been workin since 8 a.m. S ‘he has been staying her since April.

Prepositions, the ones like ‘on, at, of , for’ (mostly monosyllables), are called Simle Prepositions while those consisting of two or more words like search of, in front of are called Complex Prepositions (or Phrasal Prepositions )
Here is a list of prepositions that go with certain ver bs/adjectives, etc.

Exercise

I. Fill in the blanks with suitable prepositions from the list given below.

(to, up, for, on, after, to, off, at, of, in)
1. We should not feel superior ………………….. others.
2. People usually put ………………….. new (dresses ………………….. festival days.
3. He is good ………………….. English, but Weak ………………….. Mathematics.
4. Don’t rely ………………….. others for everything.
5. If you give ………………….. the efforts, you don’t succeed.
6. I went to the airport to see ………………….. my son.
7. The minister left ………………….. Delhi yesterday.
8. We reached the station much ahead ………………….. the schedule time.
9. They have agreed ………………….. our proposal.
10. The government should look ………………….. the orphans.
Answer:
1) to
2) on, on
3) at, in
4) on
5) up
6) off
7) for
8) of
9) to

II. Fill in the blanks with suitable phrasal prepositions from the list given below.

(adjacent to, believe in, put out, abide by, agree with, deal with, made of, adapt (oneself) to, interested in, front of)

1. Shloka is ………………….. music.
2. Are you …………………..reading novels ?
3. We must ………………….. the circumstances to lead a happy life.
4. Some poems ………………….. in imaginary situations.
5. These chairs are ………………….. plastic.
6. The members must ………………….. one another to come to an agreement.
7. If you don’t ………………….. the fire immediately, it will spread fast.
8. You must ………………….. the rules and regulations.
9. SBI is located ………………….. the new shopping mall.
10. We ddn’t ………………….. superstitions.
Answer:
1) fond of
2) interested in
3) adapt (ourselves) to
4) deal with
5) made of
6) agree with
7) “put out
8) abide by
9) adjacent to
10) believe in

III. Fill in the blanks with correct prepositions.

1. We lived ………………….. (in / at) the U.S.A ………………….. (for / in) two years.
2. The office is open ………………….. (from / on) 10 a.m ………………….. (to / at) 5 p.m.
3. Abraham Lincoln came ………………….. (from / with) a poor family.
4. She has been suffering ………………….. (from / with) fever.
5. He prefers coffee ………………….. (with / to) tea.
6. He fell ………………….. (of / off) a bicycle.
7. There is a spider ………………….. (on / by) the wall.
8. We come to college ………………….. (by / in) bus.
9. The girl sat ………………….. (between / among) her parents.
10. We congratulated Ajay ………………….. (with / on) winning the award.
11. We cut fruits ………………….. (by / with) a knife.
12. Children are fond ………………….. (of / off) toys.
13. Gandhiji was born ………………….. (on / in) 1869.
14. All of us are afraid ………………….. (off / of) mad dogs.
15. The patient was shifted ………………….. (to / for) a hospital.
Answer:
1) in, for
2) from, to
3) from
4) from
5) to
6) off
7) on
8) by
9) between
10) on
11) with
12) of
13) in
14) of
15) to

IV. Fill in the blanks with correct prepositions.

1. India got independence ………………….. 1947.
2. I have been reading this book ………………….. 2018.
3. Suresh goes to college ………………….. foot.
4. He served in the military ………………….. thirty years.
5. Very few people can swim ………………….. the river Ganga.
6. The martyr wrote his final testament ………………….. blood.
7. Many great people hail ………………….. rural areas of the country.
8. The snake crawled ………………….. its pit.
9. There is a cold war ………………….. these two countries.
10. There is a beautiful painting ………………….. the wall.
11. Yoga is good ………………….. health.
12. She spoke ………………….. her travel experiences.
13. Suman left ………………….. Australia.
14. Mohan is a student ………………….. Delhi University.
15. Are you aware ………………….. Corona precautions ?
16. There are many hills ………………….. the river.
17. Wealth is inferior ………………….. learning.
18. We open locks ………………….. keys.
19. He jumped ………………….. the well.
20. The issue is ………………….. you and me.
Answer:
1) in
2) since
3) on
4) for
5) across
6) in
7) from
8) into
9) between
10) on
11) for
12) about/of
13) for
14) of
15) of
16) along / near
17) to
18) with
19) into
20) between

V. Fill in the blanks with suitable prepositions.

1. My grandson is fond ………………….. chocolates.
2. My friend lives ………………….. Delhi.
3. The apples cost ………………….. Rs. 100/- a Kg.
4. I agree ………………….. you, cent percent.
5. Can you translate this ………………….. English ………………….. Telugu ?
6. There is something extraordinary ………………….. Kohli.
7. Sheela is a nurse. She cares ………………….. the elderly.
8. Srikanth has gone away. He will be away ………………….. Monday.
9. The five thieves shared the stolen money ………………….. themselves.
10. The train started exactly ………………….. 6 o’ clock.
11. It rained ………………….. two days.
12. Switch ………………….. the light, please, it is quite dark here.
13. The trains are seldom ………………….. time.
14. We-five ………………….. the fifth floor.
15. She is familiar ………………….. computer hardware.
16. I have not slept properly ………………….. two days.
17. He trembled ………………….. fear when he was caught.
18. Looking forward ………………….. seeing you at the meeting.
19. Most foreigners dream ………………….. visiting India.
20. She insisted ………………….. joining us.
Answer:
1) of
2) in
3) X (no preposition)
4) with
5) from, to / into
6) about
7) for
8) till
9) among
10) at
11) for
12) on
13) on
14) on
15) with
16) for
17) with
18) to
19) of
20) on

VI. Fill in the blanks with suitable prepositions.

The Sides of Life

Question 1.
I want you to go out _______(1)_________ this institution so trained and so developed that you will be constantly looking _______(2)_______ the bright, encouraging arid beautiful things _______(3)_______ life.
Answer:
1) from
2) for
3) in

Question 2.
When you go _______(1)_______ your classrooms, I repeat, try to forget and overlook any weak points that you may think you see. Remember, and dwell _______(2)_______ the consideration that has been given _______(3)_______ the lesson, the faithfulness _______(4)_______ which it was prepared, and the earnestness _______(5)_______ which it is presented.
Answer:
1) into
2) upon
3) to
4) with
5) with

Question 3.
Everything that comes _______(1)_______ their mouths is unpleasant, _______(2)_______ this thing and that thing, and they make the whole atmosphere _______(3)_______ them unpleasant _______(4)_______ themselves and _______(5)_______ everybody _______(6)_______ whom they come _______(7)_______ contact.
Answer:
1) from
2) about
3) around
4) for
5) for
6) with
7) into

Question 4.
They live simply _______ the negative side of life.
Answer:
on

Father, Dear Father

Question 5.
Yetshe is _______(1)_______ peace _______(2)_______ herpots, pans, her flowers and garden, her Bhagavad Geeta and scriptures. My mother, highly qualified, is highly strung, tense and nervy. Do you think, literacy is a harbinger _______(3)_______ restlessness, fear, frustration ? Is it Adam and Eve eating the Tree _______(4)_______ knowledge, all _______(5)_______ again ?
Answer:
1) at
2) with
3) of
4) of
5) over

Question 6.
My first rank is _______ stake, you see.
Answer:
at

Question 7.
I would like you to be aware _______ my musings.
Answer:
of

Question 8.
Papa, my grandfather, speaks _______(1)_______ a carefree and beautiful childhood.
Answer:
of

The Green Champion Thimmakka

Question 9.
As the grew up, she was married _______(1)_______ Sri Bikkala Chikkayya _______(2)_______ Hulikal village _______(3)_______ whom she found a purpose to plant trees.
Answer:
1) to
2) of
3) with

Question 10.
Thimmakka and her husband used to carry four pails _______(1)_______ water _______(2)_______ a distance _______(3)_______ 4 km to water the saplings.
Answer:
1) of
2) for
3) of

Question 11.
Thimmakka continues her fight _______(1)_______ afforestation.
Answer:
for

The First Four Minutes

Question 12.
_______(1)_______ one and a half laps I was still worrying _______(2)_______ the pace. Advoice shouting ‘Relax’ penetrated _______(3)_______ me _______(4)_______ the noise _______(5)_______ the crowd.
Answer:
1) at
2) about
3) into
4) above
5) of

Question 13.
As we lined up _______(1)_______ the start I glanced _______(2)_______ the flag again. It fluttered more gently now, and the scene _______(3)_______ Shaw’s Saint Joan flashed _______(4)_______ my mind, how she, _______(5)_______ her desperate moment, waited _______(6)_______the wind to change.
Answer:
1) for
2) at
3) from
4) through
5) at
6) for

Box and Cox

Question 14.
_______(1)_______ the appearance _______(2)_______ his outward man, I should unhesitatingly set him _______(3)_______ as a gentleman connected _______(4)_______ the printing interest.
Answer:
1) from
2) of
3) down
4) with

Question 15.
He’s gone _______(1)_______ last! Really I was all _______(2)_______ a tremble _______(3)_______ fear Mr. Box would come in _______(4)_______ Mr. Cox went out.
Answer:
1) at
2) in
3) for
4) before

Question 16.
So it seems ! Far be it _______(1)_______ me, Bouncer, to hurry your movements, but I think it right to acquaint you _______(2)_______ my immediate intention _______(3)_______ divesting myself _______(4)_______ my garments, and going _______(5)_______ bed
Answer:
1) from
2) with
3) of
4) of
5) to

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

TS Inter 1st Year English Grammar Articles

Q.No. 10 (8 × 16 = 4 Marks)

• A, an and the ‘ are called articles.
  They are basically adjectives.
  ‘A/an’ is the ‘Indefinite Article’.
  The’ is the Definite Article.

A. THE USE OF THE INDEFINITE ARTICLE

The basic meaning of the Indefinite Article is ‘one’. Thererfore, it can be used only before the singular countable nouns The Definite Article, on the other hand, can be used before the singular or plural countable nouns and even before the uncountable nouns.

When to use ‘a’ or ‘an’ depends on the sound, not the letter that begins the following word. ‘An’ is used before words that begin with a vowel sound ‘A’ is used before words that begin with a consonant sound Pronunciation plays the key role in deciding the use of ‘a’ / ‘an’. Both of them are used with the same basic meaning, i.e. one.

Some examples of the use of ‘a’ and ‘an’ :

1. in the sense of ‘a certain’.
(ఏదో ఒక అనే అర్ధంతో )
A man came to see my dad.
There is an apple on the table.

2. to represent ‘a class’.
(ఒక వర్గాన్ని తెలుపుటకు)
’ peacock is a colourful bird.
An ant is a social animal.

3. in its basic sense of ‘one’.
Three feet make a yard.
She needs a one hundred rupee note.
(Note that ‘o’ in ‘one’ is a vowel letter but here sounds as a consonant. Hence ‘a’, not ‘an’.)

4. in the sense of ‘every, at the rate of, in the ratio of, etc.
(ప్రతి, ఈ లెక్కన, ఈ నిష్పత్తిలో అనే అర్థాలతో)
He pays as rent Rs. 3,000 a month.
The machine purifies 10 litres of water an hour. three times a month, ten rupees a piece, five kilometers a minute

5. before a proper noun to show that the speaker knows that man only by name.
(మాట్లాడేవారికి ఆ వ్యక్తి పేరు తప్ప ఇంక ఏమీ తెలియదనుటకు proper noun ముందు)
A Mr. Raghu is on phone. (చెబుతున్న వ్యక్తికి రఘు గురించి ఏమీ తెలియదు.)

6. in the sense of the same (ఒకటే అనే అర్థంతో)
Birds of a feather flock together.

7. before a proper noun used as a common noun. (ఒక proper noun లక్షణములు గల’ అనే అర్థంతో common noun గా వాడినప్పుడు.)
She thinks she is a Shakuntala Devi.
(Note : ఇదే అర్థంతో ‘time’, ‘space’ specifications ఉన్నట్లయితే అక్కడ ‘the’ వాడాలి. Indefinit article కాదు)
He feels he is a Sachin, (No ‘time’ or ‘space’ modification)
He is the Sachin of our college, (of – college – space specification. Hence the.

8. before the name of a profession, a trade, an occupation, a class, a religion. (వృత్తి, వ్యాపార, వ్యాపక, వర్గ, మత మొదలగువాని పేర్ల ముందు) a clerk, a lawyer, an actor, a farmer, a Hindu

9. in exclamations like (ఆశ్చర్యార్థకాలలో)
what a beautiful sight!

10. idiomatically
a little, a few (to make them mean positive)
many an accident, such a person

B. THE USE OF THE DEFINITE ARTICLE

The Definite Article is used before .
1. a noun whose identity is clear.
e.g. : The weather is fine.
What is the time ?

2. a singular noun representing the whole class.
(మొత్తం జాతిని సూచించే ఏకవచన నామవాచకాలకు ముందు)
e.g. : The cow is a useful animal.
The lion is the king of all animals.

3. a noun which is unique or one of its kind.
(ఒకే ఒకటిగా నున్న పేర్లముందు)
e.g. : the earth
the sky

4. the names of rivers.
(నదుల పేర్ల ముందు)
e.g. : the Godavari, the Nile, the Mississippi, etc.

5. the names of oceans and seas.
(మహాసముద్రాలు, సముద్రాల పేర్ల ముందు)
e.g. : the Arabian sea, the Indian ocean

6. the names of gulfs and canals.
(అగాధముల, కాలువల పేర్ల ముందు)
e.g. : the Persian gulf; the Panama canal

7. the names of mountain ranges.
(పర్వత వరుసల పేర్ల ముందు)
e.g. : the Alps, the Himalayas, the Vindhyas

8. the names of holy books.
(పవిత్ర గ్రంథాల పేర్ల ముందు)
e.g. : the Bible, the Ramayana, the Koran

9. the names of musical instruments.
(సంగీత వాయిద్యాల పేర్ల ముందు)
e.g. : the violin, the guitar, the drum, the harmonium.

10. a Proper Noun when it is qualified by an adjective.
(విశేషణముచే నిర్దేశింపబడిన నామవాచకాల ముందు)
e.g- : the great Shakespeare

11. the names of inventions, human body, articles of clothing.
(కనిపెట్టబడిన, మానవ శరీర అంగాల మరియు దుస్తుల ముందు)
e.g. : Who invented the microscope ?
He was hit on the head.
The shirt is blue in colour.

12. the names of groups of islands.
(దీవుల సముదాయాల పేర్లముందు)
e.g. : the Maldives, the Andamans

13. comparatives when they are used in a special way.
(ప్రతేక్యమైన Comparative degree లోని పదాల ముందు)
e.g : The higher you climb, the better is the view.

14. the superlative degree.
(Superlative degree లో)
e.g. : Sarala is the tallest girl in the class.

15. Comparative degree when one of the items is singled out.
(Comparative degree లో రెండు విషయాలలో ఒకదాని గురించి ప్రత్యేకంగా చెప్పేటప్పుడు)
e.g. : Of Bengaluru and Hyderabad, Bengaluru is the cooler.

16. nouns denoting units of measurement.
(తూనికల విషయంలో)
e.g. : Now we are buying water by the litre.

17. Adjectives used as Nouns.
(విశేషణాలను నామవాచకాలుగా వాడినప్పుడు)
e.g. : The brave deserve the praise.

18. abbreviations.
(సంకేతాక్షరాల ముందు)
e.g. : The C.B.I., the U.S.A.

19. the names of ships, public buildings, aeroplanes, hotels,
e.g. : Ships : the Viceroy, the Vikranth
Public buildings : the Secretariat,
the Parliament House
Hotels : the Oberio Sheraton, the Taj
Aeroplanes : the Kanishka, the Ashoka

20. words like middle, top, end, first, next, centre, etc.
e g. : the middle order the top floor
at the end the first child
the next train in the centre

C. WHERE NO ARTICLE IS USED

1. No article is used before the branches of knowledge.
(విద్య లేక జ్ఞాన సంబంధ విషయాలముందు ఎటువంటి article నుపయోగించరాదు)
e.g. : English (not the English)

2. No article is used before the names of days, months and seasons.
(దినముల, నెలల, ఋతువుల పేర్ల ముందు article నుపయోగించరాదు)
e.g. : Sunday is a holiday.'(Not the Sunday)
If winter comes, can spring be far behind ?

3. No article is used before nouns in certain phrases.
(కొన్ని phrases లోని నామవాచకాల ముందు article నుపయోగించరాదు)
e.g. by air (not by the air)
over hill and dale (not over the hill or the dale)

4. Don’t use any article before the names of games.
(ఆటల పేర్ల ముందు ఏ విధమైన article నుపయోగించరాదు)
e.g. I play hockey. (not the hockey)

5. No article is used before collective nouns.
(సామూహిక నామవాచకాల ముందు ఏ విధమైన article నుపయోగించరాదు.)
e.g. Mankind loves nature. (not the mankind)
We are members of society. (not the society)

6. No article is used before a Common Noun used in the vocative case.
(సంబోధనాత్మక నామవాచకాల ముందు ఎటువంటి article నుపయోగించరాదు. )
e.g. King Arthur … (not the King Arthur)
General Ajay… (not the General Ajay)

7. In certain phrases consisting of a preposition, no article is placed.
(కొన్ని phrases లో విభక్తి ప్రత్యయముల ముందు ఏ విధమైన article నుపయోగింపరాదు. )
e.g. on foot (not on the foot)
by train… (not by the train)

8. Don’t use any article before the names of substances.
(పదార్థాల పేర్ల ముందు ఏ విధమైన article నుపయోగింపరాదు)
e.g. Gold is a precious metal. (not the gold)

9. No article is used before nouns like school, college, hospital, prison when they are used for their primary purpose.
(school, college, hospital, prison మొదలగు పదాలు వాటి ఆశయాన్ని నిర్దేశిస్తుంటే ఏ విధమైన article ను ఆ పదాల ముందు వాడరాదు)
e.g. He likes to go to school. (not the school)
She went to hospital. (not the hospital)

10. Don’t use any article before the names of diseases.
(వ్యాధుల పేర్ల ముందు ఏ విధమైన article నుపయోగింపరాదు)
e.g. She has diabetes. (not the diabetes)

Study the following and notice die contrast.

1. It took us an hour to reach a hospital.
2. He is an M.L.A. and a man of principles.
3. He is an honest man and hasn’t got a house of his own.
4. We have to take an umbrella to go to a university in some countries.
5. Interacting with an MP is a memorable experience.

MORE EXAMPLES

1. A surgeon should be very careful, during an operation.
2. An engineer supervises the construction of a building.
3. We can take a decision.
4. Ramu and Srinu are of a size.
5. Birds of a feather flock together.
6. Tomatoes cost Rs. 40/- a kilo.
7. The Rajdhani express runs at a speed of 140 km an hour.
8. They killed a snake there.
9. There is a swimming pool in our town.
10. a piece of paper, a cup of tea, a packet of salt, a bundle of grass, a cake of soap, an item of furniture, a piece of information, etc.
11. A rose is a beautiful flower.
12. An elephant is a big animal.
13. Prathibha is a doctor.
14. Sandeep is an architect.
15. Did you order a hundred chairs for our college ?

16. Ravali faced a lot of trouble to reach her home in the rain.
17. A Mr. Bharani has come to meet my father. (Bharani is ununknown to me)
18. A Miss. Sana is waiting outside.
19. a barracks, an innings.
20. A knowledge of history is always useful.
21. It took us an hour to reach a hospital.
22. He is an M.L.A. and a man of principles.
23. He is an honest man and hasn’t got a house of his own.
24. We have to take an umbrella to go to a university in some countries.
25. Interacting with an MP is a memorable experience.
26. the Sun, the Moon, the earth, the sea, the weather, the Pyramids, the North Pole, the Charminar, the Warangal Fort, the Church of South India, the silent film era, the film industry, the Victorian era.
27. the railway station, the Commissioner, the Mayor.
28. Lord Krishna played the flute.
29. A.R. Rahman has impressed everyone with his composition of music on the guitar.
30. The camel is the ship of the desert.
31. The lion is the king of the jungle.
32. The heart is a very important organ of our body.
33. The tongue decides the taste factor.
34. The blind are very active, (the blind = blind persons)
35. We have to help the poor, (the poor = poor persons)

36. The minister is arriving in the morning.
37. We will go and meet them in the evening.
38. I met a girl and a boy at a railway station. The girl is about ten years old and the boy is about five years old.
39. The student whom I motivated became a doctor.
40. The novel I bought yesterday is interesting.
41. R.K. Naryan is one of the greatest Indian writers in English.
42. Honesty is the best policy.
43. Vishwanathan Anand is one of the most famous Chess players in the world.
44. Rakesh Sharma was the first Indian to go into the space.
45. The Padma Shri is the fourth highest civilian award in India.
46. My parents will celebrate the 25th wedding anniversary next year.
47. Vijay was the only student who raised a doubt about articles.
48. Abdul Kalam is the only President who was also a scientist.
49. the Pacific ocean, the Himalayas, the Andamans, the Niagara, the Kuntala Waterfalls, the Godavari, the Persian Gulf, the Kakatiya Canal.
50. the United States of America; the United Kingdom; the United Arab Emirates, the Republic of Germany, the Netherlands.
51. the Gita, the Bible, the Quran, the Guru Granth Sahib
52. the Mahabharata – but – Vyasa’s Mahabharata
53. The breakfast served at Taj Hotel is very tasty.
54. The more you concentrate, the more you understand.
55. The less you work, the less you get.

56. Kumar is the Sachin of their team.
57. High – Tech city is the Silicon Valley of Telangana State.
58. The English ruled India for more than two centuries.
59. The Birlas established Kesoram Cement Factory.
60. The Tatas are pioneers in Steel Industry.

Exercises

I. Fill in the blanks with ‘a’/an

1. ………………. ant is ………………. industrious creature.
2. We can’t live without ………………. fan nowadays.
3. ………………. apple ………………. day keeps the doctor away.
4. ………………. ATM is ………………. useful machine.
5. ………………. honest man is always respected.
6. Amitabh Bacchan is ………………. famous actor.
7. Are you ………………. vegetarian ?
8. It is ………………. absurd story indeed.
9. I don’t believe him. He is ………………. liar.
10. What ………………. lovely Villa !
11. It is ………………. one-man show !
12. I never witnessed such ………………. long queue for Covaxin.
13. He is ………………. United Nations exployee.
14. We have quite ………………. few books on Yoga.
15. I saw ………………. accident this morning.
Answer:
1) An, an
2) a
3) An, a
4) An, a
5) An
6) a
7) a
8) an
9) a
10) a
11) a
12) a
13) a
14) a
15) an

II. Fill in the blanks with a, an or the and laugh out loudly.

(1) ………………. vegetable seller’s wife gave birth to (2) ………………. son. (3) ………………. customer
who heard (4) ………………. good news, congratulated (5) ………………. vegetable seller and enquired about (6) ………………. state of (7) ………………. health of (8) ………………. newly-born child.
Then he said. “Sir, it’s very fresh.”
Answers:
1) A
2) a
3) A
4) the
5) the
6) the
7) the
8) the

III. Fill in the blanks with ‘a’, ‘an’ or ‘the’ and enjoy the joke.

In ………………. accident person who lost his legs was crying. At that time, ………………. man who came there said, “Why do you cry like ………………. child ?” and said, “See that man who lost his head and ………………. hand and still not crying.”
Answer:
In an accident a person who lost his legs was crying. At that time, a man who came there said, “Why do you cry like a child ?” and said, “See that man who lost his head and the/a hand and still not crying.”

IV. Fill in the blanks with ‘a’, ‘an’ or ‘the’ in the following riddle.

Q : ………………. truck driver is going in ………………. opposite direction in ………………. one-way street. ………………. police officer sees him but doesn’t stop him. Why doesn’t ………………. police officer stop him ?
A: ………………. truck driver is walking.
Answer:
Q : A truck driver is going in the opposite direction in a one-way street. A police officer sees him but doesn’t stop him. Why doesn’t the police officer stop him ?
A : The truck driver is walking.

V. Fill in the blanks with a, an or the.

1. I bought ………………. pair of new shoes.
2. I saw ………………. movie last night.
3. It’s raining. Do you need ………………. umbrella ?
4. Look at ………………. woman over there ! She is my mother.
5. ……………….night is quiet. Let’s take a walk.
6. ………………. spider has eight legs.
7. Peter is ………………. Italian.
8. I read ………………. amazing story last Sunday.
9. ………………. tiger is in danger of dying out.
10. She has got ……………….long hair.
11. blind, ………………. deaf and ………………. dumb lead ………………. miserable life.
12. My sister is married to ………………. farmer.
13. We spent ………………. whole week in Hawaii.
14. They met ………………. Minister yesterday.
15. It was ………………. hottest day ever.
16. I put ………………. unopened letters over there.
17. Is ………………. clock slow, or is it me ?
18. Keeravani is ………………. music composer and also ………………. singer.
19. I was moved by ………………. kindness that he showed.
20 I did not know that ………………. dictionary belonged to you.
Answer:
1) a
2) a
3) an
4) the
5) The
6) A/The
7) an
8) an
9) The
10) no article
11) The,The,the,a
12) a
13) the/a
14) the
15) the
16) the
17) the
18) a ; a
19) the
20) the

VI. Fill in the blanks with a, an or the.

1. I can’t play ………………. piano.
2. You are ………………. first person to arrive here.
3. Our swimming costumes were dry, but ………………. children’s weren’t.
4. They live in ………………. old house.
5. Rajesh is ………………. enterprising businessman.
6. Our plane was delayed. We had to wait at ………………. airport for three hours.
7. ………………. idea can change your life.
8. ………………. more you learn, ………………. more you benefit.
9. Mukesh Ambani is ………………. Bill Gates of India.
10. Is there ………………. AC theatre in your town ?
11. Panaji is ………………. capital of Goa state.
12. ………………. moon is ………………. symbol of pleasantness.
13. I have given ………………. one rupee coin to ………………. beggar.
14. ………………. rabbit runs very fast.
15. Is there ………………. bank near here ?
16. ……………….talent of ……………….writer can’t be underestimated.
17. ………………. simplicity which Gandhi followed is taken as ………………. example everywhere.
18. I interviewed ………………. M.R in ………………. evening.
19. Did you get married after leaving ………………. university ?
20. Would you like to be ………………. actor ?
Answer:
1) the
2) the
3) the
4) an
5) an
6) the
7) an
8) The, the
9) the
10) an
11) the
12) The, the
13) a, the (a)
14) The/A
15) a
16) The, a / the
17) The, an
18) an, the
19) the
20) an

VII. Fill in the blanks with a, an or the.

Two Sides of Life

Question 1.
There are quite __________(1)__________ number of divisions into which life can be divided, but for __________ (2)__________ purposes of this evening I am going to speak of two; __________ (3)__________ bright side of life and __________ (4)__________ dark side.
Answer:
1) a
2) the
3) the
4) the

Question 2.
You will not accomplish __________ (1) __________ task which we expect of you go with __________ (2) __________ moody, discouraged, fault-finding disposition.
Answer:
1) the
2) a

Father, Dear, Father

Question 3.
Yes, my first rank slipped to __________ second.
Answer:
1) the

Question 4.
Do you think literacy is __________ harbinger of restlessness, fear, frustration ?
Answer:
1) a

Question 5.
From his talk, it seems studies were __________(1)__________ ancillary subject; and living and experiencing, __________(2)__________ major subject. Father, is he fibbing ? Or is it possible that __________(3)__________ world turned topsy-turvy in just about 70 years ?
Answer:
1) an
2) the
3) the

Question 6.
You know just like that boy, Vinu, in that award winning film. He prattles on __________(1)__________ Hibiscus is red __________ (2)__________ hundred times, but in his book, he colours it yellow. Are we missing out on __________(3)__________ essence of life ? Papa, that’s what happens in my craft and drawing class. My imagination wants to soar like __________(4)__________ rockets to Jupiter and Mars. To traverse new worlds, new fields.
Answer:
1) the
2) a
3) the
4) a

The Green Champion – Thimmakka

Question 7.
Thimmakka could not go to school due to poverty and lack of facilities. At __________(1)__________ early age, she had to take up grazing of sheep and cattle and also work as __________(2)__________ coolie.
Answer:
1) an
2) a

Question 8.
Thimmakka (she) has been recognized by __________(1)__________ Government of India and was recently conferred with __________(2)__________ Padma Shri award in 2019, which is __________(3)__________ fourth highest civilian award in __________(4)__________ Republic of India.
Answer:
1) the
2) the
3) the
4) the

The First Four Minutes

Question 9.
Failure is as exciting to watch as success, provided __________(1)__________ effort is absolutely genuine and complete. But __________(2)__________ spectators fail to understand – and how can they know __________(3)__________ mental agony through which __________(4)__________ athlete must pass before he can give his maximum effort.
Answer:
1) a
2) the
3) the
4) an

Question 10.
If I faltered, there would be no arms to hold me and __________(1) __________ world would be __________(2)__________ cold, forbidding place, because I had been so close. 1 leapt at __________(3 __________ tape like __________(4)__________ man taking his last spring to save himself from __________(5)__________ chasm that threatens to engulf him.
Answer:
1) the
2) a
3) the
4) a
5) the

Box and Cox

Question 11.
I can’t say I did, Mrs. B. I should feel obliged to you, if you could accommodate me with __________(1)__________ more protuberant bolster, Mrs. B. The one I’ve got now seems to me to have about __________(2)__________ handful and __________(3)__________ half of feathers at each end, and nothing what¬ever in (4) middle.
Answer:
1) a
2) a
3) a
4) the

Question 12.
It is not __________(1)__________ case only with __________(2)__________ coals, Mrs. Bouncer, but I’ve lately observed __________(3) __________ gradual and steady increase of evaporation among my candles, wood, sugar and matches.
Answer:
1) the
2) the
3) a

Question 13.
Why __________(1)__________ gentleman who has got __________(2)__________ attic is hardly ever without __________(3)__________ pipe in his mouth and there he sits with his feet upon __________(4)__________ mantelpiece. From __________(5)__________ appearance of his outward man, I should unhesitatingly set him down as __________(6)__________ gentleman connected with __________(7)__________ printing interest.
Answer:
1) the
2) the
3) a
4) the
5) the
6) a
7) the

Telangana TSBIE TS Inter 1st Year Physics Study Material 11th Lesson Mechanical Properties of Fluids Textbook Questions and Answers.

TS Inter 1st Year Physics Study Material 11th Lesson Mechanical Properties of Fluids

Very Short Answer Type Questions

Question 1.
Define average pressure. Mention it’s unit and dimensional formula. Is it a scalar or a vector? [AP Mar. ’17]
Answer:
Average pressure (P_av) :
The normal force acting per unit is called average pressure.
⇒ P_av = \(\frac{F}{A}\)
Units : In SI = Nm^-1
The dimensional formula : ML^-1T^-2
It is a scalar quantity.

Question 2.
Define Viscosity. What are its units and dimensions? [AP May ’16, ’13; TS May ’18, June ’15)
Answer:
Viscosity :
The property of a fluid which opposes the relative motion between the layers is called viscosity.

Units in SI:
Coefficient of viscosity Nm^-2 s (or) Pa – s. (or) Poiseuille
Units in C.G.S : Coefficient of viscosity = poise.
The dimensional formula = ML^-1 T^-1.

Question 3.
What is the principle behind the carburetor of an automobile? [TS Mar. ’18, ’17; AP Mar. ’19, ’15; June ’15]
Answer:
Carburetor of an automobile is based on the principle of “Bernoulli’s theorem”.

Question 4.
What is magnus effect? [AP May ’18, ’17, Mar. ’15; TS Mar. ’19, ’16]
Answer:
Magnus effect :
When a spinning ball is thrown it deviates from its usual path in flight. This effect is called Magnus effect.

Question 5.
Why are drops and bubbles spherical? [AP Mar. ’18, ’17, ’16, ’14, May ’18, ’17, ’16, ’14, ’13; TS May ’18, ’17, ’16]
Answer:
Due to property of surface tension, the surface of liquid behaves like a stretched membrane and has a tendency to acquire minimum surface area. The sphere has minimum surface area when compared to other shapes of same volume.

Therefore, drops and bubbles acquire spherical shape in order to have the minimum surface area.

Question 6.
Give the expression for the excess pressure in a liquid drop. [TS Mar. ’17]
Answer:
Excess of pressure in a liquid drop is,
p = \(\frac{2s}{r}\) where ‘s’ = surface tension and ‘r’ = the radius of the liquid drop.

Question 7.
Give the expression for the «<cess pressure in an air bubble inside the iquid. [AP Mar. ’19]
Answer:
Excess of pressure in an air buble inside the liquid is, P = \(\frac{2S}{R}\)
where S = Surface Tension, R = Radius of air bubble of liquid.

Question 8.
Give the expression for the excess pressure in a soap bubble in air. [TS Mar. ’16]
Answer:
Excess of pressure in a soap bubble is, p = \(\frac{4s}{r}\) where
‘s’ = surface tension and
‘r’ = radius of the drop.

Question 9.
What are water proofing agents and water wetting agents? What do they do?
Answer:
Water proofing agents :
The substances which are used to increase the angle of contact are called “water proofing agents”.

Wetting agents:
The substances which are used to decrease the angle of contact are called “wetting agents”.
Ex: Soaps, detergents and dying substances.

Question 10.
Why water droplets wet the glass surface and does not wet lotus leaf? [TS Mar. ’15]
Answer:
Angle of contact between water drop and glass is less than 90° so water drop will wet glass surface.
Angle of contact between water and lotus leaf is greater than 90°. So water drops cannot wet lotus leaf.

Question 11.
What is angle of contact? [AP May ’14, Mar. 16]
Answer:
Angle of contact: It is the angle between the walls of the container and the tangent drawn over the surface of the liquid. This angle must be. measured in the interior side of the liquid.

Question 12.
Mention any two examples (or) applications that Obey Bernoullis theorem and justify them. [AP Mar. ‘ 18; TS Mar. 15]
Answer:
Applications of Bernoulli’s theorem :

1. Dynamic lift on the wings of an aeroplane
2. Swinging of a spinning cricket ball is a consequence of Bernoulli’s theorem.
3. During cyclones, the roof of thatched houses will fly away. This is a consequence of Bernoulli’s theorem.

Question 13.
When water flows through a pipe, which of the layers moves fastest and slowest? [TS June ’15]
Answer:
When water is flowing through a pipe water layers in contact with bottom layers of pipe will have lowest velocity and water layer just below the top of inner layer of pipe will have highest velocity.

Question 14.
“Terminal velocity is more if surface area of the body is more.” Give reasons in support of your answer.
Answer:
Yes, Terminal velocity of a body is more when surface area of a body is more.

According to Stokes formula, terminal velocity of a smooth spherical body is,

The surface area of a spherical body A = 4πr². So when surface increases, ‘r²’ value increases. Hence from Stoke’s formula, Teminal velocity increases.

Short Answer Questions

Question 1.
What is atmospheric pressure and how is it determined using Barometer?
Answer:
The atmospheric pressure at any point is equal to the weight of a vertical column of air of unit cross-sectional area extending from that point to the top of tfie earth’s atmosphere.

Determination of atmospheric pressure using Barometer :
A long tube closed at one end and filled with mercury is inverted into a trough of mercury. This device is known as mercury barometer. The space above the mercury column in the tube contains only mercury vapour whose pressure p is so small that it may be neglected. Otherwise there is a perfect vacuum, which is called Torricellian vacuum.

The pressure inside the column at point A must equal the pressure at point B, which is at the same level.

‘P’ at A = Pressure at B = atmospheric pressure = Pa
Pa = ρgh …………. (1)
where ρ = density of mercury
h = height of mercury column

In this experiment, it is found that the mercury column in the barometer has a height of about 76 cm at sea level equivalent to one atmosphere (1 atm).

At sea level, atmospheric pressure is the pressure exerted by 0.76 m of mercury column, i.e., h = 0.76 m
ρ = 13.6 × 10³ kg m^-3 And g = 9.8 ms^-2.
∴ Atmospheric pressure, Pa = hρg
= 0.76 × (13.6 × 10³) × 9.8
= 1.013 × 10⁵ Nn^-2 (or) Pa

A common way of stating pressure is in terms of cm or mm of mercury (Hg). A pressure equivalent to 1 mm is called a torr.
1 torr = 133 Pa.

Question 2.
State Dalton’s law of partial pressures. [AP Mar. ’14]
Answer:
Dalton’s law of partial pressures :
For a mixture of non interacting ideal gases at same temperature and volume total pressure in the vessel is the sum of partial pressures of individual gases.
i.e. P = P₁ + P₂ + ……….. total pressure
P₁, P₂, ……… etc. are individual pressures of each gas.

Question 3.
What is gauge pressure and how is a manometer used for measuring pressure differences?
Answer:
Gauge Pressure :
The pressure p, at depth below the surface of a liquid open to the atmosphere is greater than atmospheric pressure by an amount ρgh. The excess pressure (P – Pa), at depth h is called as “gauge pressure at that point.”

Measurement of pressure difference using a Manometer :
An open tube manometer is a useful instrument for measuring pressure differences. It consists of a U-tube containing a suitable liquid i.e., a low density liquid (such as oil) for measuring small pressure differences and high density liquid (such as mercury) for large pressure differences. One end of the tube is open to the atmosphere and other end is connected to the system whose pressure to be measured.

The pressure P at A is equal to pressure at point B. If the pressure in the vessel is more than the earth’s atmospheric pressure, then the level of liquid in arm-I of U-tube will go down upto point A and the level of liquid in arm-II of U-tube will rise up to point C. Then the pressure of air in vessel is equal to pressure at point A. Let ‘h’ be the difference of liquid levels in the two arms of U-tube. Let ρ be the density of liquid in U-tube and Pa be the atmospheric pressure.

Since, the pressure is same at all points, at the same level, so pressure at point A,
P_A = pressure at point B
= pressure at C + pressure due to column of liquid of height ‘h’.
So, P_A = P_C + hρg or P_A – P_C = hρg ………… (1)
Here, P_C = Pa = atmospheric pressure.
If P_A = P, then from eq ………. (1)
P – Pa = hρg
Here, P – Pa = P_g = gauge pressure = hρg.

Question 4.
State Pascal’s law and verify it with the help of an experiment.
Answer:
Pascal’s law:
It states that “the pressure in a fluid at rest is the same at all points if they are at the same height”.

Proof of Pascal’s law:
Consider an element in the interior of a fluid at rest as shown in the figure. The element ABC – DEF is in the form of a right-angled prism.

In principle, this prismatic element is very small so that every part of it can be considered at the same depth from the liquid surface and therefore, the effect of gravity is the same at all these points.

The forces on this element are those exerted by the rest of the fluid and they must be normal to the surfaces of the element.

Thus, the fluid exerts pressures P_a, P_b and P_c on this element of area corresponding to the normal forces F_a, F_b and F_c as shown in fig. on the faces BEFC, ADFC and ADEB denoted by A_a, A_b and A_c respectively. Then,
F_b sin θ₂ = F_c and F_b cos θ₂ = F_a (by equilibrium)
A_b sin θ₂ = A_c and A_b cos θ₂ = A_a (by geometry)
Thus, \(\frac{F_b}{A_b}=\frac{F_c}{A_c}=\frac{F_a}{A_a}\) ⇒ P_b = P_c = P_a
Hence, pressure exerted is same in all directions in a fluid at rest.

This proves the Pascal’s law.

Question 5.
Explain hydraulic lift and hydraulic brakes.
Answer:
Hydraulic lift and Hydraulic brakes are based on the Pascal’s law. The principle states that “whenever external pressure is applied on any part of a fluid contained in a vessel, it is transmitted undiminished and equally in all directions

Hydralic lift:
In a hydraulic lift, two pistons are separated by the space filled with a liquid as shown in fig.

A piston of small cross-section A₁ is used to exert a force F, directly on the liquid.

The pressure, P = \(\frac{F_1}{A_1}\) is transmitted throughout the liquid to the larger cylinder attached with a larger piston of area A₂, which results in an upward force of P × A₂.

Therefore, the piston is capable of supporting large force.
F₂ = PA₂ = \(\frac{F_1A_2}{A_1}\)

By changing the force at A₁, the platform can be moved up or down. Thus, the applied force has been increased by a factor of \(\frac{A_2}{A_1}\) and this factor is the mechanical advantage of the device.

Hydraulic brakes :
Hydraulic brakes in automobiles also work on Pascal’s principle. When we apply a little force on the pedal with our foot, the master piston moves inside the master cylinder, and the pressure caused is transmitted through the brake oil to act on a piston of larger area. A large force acts on the piston and is pushed down expanding the brake shoes against brake lining. In this way, a small force on the pedal produces a large retarding force on the wheel.

An important advantage of the system is that the pressure set up by pressing pedal is transmitted equally to all cylinders attached to the four wheels so that the braking effort is equal on all wheels.

Question 6.
What is hydrostatic paradox?
Answer:
Hydrostatic paradox :
This is useful to prove that the liquid pressure is the same at all points at the same horizontal level.

Consider three vessels A, B and C of different shapes as shown in the figure. They are connected at the bottom by a horizontal pipe. On filling with water, the level in the three vessels is the same though they hold different amounts of water. This is so, because water at the bottom has the same pressure below each section of the vessel.

Thus, it proves that the height of the fluid column is independent of the cross sectional or base area and the shape of the container

Question 7.
Explain how pressure varies with depth.
Answer:
Variation of pressure with depth:
Consider a fluid at rest in a container. Let point 1 is at a height h’ above a point 2 as shown in the figure. Consider a cylindrical element of fluid having area of base ‘A’ and height ‘h’. As the fluid is at rest, the resultant horizontal forces should be zero and the resultant vertical forces should balance the weight of the element. The forces acting in the vertical direction are due to the fluid pressure at the top (P₁A) acting downward, at the bottom (P₂A) acting upward.

If ‘mg’ is weight of the fluid in the cylinder, we have
(P₂ – P₁) A = mg …………. (1)
Now, if ρ is the mass density of the fluid, then mass of fluid, m = ρv
⇒ m = ρhA …………. (2)
∴ From (1) and (2)
P₂ – P₁ = ρgh …………. (3)

Pressure difference depends on the vertical distance ‘h’ between the points (1 and 2), mass density of the fluid p and acceleration due to gravity ‘g’.

If the point 1 under discussion is shifted to the top of the fluid, which is open to the atmosphere, P₁ may be replaced by atmospheric pressure (Pa) and we replace P₂ by P₂ then eq.(2) becomes
P – Pa = ρgh ⇒ P = Pa + ρgh

Thus, the pressure P, at depth below the surface of a liquid open to the atmosphere is greater than atmospheric pressure by an amount ρgh.

Question 8.
What is Torricelli’s law? Explain how the speed of efflux is determined with an experiment.
Answer:
Torricelli’s law :
Torricelli discovered that the speed of efflux from an open tank is given by a formula identical to that of a freely falling body. The word efflux means ‘fluid outflow’.

Determination of speed of Efflux:
Consider a tank containing a liquid of density ‘ρ’ with a small hole at a height ‘y₁‘, from the bottom as shown in the figure.

The air above the liquid, whose surface is at height ‘y₂‘, is at pressure, P.

From the equation of continuity, we have
V₁ A₁ = V₂A₂ ⇒ V₂ = \(\frac{A_1}{A_2}\)V₁ …….. (1)

It the cross sectional area of the tank, A₂ is much larger than that of the hole (i.e., A₂ >> A₁), then we may consider the fluid to be approximately at rest at the top. i.e., V₂ = o.

Now, applying the Bernoulli equation at points (1) and (2) and noting that, at the hole P₁ = Pa, the atmospheric pressure, we get.
Pa + \(\frac{1}{2}\)ρv²₁ + ρgy₁ = P + ρgy₂
Taking y₂ – y₁ = h, we have

When P > > Pa and 2gh may be ignored, the speed of efflux is determined by the container pressure. Such a situation occurs in rocket propulsion. On the other hand if the tank is open to the atmosphere, then P = Pa and from eq (2), we get
V₁ = \(\sqrt{2gh}\) ………….. (3)

This is the speed of a freely falling body, at any point of height ‘h’ during its fall. This equation is known as “Torricelli’s law”.

Question 9.
What is Venturimeter? Explain how it is used.
Answer:
Venturi-meter :
The venturi meter is a device to measure the flow speed of incompressible fluid.

It consists of a tube with a broad diameter and a small constriction at the middle as shown in the figure.

The manometer contains a liquid of density ρ_m. The speed ν₁ of the liquid flowing through the tube at the broad neck area A is to be measured. From equation of continuity, the speed at the constriction, ν₂ = \(\frac{A}{a}\) ν₁
According to Bernoulli’s equation,

This pressure difference causes the fluid in the U-tube connected at the narrow neck to rise in comparison to the other arm.

The difference in height h measures the pressure difference.

Uses: Venturi meter is used for measuring the speed of incompressible liquid and rate of flow of liquid through pipes.

Question 10.
What is Reynold’s number? What is its significance?
Answer:
Reynold’s number R_e :
Reynold’s number is a pure number which determines the nature of flow of liquid through a pipe.
R_e = \(\frac{\rho v d}{\eta}\)
where
η = coefficient of viscosity of the liquid.
ρ = density of liquid
ν = critical velocity of the liquid flowing through the pipe.
d = diameter of the pipe.

Significance :
R_e is dimensionless number and therefore, it remains same in any system of units.

The critical Reynold’s number for the onset of turbulence is in the range 1000 to 10000, depending on the geometry of the flow. For most cases

R_e < 1000 signifies laminar flow.
1000 < R_e < 2000 is unsteady flow.
R_e < 2000 implies turbulent flow.

Reynold’s number describes the ratio of the inertial force per unit area to the viscous force per unit area for a flowing fluid.

Question 11.
Explain dynamic lift with examples.
Answer:
Dynamic lift on a spinning ball :
Consider the motion of a spinning ball. Its motion consists of two parts 1) Translatory motion 2) Self rotation called spinning.

1) Translatory motion:
Due to translatory motion it passes through the medium air with a velocity say (V). Due to translatory motion the number of streamlines on the top of the ball and at the bottom of the ball are equal. So there is no resultant force on the ball due to translatory motion through the fluid. Hence dynamic lift is zero.

2) For spinning motion :
Let the ball rotates about its axis with a velocity say ∆V in clockwise direction since surface of ball is not perfectly smooth it will drag air molecules with it. So at the top layers the velocity of air is V + ∆V due to air drag. At bottom layers the velocity of air is V – ∆V.

As velocity is more at top layers pressure is less and velocity is less at bottom layers, so pressure is high at bottom layers. This is due to Bernoulli’s theorem.

Due to the pressure difference at bottom layers and top layers some upward thrust will act on the ball. So some dynamic lift will act on a spinning ball. As a result the path of a spinning ball is curved.

Question 12.
Explain Surface Tension and Surface energy. [AP Mar. ’13]
Answer:
Surface tension the force per unit length on an imaginary line drawn on the surface of the liquid and acting perpendicular to it.

Surface energy:
The work done to increase the surface area of a liquid is called surface energy.
Surface energy = Surface tension × Increase in surface area.

Question 13.
Explain how surface tension can be measured experimentally.
Answer:
To find surface tension of a liquid in laboratory torsional balance is used. It is as shown in figure. It consists of a movable metallic rod fixed on a stretched wire. The position of rod can be adjusted. A glass plate is attached at one end of the rod and weight’s pan is connected at the other end of the rod.

Procedure :
A cleaned glass plate is taken. Its length ‘l’ and thickness ‘t’ is measured. Since thickness ‘l’ is very small when compared with length t, thickness ‘t’ is ignored.

Glass plate is fixed to metallic rod. Necessary weights are placed in the pan and glass plate is made horizontal to the table. Weights in pan W₀ is measured. Pure liquid whose surface tension is to be determined is taken in a glass beaker. The liquid is poured until it just touches the glass plate. Now plate is pulled down with some force due to surface tension of liquid. Weights in the pan are gradually increased until the glass plate is just escaped from forces of surface tension. Weights W₁ are noted. The experiment is repeated for three to four times and average weight W₁ is noted.

Long Answer Questions

Question 1.
State Bernoulli’s principle. From conservation of energy in a fluid flow through a tube, arrive at Bernoulli’s equation. Give an application of Bernoulli’s theorem.
Answer:
Bernoulli’s theorem :
Bernoulli’s theorem states that “when a non viscous liquid flows between two points then the sum of pressure energy, kinetic energy and potential energy per unit mass is always constant at any point in the path of that liquid”.

Bernoulli’s theorem is applicable to non viscous, incompressible and irrotational liquids in streamline flow only.

Proof :
Let us consider that a liquid of density ‘ρ’ is flowing through a pipe of different area of cross sections A₁ and A₂ as shown.

Let the liquid enters at A₁ with a velocity V₁ and with a pressure P₁, density of liquid at A₁ is say ρ. Let the liquid leaves the pipe through A₂ with a velocity V₂ and pressure P₂. Density of liquid at A₂ is say ρ.

Since liquid is incompressible, p is con-stant.

At region 1 the liquid will move a distance of V₁ ∆t where ∆t is very small time interval. Similarly at region 2 the liquid will move through a distance V₂ ∆t.
Work done on fluid at region 1 = W₁ = P₁ A₁
V₁ ∆t = P₁∆V

Work done on fluid at region 2 = W₂ = P₂ A₂ V₂ ∆t = P₂ ∆V

Since same volume of liquid pass through the pipe, ∆ is constant.

∴ Work done by fluid = W₁ – W₂ = (P₁ – P₂) ∆V → 1

∵ Liquid is uncompressible ‘ρ’ is constant.

So mass of liquid entering the pipe and leaving the pipe ∆m is given by
∆m = ρA₁V₁∆t = ρ∆V
Change in potential energy of liquid
∆U = ρg∆v(h₂ – h₁) → 2
Change in kinetic energy of liquid
∆K = \(\frac{1}{2}\)ρ∆v(V²₁ – V²₂)
From work energy theorem work done = change in energy
∴ ∆W = ∆U + ∆K

i.e., sum of pressure energy, potential energy and kinetic energy of the fluid is always constant.

Limitations :
Bernoulli ‘s theorem is applicable to non-viscous and uncompressible liquids only.

Applications of Bernoulli’s theorem :

1. Dynamic lift on the wings of an aeroplane is due to Bernoulli’s theorem.
2. Swinging of a spinning cricket ball is a consequence of Bernoulli’s theorem.
3. During cyclones, the roof of thatched houses will fly away. This is a consequence of Bernoulli’s theorem.

Question 2.
Define coefficient of viscosity. Explain Stoke’s law and explain the conditions under which a rain drop attains terminal velocity, υ_t. Give the expression for υ_t.
Answer:
Coefficient of viscosity (η) :
The viscous force acting tangentially on unit area of the liquid when there is a unit velocity gradient in the direction perpendicular to the flow is defined as “Coefficient of viscosity.”

Coefficient of viscossity η = \(\frac{-F}{A}\frac{dx}{dv}\)
Unit Nm^-2 – s (or) pascal – second.

According to Stoke’s law, the viscous force acting on a freely falling, smooth spherical body of radius ‘a’ is proportional to the coefficient of viscosity η, radius ‘a’ and velocity ‘υ’ of the body.
∴ F ∝ ηav or F = 6 π η av, where 6π is the proportionality constant.

A rain drop of radius ‘ω’, density ρ falling under gravity through air of density a experiences a force of buoyancy equal to the weight of displaced air which is (\(\frac{1}{2}\)πa³) σg.

The weight of the rain drop acting downwards = (\(\frac{1}{2}\)πa³) ρg.

∴ Resultant force acting downwards = \(\frac{1}{2}\)πa³ρg – \(\frac{1}{2}\)πa³σg

When this force is equal to the viscous drag acting upwards, then the rain drop acquires a constant velocity called terminal velocity, v_t.

At terminal velocity viscous drag = 6πηav.

Definition:
Terminal velocity of a body falling through a liquid is defined as that constant velocity which the body acquires when it falls in a fluid.

Problems

Question 1.
Find the excess pressure inside a soap bubble of radius 5 mm. (Surface tension is 0.04 N/m). [TS May ’16]
Solution:
Radius r = 5 mm = 5 × 10^-3 m.
Surface tension S_T = 0.04 N/m
= 4 × 10^-2 N/m.
Excess pressure inside soap bubble

Question 2.
Calculate the work done in blowing a soap bubble of diameter 0.6 cm. against the surface tension force. (Surface tension of soap solution = 2.5 × 10^-2 Nm^-1)
Solution:
Work done = Surface tension (S) × increase of area (2 × 4πr²)
∴ W = S ( 4πr² ) × 2
(since the bubble has two surfaces)

Question 3.
How high does methyl alcohol rise in a glass tube of diameter 0.06 cm? (Surface tension of methyl alcohol = 0.023 Nm^-1 and density = 0.8 gmcm^-3. Assume that the angle of contact is zero)
Solution:
Surface tension of methyl alcohol (S) = 0.023 N/m.
Density, ρ = 0.8 gr/cm³ = 800 kg/m³
Diameter of tube, D = 0.06 cm

Question 4.
What should be the radius of a capillary tube if water has to rise to a height of 6 cm in it ? (Surface tension of water – 7.2 × 10^-2 Nm^-1)
Solution:
Surface Tension of water,
S = 7.2 × 10^-2 N/m
Height of water, h = 6 cm = \(\frac{6}{100}\) m
Radius of capillary tube r = ?

Question 5.
Find the depression of the meniscus in the capillary tube of diameter 0.4 mm dipped in a beaker containing mercury. (Density of mercury = 13.6 × 10³ Kg m^-3 and surface tension of mercury = 0.49 Nm^-1 and angle of contact = 135°).
Solution:
Diameter of tube = 0.4 mm ;
∴ Radius, r = 0.2 mm = \(\frac{0.2}{10^3}\) m
Density of mercury = 13.6 × 10³ kg/m³
Angle of contact, 0 = 135°
Surface tension of mercury, S = 0.49 N/m.

Question 6.
If the diameter of a soap bubble is 10 mm and its surface tension is 0.04 Nm-1, find the excess pressure inside the bubble. [TS Mar. ’18, My ’16; AP June ’15; Mar. ’14]
Answer:
Diameter of soap bubble =10 mm
Radius, r = 5 mm = 5 × 10^-3m
Surface tension, S = 0.04 Nm^-1
Excess pressure inside the soap bubble, P = \(\frac{4S}{r}\)

Question 7.
If work done by an agent to form a bubble of radius R is W, then how much energy is required to increase its radius to 2R?
Solution:
Energy required to form soap bubble of radius, R = W .
∴ w = 8πR²
Work done to blow a bubble of Radius 2R = 8π(2R)² = 4w
∴ Work done to increase the radius from R to 2R = 4w – w = 3w

Question 8.
If two soap bubbles of radii R₁ and R₂ (in vacuum) coalasce under isothermal conditions, what is the radius of the new bubble. Take T as the surface tension of soap solution.
Solution:
When joined in isothermal condition change in temperature of system is zero. So change in internal energy of the system is zero.
Let
Surface energy of 1st bubble U₁ = 8πR2S
Surface energy of 2nd bubble U₂ = 8πR²₁S
Surface energy of new bubble U = 8πR²₂S
But 8πR²S= 8πR²₁S + 8πR²₂S
⇒ R² = R²₁ +R²₂
Radius of new bubble R² = \(\sqrt{\mathrm{R}_1^2+\mathrm{R}_2^2}\)

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

TS Inter 1st Year English Grammar Parts of Speech

Q.No. 9 (8 × 1/2 = 4 Marks)

In our conversation we use different words. Each word has a specific function. The words are divided into various classes, according to their use. All the words in English can be classified into eight classes which are called parts of speech. They are:

1. Noun
2. Pronoun
3. Adjective
4. Preposition
5. Verb
6. Adverb
7. Conjunction
8. Interjection.

1. NOUN

A noun is a naming word.
e.g. : boy, tree, king, Hyderabad, rose, happiness, etc.
Kinds of nouns : Nouns are divided into four kinds. They are :
1. Proper Nouns : A proper noun is the name of a particular person, place, river, country, mountain, etc.
Kumar (person), Delhi (place), Godavari (river), Sri Lanka (country), Vmdhyas (mountains)

2. Common Nouns : A common noun refers to a kind or class of things.
e g. : tiger, sugar, wall, bag, building, etc.
Common Nouns are again classified into countable nouns and uncountable nouns.
Countable Nouns : These can be counted.
Eg : boys (ten boys), flowers (three flowers, etc.)
Uncountable Nouns : These cannot be counted. They remain in mass, e.g. : Copper, rice, water.

3. Collective Nouns : They are the groups of the same class.
e.g. : crowd, herd, government, army, family, parliament, etc.

4. Abstract Nouns : They are the names of quality or state.
e.g. : Kindness, childhood, youth, fear, etc.

2. PRONOUN

A pronoun is a word used instead of a noun.
e.g. : he, she, it, we, mine, those, etc.
Personal pronouns : I, me, you, he him, etc.
Reflexive pronouns : myself, herself, himself, themselves, itself, etc.

3. ADJECTIVE

An adjective is a qualify defining word.
e.g. : beautiful (Mar. ’19), clever, neat, enough, red, pure, etc.
Kinds of Adjectives :

1. Adjectives of Quality : honest, good, clever, etc.
2. Adjectives of Quantity : little, some, all, no, half, etc.
3. Adjectives of Number : five, few, second, most, etc.
4. Demonstrative Adjectives : this, these, those, such, etc.
5. Interrogative Adjectives : what, which, whose, etc.

4. PREPOSITIONS

A preposition is a word placed before a noun or a pronoun to show in what relation the person or thing denoted by it stands in regard to something else.
Kinds of Prepositions :

1. Simple Prepositions : to, up, with, at, by, from, in, of (Mar. ’19)) off, etc.
2. Compound Prepositions : across, above, beyond, underneath, without, etc.
3. Phrase Prepositions : jn front of, by means of, with regard to, in favour of, etc.

5. VERB

A verb shows action, state, possession, change in state.
e.g. : laugh, say, sing, gather, kill, etc.
Kinds of verbs :

1. Transitive Verb : It has an object.
   e.g. : The boys are playing football.
   I have done my homework.
2. Intransitive Verb : It has no object.
   e.g. : She sleeps.
   The moon shines.
   Ants fight.

6. ADVERB

An Adverb modifies the meaning of a verb, an adjective or another adverb.
e.g. : She writes neatly.
Kinds of Adverbs :

1. Adverbs of Time : before, now, yesterday, never, etc.
2. Adverbs of Frequency : again, twice, always, seldom, etc.
3. Adverbs of Place : out, near, here, there, etc.
4. Adverbs of Manner : well, thus, sadly, so, etc.
5. Adverbs of Degree : too, almost, better, clever, partly, fully, etc.
6. Adverbs of Reason : hence, so, therefore, etc.

7. CONJUNCTION

A joining word is a conjunction.
e.g. : and; or; but; if
Kinds of Conjuctions :

1. Correlative Conjunctions : both … and, not only … but also, either … or, neither … nor, etc.
2. Compound Conjunctions : even if, so that, as well as, etc.
3. Subordinating Conjunctions : after, because, if, unless, as, when, while, etc.

8. INTERJECTION

The words which express sudden feeling or emotion are Interjections.
e.g. : Oh ! Hurrah ! Alas ! Hello ! Ooch ! Hey !, etc.
Sing a song about the parts of speech in English.
A noun is the name of a thing.
As a school, a garden, a kite, or a king;
Adjectives tell the kind of noun,
As great, small, pretty, white, or brown;
Instead of nouns the pronouns stand,
He, she, it, I, you, we, they-all in hand;
Verbs tell us of something being done,
To read, count, laugh, cry, or run;
How things are done the adverbs tell,
As slowly, quickly, very, or well;
Conjunctions join the words together,
As men and women, wind and weather,
The preposition stands before Ac noun, as in near or through a door;
The interjection shows surprise,
As-Oh ! Ow ! Aha ! Ah ! How wise !
These are the eight parts of English speech,
Which reading, writing, speaking teach.

Remember that the part of speech of a given word is decided by the part that word plays in a sentence. The same word may function in various ways in different sentences. Look at the examples Carefully.

a. We water plants regularly, (water – verb – నీరు పోయుట)
water is precious, (water – noun – నీరు)

b. There is a man waiting for you. (man – noun)
Two persons man our gates round the clock, (man – కాపలకాయుట – v)

c. He is a fast bowler, (fast – adjective – వేగ)
She drives cars very fast. (fast – adverb వేగంగా )

d. Heat expand metals, (heat = $» – i5& – noun)
Don’t heat it. It gets damaged (heat = i§&i5cfto – verb)

e. Hard work always pays, (hard = కష్ట – adjective)
She works very hard. (hard = £కష్టపడి – adverb)

Exercises

I. Read the following passage and identify the part of speech of the each underlined word.

There was a farmer (1) who grew (2) superior (3) quality rice. Every year, his rice won prizes in the state competition (4). Once a newspaper reporter interviewed (5) him and discovered that the farmer shared his seed rice with his neighbours (6). “How can you afford to share your best seed rice with (7) your neighbors when they are entering their own produce (8) in competition with yours, each year ?” The reporter asked. The farmer replied, “Didn’t you know ? The wind (9) picks up pollen grains from (10) the ripening paddy and swirls (11) it from field to field. If my neighbors grow inferior, substandard and poor (12) quality rice, cross-pollination will steadily (13) degrade the quality (14) of my produce. If I have to grow good rice I must help (15) my neighbors to grow good rice.”
Answer:
1) farmer n noun
2) grew n verb
3) superior n adjective
4) competition n noun
5) interviewed n verb
6) neighbours n noun
7) with n preposition
8) produce n noun
9) wind n noun
10) from n preposition
11) swirls n verb
12) poor n adjective
13) steadily n adverb
14) quality n noun
15) help n verb

II. Identify the parts of speech of the underlined words.

1. Hyderabad is a historical city.
2. Children are a source of joy to the parents.
3. Honesty is the best policy.
4. We learn many firings through observation.
5. Since it was raining, he took an umbrella with him.
6. Alas ! Abdul Kalam is dead.
7. They themselves interfered in the dispute.
8. The boy ran into the park joyfully.
9. Music draws the attention of everyone.
10. Cricket match is watched by lakhs of people.
Answer:
1) adjective
2) noun
3) noun
4) verb
5) since n conjunction; with n preposition
6) interjection
7) pronoun
8) adverb
9) pronoun
10) noun

III. Identify the part of speech of the bold words in the following sentences.

1. Several writers wrote about education.
2. The hungry dogs are howling.
3. People eat vegetables across the world.
4. An idea can change a life.
5. Food is a necessity for life.
6. I invited him to the party.
7. She is interested in painting.
8. He completed the whole work successfully.
9. The woman beside David is my cousin.
10. She has two children.
11. Treatment heals wounds.
12. Ah ! don’t say you don’t agree with me.
13. Since he was tired, he went to bed early.
14. I love singing because it is interesting.
15. I can’t be at ease until I wash my face.
16. Eureka ! I got it.
17. I like salt and pepper. ,
18. Have you passed ? Congratulations !
19. Make hay while the sun shines.
20. Wake up early so that you can study.
Answer:
1) several – adjective ; about – preposition
2) hungry – adjective
3) vegetables – noun ; world – noun
4) an – adjective (article, determiner)
5) food – noun ; life – noun
6) him – pronoun
7) interested – adjective
8) whole – adjective
9) beside – preposition
10) two – adjective (numeral)
11) treatment – noun ; wounds – noun
12) Ah ! – interjection
13) since – conjunction
14) because – conjunction
15) until – conjunction
16) Eureka ! – interjection
17) and – conjunction
18) Congratulations ! – noun
19) while – conjunction
20) early – adverb

IV. Identify the part of speech of the following underlined words.

Two Sides of Life

Question 1.
It is a very (1) bad habit (2) to get into (3), that of being continually (4) moody (5) and discouraged, and (6) of (7) making the atmosphere (8) uncomfortable for everybody who comes (9) within ten (10) feet of you.
Answer:
1) very n adverb
2) habit n noun
3) into – preposition
4) continually – adverb
5) moody – adjective
6) and – conjunction
7) of – preposition
8) atmosphere – noun
9) comes – verb
10) ten – adjective (numeral)

Father, Dear Father

Question 2.
Do you (1) think, literacy (2) is a harbinger (3) of restlessness, fear (4), frustration ? Is it (5) Adam (6) and (7) Eve eating the Tree (8) of (9) knowledge, all (10) over again ?
Answer:
1) you – pronoun
2) literacy – noun
3) harbinger – noun
4) fear – noun
5) It – pronoun
6) Adam – noun
7) and – conjunction
8) tree – noun
9) of – preposition
10) all – adverb

Green Champion –

Question 3.
Although (1) Thimmakka did not receive (2) formal (3) education, her (4) work (5) has been honoured (6) with (7) the National (8) Citizen’s Award (9) of (10) India.
Answer:
1) although – conjunction
2) receive – verb
3) formal – adjective
4) her – possessive pronoun (adjective)
5) work – noun
6) honoured – verb
7) with – preposition
8) national – adjective
9) award – noun
10) of – preposition

The First Four Minutes

Question 4.
I had (1) a moment (2) of (3) mixed joy (4) and anguish, when (5) my mind (6) took over. It (7) faced well (8) ahead of mu body and (9) drew mu body compellingly (10) forward.
Answer:
1) had – verb
2) moment – noun
3) of – preposition
4) joy – noun
5) when – pronoun
6) mind – noun
7) it – pronoun
8) well – adverb
9) and – conjunction
10) compelling – adverb

Box and Cox

Question 5.
Box : Stop ! (1) Can you (2) inform (3) me who (4) the individual (5) is that I invariably (6) encounter (7) going downstairs when I’m coming up (8), and (9) coming upstairs (10) when I’m going down ?
Answer:
1) stop – verb
2) you – pronoun
3) inform – verb
4) who – pronoun
5) individual – noun
6) invariably – adverb
7) encounter – verb
8) up – adverb
9) and – conjunction
10) upstairs – adverb

Question 6.
Ah (1), then you (2) mean to say that this (3) gentleman’s smoke (4), instead of emulating the example of all (5) other sorts of (6) smoke, and (7) going up the chimney, thinks (8) proper to affect a singularity (9) by taking the contrary (10) direction.
Answer:
1) Ah – interjection
2) you – pronoun
3) this – adjective (determiner)
4) smoke – noun
5) all – adverb
6) of – preposition
7) and – conjunction
8) thinks – verb
9) singularity – noun
10) contrary – adjective

V. Identify the part of speech of the bold words in the following sentences.

1. What is the result of that kind of schooling ?
2. I cannot answer that question.
3. Each individual who wishes to succeed must get that kind of discipline.
4. Such persons are surely und esirable.
5. I asked my Biology teacher what I should do to save it.
6. From his talk it seems studies were an ancillary subject; and living and experiencing, the major subject.
7. And she was cross.
8. Papa, that’s what happens in my craft and drawing class.
9. Anyway, Papa, do you know where lost that quarter mark that brought about my fall ?
10. Thimmakka could not go to school due to poverty and lack of facilities.
11. The decision was mine alone.
12. The attempt was on.
13. My knowledge of pace deserted me
14. A voice shouting ‘Relax’ penetrated into me above the noise of the crowd.
15. There was no pain, only a great unity of movement and aim.
16. The world seemed to stand still or did not exist.
17. The noise in my ears was that of the faithful Oxford crowd.
18. There were only fifty yards more.
19. I felt like an exploded flashlight with no will to live.
20. Well wonders will never cease.
Answer:
1) schooling – noun
2) answer – verb
3) wishes – verb
4) purely – adverb
5) what – pronoun
6) talk – noun; ancillary – adjective
7) and – conjunction
8) what – pronoun fall – noun
9) where – adverb; quarter – noun;
10) lack – noun

11) alone – adverb
12) attempt – noun
13) deserted – verb
14) above – preposition
15) only – adjective
16) still – adjective
17) that – pronoun
18) more – pronoun – determiner
19) will – noun
20) well – interjection