TS Inter 1st Year Maths 1A Ratios up to Transformations Important Questions Long Answer Type

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

TS Inter 1st Year Maths 1A Ratios up to Transformations Important Questions Long Answer Type

Question 1.
If A, B, Care the angles of a triangle, prove that sin 2A + sin 2B + sin 2C = 4 sin A sin B sin C.
Answer:
Given A + B + C = 180°
LHS = sin 2A + sin 2B + sin 2C
= 2sin\(\left(\frac{2 \mathrm{~A}+2 \mathrm{~B}}{2}\right)\) cos\(\left(\frac{2 \mathrm{~A}-2 \mathrm{~B}}{2}\right)\) + sin 2C
= 2 sin (A + B) cos (A – B) + sin 2C
= 2 sin (180° – C) cos (A – B) + sin 2C
= 2 sin C cos (A – B) + 2 sin C cos C
= 2 sin C [cos (A – B) + cos C]
= 2 sin C [cos (A – B) + cos [180° – (A + B)]
= 2 sin C[cos (A – B) – cos (A + B)]
= 2 sin C (2 sin A sin B)
= 4 sin A sin B sin C = RHS

Question 2.
If A, B, C are angles of a triangle, prove that cos 2A + cos 2B + cos 2C = – 4cos A cos B cos C – 1.
Sol. Given A + B + C = 180°
LHS = cos 2A + cos 2B + cos 2C
= 2cos\(\left(\frac{2 \mathrm{~A}+2 \mathrm{~B}}{2}\right)\) cos\(\left(\frac{2 \mathrm{~A}-2 \mathrm{~B}}{2}\right)\) + cos 2C
= 2 cos (A + B) cos (A – B) + cos 2C
= 2 cos (180° – C) cos (A – B) + cos 2C
= – 2 cos C cos (A – B) + 2 cos2C – 1
= – 2 cos C [cos (A – B) – cos C] – 1
= – 2 cos C [cos (A – B) – cos [180° – (A + B)]] -1
= -2 cos C [cos (A – B) + cos (A + B)] – 1
= – 2cos C (2 cos A cos B) – 1
= – 4 cos A cos B cos C – 1 = RHS

Question 3.
If A + B + C = \(\frac{3 \pi}{2}\), prove that cos 2A + cos 2B + cos 2C = 1 – 4sinA.sinB.sinC. [Mar. ’13, ’01]
Answer:
Given A + B + C = \(\frac{3 \pi}{2}\)
L.H.S. = cos 2A + cos 2B + cos 2C
= 2 cos (A + B) cos (A – B) + cos 2C
= -2 sin C cos (A – B) + 1 – 2 sin2C
[A + B = \(\frac{3 \pi}{2}\) ⇒ cos (A + B) = – sin C]
= 1 – 2 sin C [cos (A – B) + sin C]
= 1 – 2 sin C [cos (A – B) – cos (A + B)]
= 1 – 2 sin C (2 sin A sin B)
= 1 – 4 sin A sin B sin C = RHS
∴ cos 2A + cos 2B + cos 2C = 1 – 4 sin A sin B sin C

TS Inter First Year Maths 1A Ratios up to Transformations Important Questions Long Answer Type

Question 4.
If A + B + C = \(\frac{3 \pi}{2}\), prove that cos 2A + cos 2B + cos 2C = 1 + 4 sin A. sin B sin C.
Answer:
Given A + B + C = 90°
LHS = cos 2A + cos 2B + cos 2C
= 2 cos\(\left(\frac{2 \mathrm{~A}+2 \mathrm{~B}}{2}\right)\) cos\(\left(\frac{2 \mathrm{~A}-2 \mathrm{~B}}{2}\right)\) + cos 2C
= 2 cos (A + B) cos (A – B) + cos 2C
= 2 cos (90° – C) cos (A – B) + cos 2C
= 2 sin C cos (A – B) + 1 – 2 sin2C
= 1 + 2 sin C [cos (A – B) – sin C]
= 1 + 2 sin C [cos (A – B) – sin [90° – (A + B)]]
= 1 + 2 sin C [cos (A – B) – cos (A + B)]
= 1 + 2 sin C (2 sin A sin B)
= 1 + 4 sin A sin B sin C = RHS.

Question 5.
If A, B, C are angles in a triangle, then prove that cos A + cos B + cos C = 1 + 4 sin \(\frac{A}{2}\) sin \(\frac{B}{2}\) sin \(\frac{C}{2}\). [Mar. ’18(AP); May ’09]
Answer:
Given A + B + C = 180°
L.H.S = cos A + cos B + cos C
TS Inter First Year Maths 1A Trigonometric Ratios up to Transformations Important Questions Long Answer Type 1

Question 6.
If A, B, C are angles in a triangle, then prove that cos A + cos B – cos C = -1 + 4 cos \(\frac{A}{2}\) cos \(\frac{B}{2}\) sin \(\frac{C}{2}\). [Mar. ’19(TS); May ’06]
Answer:
Given A + B + C = 180°
L.H.S = cos A + cos B – cos C
TS Inter First Year Maths 1A Trigonometric Ratios up to Transformations Important Questions Long Answer Type 2

Question 7.
If A, B, C are angles in a triangle, then prove that sin2\(\frac{A}{2}\) + sin2\(\frac{B}{2}\) – sin2\(\frac{C}{2}\) = 1 – 2cos \(\frac{A}{2}\). cos \(\frac{B}{2}\). sin \(\frac{C}{2}\). [Mar. ’16(AP), ’06; May ’15(TS), ’11; B.P]
Answer:
Given A + B + C = 180°
L.H.S = sin2\(\frac{A}{2}\) + sin2\(\frac{B}{2}\) – sin2\(\frac{C}{2}\)
TS Inter First Year Maths 1A Trigonometric Ratios up to Transformations Important Questions Long Answer Type 3

TS Inter First Year Maths 1A Ratios up to Transformations Important Questions Long Answer Type

Question 8.
If A + B + C = π, then prove that cos2\(\frac{A}{2}\) + cos2\(\frac{B}{2}\) – cos2\(\frac{C}{2}\) = 2(1 + sin \(\frac{A}{2}\). sin \(\frac{B}{2}\). sin \(\frac{C}{2}\)). [Mar. ’12, Mar. ’15(AP & TS)]
Answer:
Given A + B + C = π
L.H.S = cos2\(\frac{A}{2}\) + cos2\(\frac{B}{2}\) – cos2\(\frac{C}{2}\)
TS Inter First Year Maths 1A Trigonometric Ratios up to Transformations Important Questions Long Answer Type 4

Question 9.
If A+ B + C = π, then prove that cos2\(\frac{A}{2}\) + cos2\(\frac{B}{2}\) – cos2\(\frac{C}{2}\) = 2 cos\(\frac{A}{2}\) cos\(\frac{B}{2}\) sin\(\frac{C}{2}\). [May ’10]
Answer:
Given A + B + C = π
L.H.S = cos2\(\frac{A}{2}\) + cos2\(\frac{B}{2}\) – cos2\(\frac{C}{2}\)
TS Inter First Year Maths 1A Trigonometric Ratios up to Transformations Important Questions Long Answer Type 5

Question 10.
If A, B, C are the angles in a triangle, then prove that sin\(\frac{A}{2}\) + sin\(\frac{B}{2}\) + sin \(\frac{C}{2}\) = 1 + 4sin\(\left(\frac{\pi-A}{4}\right)\)sin\(\left(\frac{\pi-B}{4}\right)\)sin\(\left(\frac{\pi-C}{4}\right)\). [Mar. ’14, ’11, ’96]
Answer:
Given A + B + C = 180°
TS Inter First Year Maths 1A Trigonometric Ratios up to Transformations Important Questions Long Answer Type 6

Question 11.
In triangle ABC, prove that cos\(\frac{1}{2}\) + cos\(\frac{B}{2}\) + cos\(\frac{C}{2}\) = 4 cos\(\left(\frac{\pi-A}{4}\right)\) cos\(\left(\frac{\pi-B}{4}\right)\) cos\(\left(\frac{\pi-C}{4}\right)\). [Mar ’14, ’13, ’07, ’97; Mar. ’10, ’07, ’05, ’03]
Answer:
In ΔABC, A + B + C = 180°
TS Inter First Year Maths 1A Trigonometric Ratios up to Transformations Important Questions Long Answer Type 7
∴ cos\(\frac{1}{2}\) + cos\(\frac{B}{2}\) + cos\(\frac{C}{2}\) = 4 cos\(\left(\frac{\pi-A}{4}\right)\) cos\(\left(\frac{\pi-B}{4}\right)\) cos\(\left(\frac{\pi-C}{4}\right)\)

TS Inter First Year Maths 1A Ratios up to Transformations Important Questions Long Answer Type

Some More Maths 1A Ratios up to Transformations Important Questions

Question 1.
If sin θ = \(\frac{4}{5}\) and θ is not in the first quadrant, find the value of cos θ.
Answer:
Given sin θ = \(\frac{4}{5}\)
Since θ is not in the first quadrant and sin θ > 0 we have 90° < θ < 180°
∴ cos θ = \(\sqrt{1-\sin ^2 \theta}=\sqrt{1-\frac{16}{25}}=\frac{-3}{5}\)

Question 2.
If cosec θ + cot θ = find cos θ and determine the quadrant In which θ lies.
Answer:
We have cosec2 θ – cot2 θ = 1
(cosec θ + cot θ) (cosec θ – cot θ) = 1
= cosec θ – cot θ = \(\frac{1}{{cosec} \theta+\cot \theta}\) = 3
= cosec θ + cot θ = 3 …………………… (1)

Given cosec θ + cot θ = \(\frac{1}{3}\) …………………. (2)
Solving(1)& (2)
∴ 2cosec θ = 3 + \(\frac{1}{3}=\frac{10}{3}\)
⇒ cosec θ = \(\frac{5}{4}\)
⇒ sin θ = \(\frac{3}{5}\)

Also 2 cot θ = \(\frac{1}{3}\) – 3 = \(\frac{-8}{3}\)
⇒ cot θ = \(\frac{-4}{3}\)
⇒ tan θ = \(\frac{-3}{4}\)

cos θ = cot θ.sinθ = \(\left(-\frac{4}{3}\right)\left(\frac{3}{5}\right)=-\frac{4}{5}\)
sin θ is positive and cos θ is a negative
⇒ θ lies in II quadrant.

Question 3.
If sec θ + tan θ = 5, find the quadrant in which θ lies and find the value of sin θ.
Answer:
We have sec2θ – tan2θ = 1
⇒ (sec θ + tan θ) (sec θ – tan θ) = 1
⇒ sec θ – tan θ = \(\frac{1}{5}\) ………….. (1)
Also given sec θ + tan θ = 5 ………………………. (2)

Adding (1) and (2), 2sec θ = 5 + \(\frac{1}{5}\) = \(\frac{26}{5}\)
TS Inter First Year Maths 1A Trigonometric Ratios up to Transformations Important Questions Long Answer Type 8
tan θ is +ve, sec θ is + ve
⇒ θ lies in first quadrant

Question 4.
Prove that cot\(\frac{\pi}{16}\).cot\(\frac{2 \pi}{16}\).cot\(\frac{3 \pi}{16}\)………………cot\(\frac{7 \pi}{16}\) = 1.
Answer:
TS Inter First Year Maths 1A Trigonometric Ratios up to Transformations Important Questions Long Answer Type 9

Question 5.
If a cos θ – b sin θ = c, then show that a sin θ + b cos θ = ± \(\sqrt{\mathbf{a}^2+\mathbf{b}^2-\mathbf{c}^2}\).
Answer:
Given a cos θ – b sin θ
= c and let asin θ + b cos θ = x
squaring and adding, we get
(a cos θ – b sin θ)2 + (a sin θ + b cos θ) = c2 + x2
a2 (cos2 θ + sin2 θ)2 + b2 (sin2 θ + cos2 θ) = c2 + x2
⇒ a2 + b2 = c2 + x2 ⇒ x2 = a2 + b2 – c2
⇒ x = ±\(\sqrt{\mathbf{a}^2+\mathbf{b}^2-\mathbf{c}^2}\)

TS Inter First Year Maths 1A Ratios up to Transformations Important Questions Long Answer Type

Question 6.
If 3 sin A + 5 cos A = 5, then show that 5 sin A – 3 cos A = ± 3.
Answer:
Given that 3 sin A + 5 cos A = 5
Let 5 sin A – 3 cos A = x
Squaring and adding, we get
(3 sin A + 5 cos A)2 + (5 sin A – 3 cos A)2
⇒ 9 (sin2A + cos2A) + 25 (cos2A + sin2A) = 25 + x2
⇒ 34 = 25 + x2
⇒ x2 = 9
⇒ x = ± 3
∴ 5 sin A – 3 cos A = ± 3

Question 7.
If tan 20° = p, Prove that \(\frac{\tan 610^{\circ}+\tan 700^{\circ}}{\tan 560^{\circ}-\tan 470^{\circ}}=\frac{1-p^2}{1+p^2}\).
Answer:
Given that tan 20° = p, then
TS Inter First Year Maths 1A Trigonometric Ratios up to Transformations Important Questions Long Answer Type 10

Question 8.
Evaluate sin282\(\frac{1}{2}^{circ}\) – sin2 22\(\frac{1}{2}^{circ}\).
Answer:
sin282\(\frac{1}{2}^{circ}\) – sin2 22\(\frac{1}{2}^{circ}\)
= sin[82\(\frac{1}{2}^{circ}\) + 22\(\frac{1}{2}^{circ}\)] + sin[82\(\frac{1}{2}^{circ}\) – 22\(\frac{1}{2}^{circ}\)]
= sin 105°. sin 60°
[∵ Use sin2A – sin2B] = sin(A +B) sin (A – B)
= sin 60° sin(60° + 45°)= sin 60°
[= sin 60° cos 45° + cos 60° sin 45°]
\(\frac{\sqrt{3}}{2}\left[\frac{\sqrt{3}}{2 \sqrt{2}}+\frac{1}{2 \sqrt{2}}\right]=\frac{\sqrt{3}(\sqrt{3}+1)}{4 \sqrt{2}}=\frac{3+\sqrt{3}}{4 \sqrt{2}}\)

Question 9.
Evaluate cos2112\(\frac{1}{2}^{circ}\) – sin252\(\frac{1}{2}^{circ}\).
Answer:
Use cos2A – sin2B = cos(A + B) cos (A – B)
= cos2112\(\frac{1}{2}^{circ}\) – sin252\(\frac{1}{2}^{circ}\)
= cos [112\(\frac{1}{2}^{circ}\) + 52\(\frac{1}{2}^{circ}\)] cos[112\(\frac{1}{2}^{circ}\) – 52\(\frac{1}{2}^{circ}\)]
= cos 165° . cos 60
= cos 60° cos(180 – 15) = – cos 60°. cos 15°
= \(-\frac{1}{2}\left[\frac{\sqrt{3}+1}{2 \sqrt{2}}\right]=-\frac{\sqrt{3}+1}{4 \sqrt{2}}\)

Question 10.
Prove that tan 72° = tan 18° + 2 tan 54°.
Answer:
We have cot A – tan A = \(\frac{1}{\tan A}\) – tan A
⇒ \(\frac{1-\tan ^2 \mathrm{~A}}{\tan \mathrm{A}}=\frac{2\left(1-\tan ^2 \mathrm{~A}\right)}{2 \tan \mathrm{A}}=\frac{2}{\tan 2 \mathrm{~A}}\) = 2 cot 2A
∴ cot A – tan A = 2 cot 2A
⇒ cot A = tan A + 2 cot 2A

Take A = 18°, then cot 18°
= tan 18° + 2 cot 36°
⇒ cot (90 – 72)
= tan 18° + 2 cot (90 – 54)
⇒ tan 72° = tan 18° + 2 tan 54°

Question 11.
Find the value of tan 56° – tan 11° -tan 56°. tan 11°.
Answer:
Consider 56° – 11° = 45°
⇒ tan (56° -11°) = tan 45° = 1
⇒ \(\frac{\tan 56^{\circ}-\tan 11^{\circ}}{1+\tan 56^{\circ} \tan 11^{\circ}}\) = 1
⇒ tan 56° – tan 110 – tan 56° tan 11° = 1.

Question 12.
If tan θ = \(\frac{\cos 11^{\circ}+\sin 11^{\circ}}{\cos 11^{\circ}-\sin 11^{\circ}}\) and θ is in the third quadrant, find θ.
Answer:
Given tan θ = \(\frac{\cos 11^{\circ}+\sin 11^{\circ}}{\cos 11^{\circ}-\sin 11^{\circ}}\)
= \(\frac{1+\tan 11^{\circ}}{1-\tan 11^{\circ}}\) = tan(45 + 11) = tan 56°
Since θ is in the third quadrant,
tan 56° = tan (180 + 56) = tan 236°
∴ θ = 236°

Question 13.
Show that cos 35° + cos 85° + cos 155° = 0.
Answer:
cos 35° + cos 85° + cos 155°
= cos 35° + 2cos\(\left(\frac{85+155}{2}\right)\) cos\(\left(\frac{85-155}{2}\right)\)
= cos 35° + 2 cos 120° cos (-35°)
= cos 35° – cos 35° = 0

Question 14.
Simplify cos 100°. cos 40° + sin 100°. sin 40°.
Answer:
Use cos A. cos B + sin A sin B = cos (A – B)
∴ cos 100°. cos 40° + sin 100° . sin 40°
= cos (100° – 40°) = cos 60° = \(\frac{1}{2}\)

Question 15.
Prove that sin 750°. cos 480° + cos 120°. cos 60° =\(\frac{1}{2}\)
Answer:
L.H.S = sin 750°. cos 480° + cos 120°. cos 60°
= sin [2.(360) + 30] cos [360 +120] + cos 120 cos 60
= sin 30 cos 120 + cos 120 cos 60
= \(\left(\frac{1}{2}\right)\left(-\frac{1}{2}\right)+\left(-\frac{1}{2}\right)\left(\frac{1}{2}\right)=\frac{-1}{2}\)

Question 16.
Prove that \(\frac{1}{\cos 290^{\circ}}+\frac{1}{\sqrt{3} \sin 250^{\circ}}=\frac{4}{\sqrt{3}}\).
Answer:
TS Inter First Year Maths 1A Trigonometric Ratios up to Transformations Important Questions Long Answer Type 11

TS Inter First Year Maths 1A Ratios up to Transformations Important Questions Long Answer Type

Question 17.
Prove that √3 cosec 20° – sec 20° = 4.
Answer:
L.H.S = √3 cosec 20° – sec 20°
TS Inter First Year Maths 1A Trigonometric Ratios up to Transformations Important Questions Long Answer Type 12

Question 18.
Find the period of cos (3x + 5) + 7.
Answer:
Let f(x) = cos (3x + 5) + 7
We have period of cos x is 2π ∀ x ∈ R.
∴ f (x) is periodic and period of f is \(\frac{2 \pi}{|3|}\)
\(\frac{2 \pi}{3}\) (or) f(x + p) = f(x)
⇒ cos (3x + 3p + 5) + 7 = cos (2π + 3x + 5) + 7
∴ 3x + 3p + 5 = 2π + 3x + 5
⇒ 3x = 2π
⇒ x = \(\frac{2 \pi}{3}\)

Question 19.
Find the maximum and minimum values of f(x) = 3 sin x – 4 cos x.
Answer:
Given f(x) = 3 sin x – 4 cos x
Comparing with a cos x + b sin x + c
We get a = – 4, b = 3, c = 0
Maximum value = c + \(\sqrt{a^2+b^2}\)
= 0 + \(\sqrt{16+9}=\sqrt{25}\) = 5
Minimum value = c – \(\sqrt{a^2+b^2}\)
= 0 – \(\sqrt{16+9}=\sqrt{25}\) = -5

Question 20.
Find the range of 7 cos x – 24 sin x + 5.
Answer:
Let f(x) = 7 cos x – 24 sin x + 5
a = – 24, b = 7, c = 5

Range = [c – \(\sqrt{a^2+b^2}\), c + \(\sqrt{a^2+b^2}\)]
=[5 – \(\sqrt{576+49}\), 5 + \(\sqrt{576+49}\)]
= [5 – \(\sqrt{625}\), 5 + \(\sqrt{625}\)]
= [5 – 25, 5 + 25] = [-20, 30]

Question 21.
If A – B = \(\frac{3 \pi}{4}\), then show that (1 – tan A)(1 + tan B) = 2.
Answer:
A – B = \(\frac{3 \pi}{4}\)
⇒ tan(A – B) = tan\(\frac{3 \pi}{4}\)
⇒ \(\frac{\tan A-\tan B}{1+\tan A \tan B}\) = -1
⇒ tan A – tan B = – 1 – tan A tan B
⇒ tan A – tan B + tan A tan B = -1
⇒ – tan A + tan B – tan A tan B = 1
⇒ (1 – tan A) + tan B (1 – tan A) = 1 + 1 = 2
⇒ (1 – tan A) (1 + tan B) = 2

Question 22.
If A, B, C are the angles of a triangle and if none of them is equal to \(\frac{\pi}{2}\) then prove that cot A cot B + cot B cot C + cot C cot A = 1.
Answer:
Given A + B + C = π, A + B = π – C
⇒ cot (A + B) = cot (π – C)
⇒ \(\frac{\cot A+\cot B-1}{\cot B+\cot A}\) = – cot C
⇒ cot A cot B – 1 = – cot B cot C – cot C cot A
⇒ cot A cot B + cot B cot C + cot C cot A = 1

Question 23.
If A + B + C = \(\frac{\pi}{2}\) and if none of A, B, C is n an odd multiple of \(\frac{\pi}{2}\), then prove that tan A tan B + tan B tan C + tan C tan A = 1.
Answer:
Given A + B + C = \(\frac{\pi}{2}\)
⇒ A + B = \(\frac{\pi}{2}\) – C
⇒ tan(A + B) = tan(\(\frac{\pi}{2}\) – C)
⇒ \(\frac{\tan A+\tan B}{1-\tan A \tan B}\) = cot C = \(\frac{1}{\tan C}\)
⇒ tan A tan C + tan B tan C = 1 – tan A tan B
⇒ tan A tan B + tan B tan C + tan C tan A = 1

Question 24.
Prove that cos A. cos(\(\frac{\pi}{2}\) + A) cos(\(\frac{\pi}{2}\) -A) = \(\frac{1}{4}\)cos 3A and hence deduce that cos\(\frac{\pi}{2}\)cos\(\frac{2 \pi}{2}\)cos\(\frac{3 \pi}{2}\).cos\(\frac{4 \pi}{2}\) = \(\frac{1}{16}\)
Answer:
L.H.S = cos A.cos(60 + A) cos(60 – A)
= cos A (cos2 60 – sin2 A)
TS Inter First Year Maths 1A Trigonometric Ratios up to Transformations Important Questions Long Answer Type 13

TS Inter First Year Maths 1A Ratios up to Transformations Important Questions Long Answer Type

Question 25.
Show that cos4\(\frac{\pi}{8}\) + cos4\(\frac{3 \pi}{8}\) + 4\(\frac{5 \pi}{8}\) + cos4\(\frac{7 \pi}{8}\) = \(\frac{3}{2}\)
Answer:
TS Inter First Year Maths 1A Trigonometric Ratios up to Transformations Important Questions Long Answer Type 14

Question 26.
Prove that tan α = \(\frac{\sin 2 \alpha}{1+\cos 2 \alpha}\) and hence deduce the values of tan 15° and tan 22\(\frac{1}{2}^{\circ}\)
Answer:
TS Inter First Year Maths 1A Trigonometric Ratios up to Transformations Important Questions Long Answer Type 15

Question 27.
If cos θ > θ, tan θ + sin θ = m and tan θ – sin θ = n then show that m2 – n2 = 4\(\sqrt{mn}\)
Answer:
Given that m = tan θ + sin θ, n = tan θ – sin θ
m + n = 2 tan θ, m – n = 2 sin θ and (m + n) (m -n)
TS Inter First Year Maths 1A Trigonometric Ratios up to Transformations Important Questions Long Answer Type 16

Question 28.
If 0° < A, B < 90°, cos A = \(\frac{5}{13}\) and sin B = \(\frac{4}{5}\), then find the value of sin(A+ B).
Answer:
0° < A, B < 90°, cos A = \(\frac{5}{13}\) ⇒ sin A = \(\frac{12}{13}\)
0° < A, B < 90°, sin B = \(\frac{4}{5}\) ⇒ cos B = \(\frac{3}{5}\)
∴ sin(A + B) = sin A cos B + cos A sin B
= \(\frac{12}{13} \cdot \frac{3}{5}+\frac{5}{13} \cdot \frac{4}{5}=\frac{36}{65}+\frac{20}{65}=\frac{56}{65}\)

Question 30.
If sin A = \(\frac{12}{13}\), cos B = \(\frac{3}{5}\) and neither A nor B is in the first quadrant, then find the quadrant in which A + B lies.
Answer:
Given sin A = \(\frac{12}{13}\)
A is not in the first quadrant then A lies in the Q2.
∴ cos A = \(\frac{-5}{13}\) ⇒ cos B = \(\frac{3}{5}\)

B is not in the Q1 then B lies in the Q4.
∴ sin B = \(\frac{-4}{5}\)
Now sin (A + B) = sin A cos B + cos A sin B
= \(\left(\frac{12}{13}\right)\left(\frac{3}{5}\right)+\left(\frac{-5}{13}\right)\left(\frac{-4}{5}\right)=\frac{36}{65}+\frac{20}{65}=\frac{56}{65}\)

cos (A + B) = cos A . cos B – sin A sin B
= \(\left(\frac{-5}{13}\right)\left(\frac{3}{5}\right)-\left(\frac{12}{13}\right)\left(\frac{-4}{5}\right)=\frac{-15}{65}+\frac{48}{65}=\frac{33}{65}\)
sin (A + B) > 0 & cos (A + B) > 0 then A + B lies in the first quadrant.

Question 31.
Let ABC be a triangle such that cot A + cot B + cot C = √3 then prove that ABC is an equilateral triangle.
Answer:
Given that A + B + C = 180°
We have Σ cot A cot B = 1 …………………(1)
Σ(cot A – cot B)2
= Σ(cot2 A + cos2 B – 2 cot A cot B)
= 2 cot2 A + 2 cot2 B + 2 cot2 C – 2 cot A cot B – 2 cot B cot C – 2 cot C cot A
= 2 [cot A + cot B + cot C]2 – 6 [cot A cot B + cot B cot C + cot C cot A]
= 2 [(√3 )2 ] – 6(1) = 6 – 6 = 0
∴ Σ (cot A – cot B)2 = 0
⇒ cot A = cot B = cot C
⇒ cot A = cot B = cot C = \(\frac{\sqrt{3}}{3}=\frac{1}{\sqrt{3}}\) (∵ cot A + cot B + cot C = 73 )
⇒ A = B = C = 60°
⇒ ΔABC is an equilateral triangle.

TS Inter First Year Maths 1A Ratios up to Transformations Important Questions Long Answer Type

Question 32.
Simplify tan[\(\frac{\pi}{4}\) + θ]. tan[\(\frac{\pi}{4}\) – θ]
Answer:
TS Inter First Year Maths 1A Trigonometric Ratios up to Transformations Important Questions Long Answer Type 17

Question 33.
Simplify tan 75° + cot 75°.
Answer:
(2 + √3)(2 – √3) = 4

Question 34.
Evaluate sin2\(\left[\frac{\pi}{8}+\frac{A}{2}\right]\) – sin2\(\left[\frac{\pi}{8}-\frac{A}{2}\right]\)
Answer:
[∵ sin2A – sin2B = sin (A + B)sin(A – B)
TS Inter First Year Maths 1A Trigonometric Ratios up to Transformations Important Questions Long Answer Type 18

Question 35.
If A + B, A are acute angles such that sin (A + B) = \(\frac{24}{25}\) and tan A = \(\frac{3}{4}\), then find the value of cos B.
Answer:
A + B, A are acute angles ⇒ B is also acute.
Given sin (A + B) = \(\frac{24}{25}\), we have
cos (A + B) = \(\frac{7}{25}\) and tan (A + B) = \(\frac{24}{7}\)
Also tan A = \(\frac{3}{4}\)
We have tan(A + B) = \(\frac{24}{7}\)
TS Inter First Year Maths 1A Trigonometric Ratios up to Transformations Important Questions Long Answer Type 19

Question 36.
In a ΔABC, A is obtuse. If sin A = \(\frac{3}{5}\) and sin B = \(\frac{5}{13}\) Bien show that sin C = \(\frac{16}{65}\).
Answer:
Given, A + B + C = 180°
⇒ A + B = 180° – C
∴ sin (A + B) = sin (180° – C) = sin C .. (1)
∴ A is obtuse angle and A lies in II quadrant.
sin A = \(\frac{3}{5}\) ⇒ cos A = –\(\frac{4}{5}\)
Also sin B = \(\frac{5}{13}\) ⇒ cos B = \(\frac{12}{13}\)
∴ sin C = sin (A + B) = sin A cos B + cos A
sin B = \(\frac{3}{5} \cdot \frac{12}{13}+\left(-\frac{4}{5}\right) \cdot \frac{5}{13}=\frac{36}{65}-\frac{20}{65}=\frac{16}{65}\)

Question 37.
Find the value of sin 22\(\frac{1}{2}^{\circ}\).
Answer:
22\(\frac{1}{2}^{\circ}\) lies in first quadrant and hence all ratios are positive.
TS Inter First Year Maths 1A Trigonometric Ratios up to Transformations Important Questions Long Answer Type 20

Question 38.
If cos θ = \(\frac{-5}{13}\) and \(\frac{\pi}{2}\) < θ < π find the value of sin 2θ.
Answer:
\(\frac{\pi}{2}\) < θ < π ⇒ sin θ > 0 and cos θ = \(\frac{-5}{13}\)
⇒ sin θ = \(\frac{12}{13}\)
∴ sin 2θ = 2sin θ cos θ

Question 39.
For what values of x in the first quadrant \(\frac{2 \tan x}{1-\tan ^2 x}\) is positive?
Answer:
\(\frac{2 \tan x}{1-\tan ^2 x}\) > 0 ⇒ tan 2x > 0 ⇒ 0 < 2x < \(\frac{\pi}{2}\)
⇒ 0 < x < \(\frac{\pi}{4}\)

Question 40.
If cos θ = -3/5 and π < θ < \(\frac{3 \pi}{2}\) find the value of tan \(\frac{\theta}{2}\).
Answer:
TS Inter First Year Maths 1A Trigonometric Ratios up to Transformations Important Questions Long Answer Type 21
∴ \(\frac{\theta}{2}\) lies in second quadrant.

TS Inter First Year Maths 1A Ratios up to Transformations Important Questions Long Answer Type

Question 41.
If 3A is not an odd multiple of \(\frac{\pi}{2}\), prove that tan A tan (60 + A) tan (60 – A) = tan 3A and hence find the value of tan 6° tan 42° tan 66° tan 78°.
Answer:
L.H.S = tan A tan (60 + A) tan (60 – A)
TS Inter First Year Maths 1A Trigonometric Ratios up to Transformations Important Questions Long Answer Type 22
Take A = 6° in above we get tan 6° tan 66° tan 54° = tan 18°
take A = 18° in above result tan 18° tan 78° tan 42° = tan 54°
tan 6° tan 18° tan 42° tan 54° tan 66° tan 78 = tan 18° tan 54°
⇒ tan 6° tan 42° tan 66° tan 78° = 1

Question 42.
If a, b, c are non-zero real numbers and α, β are solutions of the equation a cos θ + b sin θ = c then show that
(i) sin α + sin β = \(\frac{2 b c}{a^2+b^2}\)
(ii) sin α .sin β = \(\frac{c^2-a^2}{a^2+b^2}\)
Answer:
Given a cos θ + b sin θ = c
⇒ a cos θ = c – b sin θ
⇒ a2 cos2 θ = c2 – 2bc sin θ + b2 sin2 θ
⇒ a2 (1 – sin2θ) = c2 – 2bc sin θ + b2 sin2 θ
⇒ (b2 + a2) sin2 θ – 2bc sin θ + (c2 – a2) = 0
This is a quadratic equation in sin θ and suppose sin α, sin β are roots of the equation.
(∵ Given α, β are solutions of the equation)
∴ sin α + sin β = \(\frac{2 b c}{a^2+b^2}\) and sin α .sin β = \(\frac{c^2-a^2}{a^2+b^2}\)

Question 43.
Prove that \(\frac{\sin \theta+\sin 2 \theta}{1+\cos \theta+\cos 2 \theta}\) = tan θ
Answer:
TS Inter First Year Maths 1A Trigonometric Ratios up to Transformations Important Questions Long Answer Type 23

Question 44.
Prove that tan 3A tan 2A tan A = tan 3A – tan 2A – tan A.
Answer:
We have 3A = 2A + A
∴ tan 3A = tan (2A + A) = \(\frac{\tan 2 \mathrm{~A}+\tan \mathrm{A}}{1-\tan 2 \mathrm{~A} \tan \mathrm{A}}\)
⇒ tan 2A + tan A = tan 3A (1 – tan 2A tan A)
⇒ tan A tan 2A tan 3A = tan 3A – tan 2A – tan A

Question 45.
Express cos6A + sin6A in terms of sin 2A.
Answer:
cos6A + sin6A = (cos2A)3 + (sin2A)3
= (cos2A + sin2A)2 – 3 cos2 A sin2 A (cos2 A + sin2 A)
= 1 – 3 cos2A sin2A ……………….(1)
= 1 – \(\frac{3}{4}\) (4 cos2 A sin2 A) = 1 – \(\frac{3}{4}\) sin22A

Question 46.
If sin α = \(\frac{3}{5}\), where \(\frac{\pi}{2}\) < α < π, evaluate cos 3α.
Answer:
Given sin α = \(\frac{3}{5}\)
\(\frac{\pi}{2}\) < α < π ⇒ a lies in the Q2
TS Inter First Year Maths 1A Trigonometric Ratios up to Transformations Important Questions Long Answer Type 24

Question 47.
In a ΔABC, if tan\(\frac{A}{2}=\frac{5}{6}\) and tan \(\frac{B}{2}=\frac{20}{37}\), then show that tan \(\frac{A}{2}=\frac{2}{5}\).
Answer:
In ΔABC, A + B + C = 180°
TS Inter First Year Maths 1A Trigonometric Ratios up to Transformations Important Questions Long Answer Type 25

TS Inter First Year Maths 1A Ratios up to Transformations Important Questions Long Answer Type

Question 48.
If cos θ = \(\frac{5}{13}\) and 270° < θ < 360°, evaluate sin\(\left(\frac{\theta}{2}\right)\) and cos\(\left(\frac{\theta}{2}\right)\)
Answer:
Given cos θ = \(\frac{5}{13}\), where 270° < θ < 360° ⇒ 135° < \(\frac{\theta}{2}\) < 180° ⇒ \(\frac{\theta}{2}\) lies in second quadrant since cos θ = \(\frac{5}{13}\)
TS Inter First Year Maths 1A Trigonometric Ratios up to Transformations Important Questions Long Answer Type 26

Question 49.
Prove that cos\(\frac{2 \pi}{7}\) cos\(\frac{4 \pi}{7}\) cos\(\frac{8 \pi}{7}=\frac{1}{8}\)
Answer:
Let \(\frac{2 \pi}{7}\) = α and x = cos α cos 2α cos 4α and y = sin α sin 2α sin 4α(suppose)
TS Inter First Year Maths 1A Trigonometric Ratios up to Transformations Important Questions Long Answer Type 27

Question 50.
Prove that cos\(\frac{\pi}{11}\) cos\(\frac{2 \pi}{11}\) cos\(\frac{3 \pi}{11}\) cos\(\frac{4 \pi}{7}\) cos\(\frac{5 \pi}{7}=\frac{1}{32}\)
Answer:
Let \(\frac{\pi}{11}\) = α and x = cos α cos 2α cos 3α cos 4α cos 5α and y = sin α sin 2α sin 3α sin 4α sin 5α
xy = \(\frac{1}{2}\)(sin2α) \(\frac{1}{2}\)sin(4α) \(\frac{1}{2}\)sin(6α) \(\frac{1}{2}\)sin(8α) \(\frac{1}{2}\)sin(10α)
= \(\frac{1}{2^5}\)sin 2α sin 4α sin(11α – 5α) sin(11α – 3a) sin(11α – α)
= \(\frac{1}{2^5}\)sin 2α sin 4α sin(π – 5α) sin(π – 3a) sin(π – α)
= \(\frac{1}{2^5}\)sin α sin 2α sin 4α sin 5α = \(\frac{1}{2^5}\)y ⇒ x = \(\frac{1}{2^5}=\frac{1}{32}\)
∴ cos\(\frac{\pi}{11}\) cos\(\frac{2 \pi}{11}\) cos\(\frac{3 \pi}{11}\) cos\(\frac{4 \pi}{7}\) cos\(\frac{5 \pi}{7}=\frac{1}{32}\)

Question 51.
If O < A < B < \(\frac{\pi}{4}\) and sin (A + B) = \(\frac{24}{25}\) and cos(A – B) = \(\frac{4}{5}\) then find the value of tan 2A. [Mar. ’15(TS)]
Answer:
O < A < B < \(\frac{\pi}{4}\) ⇒ O < A + B < \(\frac{\pi}{2}\), –\(\frac{\pi}{2}\) < A – B < O
TS Inter First Year Maths 1A Trigonometric Ratios up to Transformations Important Questions Long Answer Type 28

Question 52.
In ΔABC, prove that cos\(\frac{A}{2}\) + cos\(\frac{B}{2}\) – cos\(\frac{B}{2}\) = 4 cos\(\left(\frac{\pi+A}{4}\right)\) cos\(\left(\frac{\pi+B}{4}\right)\) cos\(\left(\frac{\pi-C}{4}\right)\). [Mar. ’05]
Answer:
In ΔABC, A + B + C = 180°
TS Inter First Year Maths 1A Trigonometric Ratios up to Transformations Important Questions Long Answer Type 29

TS Inter First Year Maths 1A Ratios up to Transformations Important Questions Long Answer Type

Question 53.
In ΔABC, prove that sin\(\frac{A}{2}\) + sin\(\frac{B}{2}\) – sin\(\frac{C}{2}\) = -1 + 4cos\(\left(\frac{\pi+A}{4}\right)\)cos\(\left(\frac{\pi+B}{4}\right)\)cos\(\left(\frac{\pi-C}{4}\right)\).
Answer:
In ΔABC, A + B + C = 180° ………….(1)
TS Inter First Year Maths 1A Trigonometric Ratios up to Transformations Important Questions Long Answer Type 30

Question 54.
If A + B + C = 2S, then prove that sin (S – A) + sin(S – B) + sin C = 4 cos \(\left(\frac{S-A}{2}\right)\) cos\(\left(\frac{S-B}{2}\right)\) sin\(\left(\frac{C}{2}\right)\).
Answer:
Given A + B + C = 2S
L.H.S = sin(S – A) + sin (S – B) + sin C
TS Inter First Year Maths 1A Trigonometric Ratios up to Transformations Important Questions Long Answer Type 31

Question 55.
Eliminate ‘θ’ from x = a cos3θ, y = b sin3θ.
Answer:
Given x = a cos3θ, y = b sin3θ.
\(\frac{x}{a}\) = cos3θ, \(\frac{y}{b}\) = sin3θ
TS Inter First Year Maths 1A Trigonometric Ratios up to Transformations Important Questions Long Answer Type 32

Question 56.
If none of the denominators is zero, prove that \(\left(\frac{\cos A+\cos B}{\sin A-\sin B}\right)^n+\left(\frac{\sin A+\sin B}{\cos A-\cos B}\right)^n\) = 2cotn\(\left(\frac{A-B}{2}\right)\), if n is even 0, if n is odd. [Mar. ’16(TS)]
Answer:
TS Inter First Year Maths 1A Trigonometric Ratios up to Transformations Important Questions Long Answer Type 33
if n is odd, since (-1)n = 1
we have LHS = 0
if n is even and (- 1)n = 1
LHS = 2cotn\(\left(\frac{A-B}{2}\right)\)

Question 57.
If A + B + C = 2S, then prove that cos(S – A) + cos(S – B) + cos C = 1 + 4cos\(\left(\frac{S-A}{2}\right)\) cos\(\left(\frac{S-B}{2}\right)\) cos\(\left(\frac{C}{2}\right)\). [Mar. ’17(TS)]
Answer:
Given A + B + C = 2S
L.H.S = cos(S – A) + cos(S – B) + cos C
TS Inter First Year Maths 1A Trigonometric Ratios up to Transformations Important Questions Long Answer Type 34

Question 58.
Prove that: sin 50° – sin 70° + sin 10° = 0
Answer:
LHS = sin 50° – sin 70° r sin 10°
= (sin 50° – sin 70°) + sin 10°
= 2 cos \(\left(\frac{50+70}{2}\right)\) sin \(\left(\frac{50-70}{2}\right)\) + sin 10°
= 2 cos 60° . sin (- 10°) + sin 10°
= – 2(\(\frac{1}{2}\)) sin 10° + sin 10° = 0

TS Inter First Year Maths 1A Ratios up to Transformations Important Questions Long Answer Type

Question 59.
If A + B + C = 2s, then prove that cos(s – A) + cos (s – B) + cos (s – C) + cos s = 4 cos\(\frac{A}{2}\) cos \(\frac{B}{2}\) cos \(\frac{C}{2}\). [Mar. ’18(TS)]
Answer:
TS Inter First Year Maths 1A Trigonometric Ratios up to Transformations Important Questions Long Answer Type 35

Question 60.
If A + B + C = 0, then prove that sin 2A + sin 2B + sin 2C = -4 sin A sin B sin C
Answer:
Given A + B + C = 0
LHS = sin 2A + sin 2B + sin 2C
= 2 sin \(\left(\frac{2 \mathrm{~A}+2 \mathrm{~B}}{2}\right)\) cos \(\left(\frac{2 \mathrm{~A}-2 \mathrm{~B}}{2}\right)\) + sin C
= 2 sin (A + B) cos (A – B) + sin 2C
= 2 sin (-C) cos (A – B) + sin 2C
= -2 sin C cos (A – B) + 2 sin C cos C
= -2 sin C [cos (A-B) – cos C]
= – 2 sin C [cos (A – B) – cos [-(A + B)]]
= – 2 sin C [cos (A-B) – cos (A + B)]
= – 2 sin C [2 sin A sin B]
= -4 sin A sin B sin C = RHS.

TS Inter 1st Year English Grammar Matching Meanings

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

TS Inter 1st Year English Grammar Matching Meanings

Learning means skill that improves comprehension and communication fast.

While looking up the the word in a dictionary for its accurate meaning is the best possible way, doing so is not always possible.

It is sometimes possible to ‘guess’ the meaning of a new word from the context in which it *- is used and from its composition.

Going through glossaries helps to a great extent in mastering this aspect.

In the Intermediate Public Examinations words for this question are usually picked up from the prescribed pieces. Hence, noting down the meanings of important words from the prescribed lessons will help the student score maximum possible marks allotted for this question.

Improving Vocabulary (word power) can be done in innumerable ways. These many various ways are easy to practise and enjoyable as one follows them. Some of them are presented here with one or more examples each.

1) From your regular reading, (Textbooks or general books) select five words a day that you do not clearly understand. Note them in a book, find out the meanings, take tips to use them in your own sentences from a good dictionary and start using those words in your speech or writing. Following this technique every day is very useful.

2) Try to guess the meanings of words from the context. But be sure to check whether your guess is correct or not.
Ex :
a) I saw a woman carrying a pitcher on her head and when she reached her home, she put down the pitcher. I saw water to its brims in that pitcher.
pitcher = a pot, a vessel, a container ………….. you are right.

TS Inter 1st Year English Grammar Matching Meanings

b) Likhitha noticed her ten-month-old daughter was not closing her eyes even when she applied soap on her face. So, Likhitha took her baby to an oculist, who declared that the baby lost her power of vision and she was blind.
Oculist: guess. Yes, absolutely right: an ophthalmologist, an eye-doctor.

3) Study words with the help of their roots, parts, prefixes, suffixes, etc.
theo = god; logy = a systematic study
theology = a systematic study of god
zoo = animals; l0gy = study; zoology = study of animals
phi! = love; biblio = books; bibliophile = one who loves books
cide = kill or killing agent; or killing
pest = minute creatures; pesticide = that which kills pests

4) Study words in groups like :
a) Synonyms : words with similar (NOT THE SAME) meanings and belonging to the same parts of speech.
i) beautiful, handsome, cute, charming, pretty, attractive
ii) intelligent, brilliant, sharp, smart, bright, clever

b) Antonyms : words that have meanings opposite to one another. Like synonyms, any two antonyms should belong to the same part of speech.
i) good × bad
ii) small × big
iii) active × inactive; passive
iv) encourage × discourage
v) bright × dark; dull
vi) slow × fast

c) Homonyms : words with the same spelling; the same pronunciation but with different meanings.

  1. book (n) = పుస్తకము
    book (v) = నమోదుచేయుట
    book (v) = కేటాయించుట
  2. bank (n) = నీధి
    bank (v) = ఆధారపడి
    bank (n) = నదీ తీరము
  3. rest = విశ్రాంతి
    rest = మిగిలిన, ఇతర
  4. point = చుక్క
    point = విషయము

TS Inter 1st Year English Grammar Matching Meanings

d) Homophones : words with different spellings and meanings but with the same pronunciation :
1 – eye; son – sun; some – sum; sight – cite – site; see – sea; seen – scene

e) Homographs : words with the same spellings but with different pronunciation and meanings :
minute (మినిట్) = నిముషము
minute (మైన్యూట్) = అతి చిన్న
live (v) (లివ్) = నివసించు
live (adj) (లైవ్) = సజీవ; ప్రతక్ష్య
And there are many more play-way methods to enrich one’s vocabulary in an entertaining way.

Special Note : Make proper use of the sections WORD STUDY and WORD GAMES in the activities part, given after lessons.

Exercises

Question 1.
Match the following words in Column A with their meanings in Column B.
Two sides of life

Column A Column B
i) accomplish a) read aloud
ii) overcast b) sadness, grief
iii) disconsolate c) character, nature, temperament
iv) unpalatable d) hard to accept, not tasting good
v) recite e) grab or catch hold of
vi) proportion f) nurture, foster, tend
vii) seize g) a part or share of a whole
viii) woe h) cloudy, dark, gloomy
ix) cultivate i) achieve something
x) disposition j) extremely sad, unhappy

Answer:
i) – i
ii) – h
iii) – j
iv) – d
v) – a
vi) – g
vii) – e
viii) – b
ix) – b
x) – c

TS Inter 1st Year English Grammar Matching Meanings

Question 2.
Match the following words in Column A with their meanings in Column B.
Father, Dear Father

Column A Column B
i) muse a) unyielding, inflexible
ii) ancillary b) willing to obey, dutiful
iii) fibbing c) travel across
iv) topsy-turvy d) secondary, additional
v) cross e) great mental pain
vi) prattle f) telling a trivial lie
vii) traverse g) annoyed, angry
viii) obedient h) upside down
ix) adamant i) reflect, think over
x) anguish j) repeat meaninglessly

Answer:
i) – i
ii) – d
iii) – f
iv) – h
v) – g
vi) – j
vii) – c
viii) – b
ix) – a
x) – e

Question 3.
Match the following words in Column A with their meanings in Column B.
The Green Champion – Thimmakka

Column A Column B
i) saplings a) buckets
ii) confer b) adopted son
iii) foster son c) exceptionally large
iv) tending d) without fail
v) massive e) a beginning
vi) conceive f) award a degree, title etc.
vii) invariably g) a particular aspect
viii) pails h) young plants
ix) onset i) to become pregnant
x) facet j) caring for

Answer:
i) – h
ii) – f
iii) – b
iv) – j
v) – c
vi) – i
vii) – d
viii) – a
ix) – e
x) – g

TS Inter 1st Year English Grammar Matching Meanings

Question 4.
Match the following words in Column A with their meanings in Column B.
The Green Champion – Thimmakka

Column A Column B
i) tremendously a) forcefully
ii) propel b) observable
iii) pace c) goal
iv) barely d) disappearance, loss, death
v) perceptible e) greatly, extremely
vi) penetrate f) tire
vii) ambition g) enter or pass through
viii) exhaust h) speed
ix) extinction i) move, push forward
x) compellingly j) to a very limited extent

Answer:
i) – e
ii) – i
iii) – h
iv) – j
v) – b
vi) – g
vii) – c
viii) – f
ix) – d
x) – a

Question 5.
Match the following words in Column A with their meanings in Column B.
Box and Cox

Column A Column B
i) crop a) expressing anger, surprise, etc
ii) bolster b) a narrow shell
iii) wobble c) deny; take away something from someone
iv) zounds d) a type of small, oily fish
v) emulating e) move unsteadily
vi) capital f) a civil subdivision of a village
vii) ledge g) a large round pillow
viii) parish h) limitating
ix) deprive i) cut
x) herrings j) excellent

Answer:
i) – i
ii) – g
iii) – e
iv) – a
v) – h
vi) – j
vii) – b
viii) – f
ix) – c
x) – d

TS Inter 1st Year English Grammar Matching Meanings

Question 6.
Match the following words in Column A with their meanings in Column B.
Two Sides of Life; Revision Test – I

Column A Column B
i) dwell upon a) repeatedly, all time
ii) consideration b) very unhappy or uncomfortable
iii) excellence c) depressed, nervous
iv) frankness d) the mixture of gases that surrounds the earth
v) charming e) the act of thinking process
vi) miserable f) slightly wet, often in a way that is unpleasant
vii) constantly g) openness, truthfulness
viii) damp h) to think or talk a lot about something
ix) atmosphere i) very pleasant or attractive
x) moody j) superiority, distinction

Answer:
i) – h
ii) – e
iii) – j
iv) – g
v) – i
vi) – b
viii) – f
ix) – d
x) – c

Question 7.
Match the following words in Column A with their meanings in Column B.
Father, Dear Father, Revision Test – II

Column A Column B
i) transgression a) irritation, disappointment
ii) philosopher b) nervous, rude
iii) plucking c) real meaning
iv) harbinger d) identify, be familiar with
v) essence e) pulling something out
vi) frustration f) skill
vii) recognize g) doing wrong, violation of a code
viii) nervy h) at risk to be lost
ix) craft i) truth-seeker, logician
x) at stake j) indication

Answer:
i) – g
ii) – i
iii) – e
iv) – j
v) – c
vi) – a
vii) – d
viii) – b
ix) – f
x) – h

TS Inter 1st Year English Grammar Matching Meanings

Question 8.
Match the following words in Column A with their meanings in Column B.
The Green Champion-Thimmakka; Revision Test – III

Column A Column B
i) stretch a) understand
ii) monsoon b) eating grass by animals
iii) capture c) clearly
iv) cherish d) huge, enormous
v) realize e) humble
vi) evidently f) unbelievable
vii) modest g) rainy season
viii) graze h) an area of land
ix) incredible i) value
x) massive j) catch hold of something

Answer:
i) – h
ii) – g
iii) – j
iv) – i
v) – a
vi) – c
vii) – e
viii) – b
ix) – f
x) – d

Question 9.
Match the following words in Column A with their meanings in Column B.
The First Four Minutes; Revision Test – IV

Column A Column B
i) resistance a) silence
ii) pounce b) suffering, agony
iii) flutter c) surround, cover
iv) anguish d) natural, on the spot
v) haven e) dared
vi) spontaneous f) refusal to obey; opposition
vii) lull g) confuse, puzzle
viii) ventured h) move lightly and quickly, tremble
ix) engulf i) safe place
x) bewilder j) jump, leap

Answer:
i) – f
ii) – j
iii) – h
iv) – b
v) – i
vi) – d
vii) – a
viii) – e
ix) – c
x) – g

TS Inter 1st Year English Grammar Matching Meanings

Question 10.
Match the following words in Column A with their meanings in Column B.
Box and Cox; Revision Test – V

Column A Column B
i) acquaint a) bottom parts of hats that stick out
ii) indignation b) flat, level
iii) confound c) control, check
iv) loft d) revenge
v) frightful e) anger
vi) contemptible f) confuse, surprise
vii) brims g) a space, room just below the roof of a house
viii) vengeance h) dreadful, awful
ix) curb i) inform, accustom
x) horizontal j) hate worthy, shameful

Answer:
i) – i
ii) – e
iii) – f
iv) – g
v) – h
vi) – j
vii) – a
viii) – d
ix) – c
x) – b

TS Inter 1st Year English Grammar Matching Meanings

Question 11.
Match the following words in Column A with their meanings in Column B.
Model Question Paper

Column A Column B
i) appreciate a) convince
ii) bring about b) the quality of being kind, generous
iii) provide c) beyond hope
iv) lighten d) acceptance as true
v) chasm e) dismiss, become free
vi) recognition f) make something happen
vii) benevolence g) gap, wide difference
viii) get rid of h) give something to somebody
ix) persuade i) value something highly
x) desperate j) reduce the amount of worry

Answer:
i) – i
ii) – f
iii) – h
iv) – j
v) – g
vi) – d
vii) – b
viii) – e
ix) – a
k) – c

Note : Go through the section “MEANINGS AND EXPLANATIONS” given at the end of all the fifteen lessons. It helps you score 28 Marks in the Public Examination. That also helps in improving your language skills.

TS Inter 2nd Year English Grammar Word Stress

Telangana TSBIE TS Inter 2nd Year English Study Material Grammar Word Stress Exercise Questions and Answers.

TS Inter 2nd Year English Grammar Word Stress

Q.No.19 (8 × 1/2 = 4 Marks)

‘Stress’ is an import aspect of the English Language. In words with two or more syllables, one syllable gets more prominence than the other syllables in pronunciation. The syllable that gets more prominence is called the stressed syllable.

That a particular syllable is stressed in the given word is shown with a small vertical bar’ placed at the beginning and just above that syllable.

Example: ‘teacher The first, syllable ‘teach’ is stressed. If the given word has only one syllable, the question of more prominence doesn’t arise. Hence monosyllabic words are not stressed. But, they may be stressed in connected speech, i.e. in sentences.

As a foreign learner, we are not habituated to placing the stress correctly. Not at all stressing or wrong placing of it leads to misunderstanding or not understanding at all. Therefore it is very much necessary to acquire the right stress habits if we want to communicate effectively.

To know the stressed syllable in a given word, listening to the native speakers and noticing stress is a natural and easy way. But we don’t have that kind of environment. The only alternative way is to depend on dictionaries. But it is very difficult to go to dictionaries every time.

Here are some general principles that help us to some extent to pick up this complex aspect.

  • Monosyllabic words in isolation have no stress.
  • Disyllabic words (words with two syllables) with word final ‘r’ have the stress on the first syllable.
    Examples: ‘father, ‘doctor, ‘teacher, ‘sister, ‘painter.

TS Inter 2nd Year English Grammar Word Stress

Examples in word stress:

1. In the following disyllabic words, the stress falls on the first syllable. Read them aloud:
TS Inter 2nd Year English Grammar Word Stress 1

2. In the following disyllabic words. on the other hand, the stress falls on syllable. Read them aloud:
TS Inter 2nd Year English Grammar Word Stress 2

1. Rules of word stress

Now it may seem that word-stress in English is upredictable.
However, the following rules of word-stress are available.
Rule I: Words with weak prefixes
The following words beginning with weak prefixes such as a, be, de, re, con, have stress on the second syllable,
TS Inter 2nd Year English Grammar Word Stress 3

Rule 2 : Compound words

A compound word is a word that is composed of two separate words. In such words stress usually falls on the first syllable.
TS Inter 2nd Year English Grammar Word Stress 4
However, there are some compound words which take stress on the second part of the word. For instance, the words that end in -ever’, ‘-self and -selves’ take stress on the second part.
TS Inter 2nd Year English Grammar Word Stress 5

Rule 3: Words which denote numbers have a specific stress pattern.

a) words that end in ‘-teen’ get the stress on ‘-teen’.
fifteen
eighteen

b) for the words that denote the multiples of ten, the stress falls on the first syllable.
‘fifty
thirty
‘sixty

TS Inter 2nd Year English Grammar Word Stress

Rule 4: Suffixes

a) Most words that end in -ee, eer, -ette, -que and -alre take stress on the last syllable.
TS Inter 2nd Year English Grammar Word Stress 6

b) Words that end in -Ion, -Ial, -Ic and -Ious/eous take stress on the penultimate syllable (i.e., second syllable from the end).
TS Inter 2nd Year English Grammar Word Stress 7

c) Words that end in -leal, -lan, -ity, -lze, -logy and -graphy take stress on the ante penultimate syllable i.e., the third syllable from the end.
TS Inter 2nd Year English Grammar Word Stress 8

Rule 5: Stress Shift

a) One very important feature of word-stress is the stress shift. That is, the stress shifts when some suffixes are added to a word.
Examples:
e’eonomy
eco’nomic
econo’metrics
‘photograph
photographer
photo’graphic
Note: In the above examples, you have seen that the addition of suffix results in stress shift. But there are some suffixes which do not affect the stress. Some of them are
TS Inter 2nd Year English Grammar Word Stress 9

TS Inter 2nd Year English Grammar Word Stress

b) There are, again, some (disyllabic) words which can be used as nouns or adjectives and also as verbs. In such cases, the stress falls on the first syllable if the words are used as nouns or adjectives. The stress shifts to the second syllable If they are used as verbs.
Examples;

Noun/Adjective Verb
‘protest pro’test
‘insult in’sult
‘convert convert –
‘export export
‘import im’port
‘present pre’sent
‘record -re’eord
‘absent ab’sent
‘conduct con’duct
‘survey sur’vey
‘permit per’mit
‘prospect pros’pect
‘suspect sus’pect
‘contract con’tract

Exercises

The following exercises are meant to make the concept clear to you. As you know, practice makes one perfect!

Examples in word-stress:

1. In the following disyllabic words the stress falls on the first syllable. Read them aloud
TS Inter 2nd Year English Grammar Word Stress 10

TS Inter 2nd Year English Grammar Word Stress

2. In the following disyllabic words, on the other hand, the stress falls on the second syllable. Read them aloud:
TS Inter 2nd Year English Grammar Word Stress 11

I. Mark the stress on the following words.
TS Inter 2nd Year English Grammar Word Stress 12
Answer:
TS Inter 2nd Year English Grammar Word Stress 13

TS Inter 2nd Year English Grammar Word Stress

II. You have read the stress rules on suffixes. Follow the rules and mark stress on the following words
TS Inter 2nd Year English Grammar Word Stress 14
Answer:
TS Inter 2nd Year English Grammar Word Stress 15

III. The following words have weak prefixes. Put a stress mark the on the words and refer dictionary.
TS Inter 2nd Year English Grammar Word Stress 16
Answer:
TS Inter 2nd Year English Grammar Word Stress 17

IV. The following words with two syllables have noun/ adjective and verb forms. Put a stress mark on the syllables based on their grammatical functions.

Noun/Adjective Verb
1) absent absent
2) convict convict
3) conflict conflict
4) contract contract
5) contrast contrast.
6) defect defect
7) export export
8) increase increase
9) invalid invalid
10) object object
11) present present
12) produce produce
13) project project
114) rebel rebel
15) record record

Answer:

Noun/Adjective Verb
1) ‘absent ab’sent
2) ‘convict convict
3) ‘conflict con’flict
4) ‘contract con’tract
5) ‘contrast /con’trast
6) ‘defect de’fect
7) ‘export ex’port
8) ‘increase in’crease
9) ‘invalid in’valid
10) ‘object object
11) ‘present pre’sent
12) ‘produce pro’duce
13) ‘project project
14) ‘rebel re’bel
15) ‘record re’cord

TS Inter 2nd Year English Grammar Word Stress

V. Place a stress mark on the following compound words. Look up the dictionary and correct your answers.
TS Inter 2nd Year English Grammar Word Stress 18
Answer:
TS Inter 2nd Year English Grammar Word Stress 19

VI. Mark stress on the right syllable.
TS Inter 2nd Year English Grammar Word Stress 20
Answer:
TS Inter 2nd Year English Grammar Word Stress 21

TS Inter 2nd Year English Grammar Word Stress

VII. Mark the stress for the following words. [Revision Test – V]
i) common
ii) adopt
iii) humility
iv) footprint
v) understand
Answer:
i) ‘common
ii) a’dopt
iii) hu’mility
iv) ‘footprint
v) understand

VIII. Mark the stress for the following words. [ModelQuestion Paper]
i) delay
ii) biography
iii) carry
iv) economic
v) sixty
vi) nature
vii) hotel
viii) victory
ix) application
x) jellyfish
Answer:
i) de’lay
ii) bi’ography
iii) ‘carry
iv) eco’nomic
v) Sixty
vi) ‘nature
vii) hotel
viii) ‘victory
ix) appli’cation
x) ‘jellyfish

TS Inter 2nd Year English Grammar Word Stress

TS Inter 2nd Year English Grammar Note Making

Telangana TSBIE TS Inter 2nd Year English Study Material Grammar Note Making Exercise Questions and Answers.

TS Inter 2nd Year English Grammar Note Making

Q.No. 18 (1 × 4 = 4 Marks)

Note making is a very frequently followed process of writing down the important ideas of a given text. Even lay persons resort to this technique in their day-to-day life situations for the sake of convenience. Though the process is a familiar exercise, in the academic context, it requires refinement. The fact that the given text is in a foreign language also adds to its complexity. Writing down salient points of a spoken text is known.as note taking. This is more difficult than note making (from a written / printed text) in more than one way.

Note making involves, first, understanding the text and then identifying the important points. Thirdly, it needs the organization of those points into relevant classes or groups. Finally, it requires the presentation of those points in such a way that facilitates easy reference and recollection. A suitable title is to be supplied.

Apart from its practice and usefulness in real life, note- making is helpful in the study of other subjects too. Practice in note-making enhances one’s understanding capacity, editing skills, presentation techniques and, above all, tl;e ability to derive pleasure from one’s study!

Points to ponder over for the purpose of Public Examination:

  • Notes may be in the form of numbered points.
  • Complete sentences need not be written; phrases / clauses serve the purpose.
  • Points that fall under a main point are to be presented below that main point.
  • Abbreviations, short forms, symbols, etc. may be used wherever possible.
  • Graphs, tables, diagrams may be used wherever the given text can be rendered into one of these forms
  • It can even be in the form of a combination of a written text and a diagram.
  • The entire notes can also be in the form of a short paragraph.
  • The notes should be brief, clear, true to the text, with no additions and easy to understand and remember.

TS Inter 2nd Year English Grammar Note Making

Format of note making:

Heading (Title)

1. Sub heading
1.1 Information (phrase)
1.2
Sub sub-heading
1.2a Information (Phrase)
1.2b Information (phrase)

2. Sub-heading
2.1 Information (Phrase)
2.2 Information (Phrase)
2.3 Sub sub-heading
2.3a Information (Phrase)
2.3b Information (Phrase)
2.4 Information (phrase)

3. Sub-heading
3.1 Information (phrase)
3.2 Information (phrase)

Key to abbreviations:

  • Max: maximum
  • Govt: Government

TS Inter 2nd Year English Grammar Note Making

Now observe the following two models of note making carefully.

1. In December 2019, the novel coronavirus called SARS-CoV-2 had resulted in a respiratory illness called COVID-19. ‘CO’ stands for corona, ‘VI’ for the virus, D stands for disease T9’ is the year in which it broke out. This virus was unknown before its outbreak in Wuhan, in China, in December 2019. Coronavirus is a family of viruses that may cause disease in animals and humans. It causes respiratory infections ranging from the common cold to more severe diseases. India has approved seven vaccines.

It’s currently using only three vaccines, Covishield, Covaxin prepared by Bharat Biotech and Sputnik V. While we are still learning how COVID-19 affects people, aged people and people with pre-existing medical conditions like high blood pressure, heart disease, lung disease, cancer etc. appear to be at greater risk than others. We can reduce the chances of being infected with COVID-19 by taking simple precautions.

We should clean our hands with sanitiser or wash them with soap water because this action kills viruses on our hands. Everyone must maintain 6 feet distance from others. Once contaminated, hands can transfer the virus to your eyes, nose or mouth, so avoid touching eyes, nose and mouth. Droplets of saliva spread the virus. So distance needs to be maintained. Good respiratory hygiene protects the people around you from viruses such as cold, flu, and COVID -19. Therefore masks need to be worn.

Notes:
Title: Corona Virus

Covid 19

  • CO-corona
  • VI -virus
  • D-Disease
  • 19 – year it appeared

Corona Virus

  • Family of SARS-CoV-2
  • Causes illness
  • Respiratory infection

TS Inter 2nd Year English Grammar Note Making

Symptoms

  • Fever
  • dry cough
  • tiredness

accine, drug or treatment

  • Covishield – SII
  • Covaxin – Bharat Biotech
  • SputnikV

At the risk of severe illness

  • Older persons
  • Persons with chronic problems

Precautions

  • Cleaning hands frequently
  • Maintaining 6 feet distance
  • Avoid.touching eyes, nose and mouth
  • Wearing masks

2. Biodiversity refers to the variability and variety of different species of plants and animals on Earth. This variety contributes towards making our planet inhabitable. The reason for the unequal distribution of various organisms in different parts of the world is due to varied climatic conditions. There is greater terrestrial biodiversity near the equator and this is caused due to warm climate and high primary productivity.

On the other hand, marine biodiversity is highest along the coasts in the Western Pacific as it has the highest sea surface temperature. Biodiversity basically clusters in hotspots and while it has been on a rise though time researchers state that it is likely to slow down in the times to come. It is essential to maintain rich diversity to build a harmonious environment.

It enables the survival of human beings by providing them with their basic needs such as’ food, shelter, medicines, etc. However, the increasing pollution which is continually degrading the environment is also having a negative impact on biodiversity. Several species that inhabited Earth earlier are now extinct and many others are feared to become extinct in the coming years. This will further lead to environmental imbalance and can prove to. be hazardous for the human species
TS Inter 2nd Year English Grammar Note Making 1

Exercises

Read the following passage and make notes. Add suitable title.

Question 1.
Sripathi Panditaradhyula Balasubrahmanyam also known as SPB or Balu, was an Indian playback singer, television presenter, music director, actor and film producer who worked predominantly in Telugu, Tamil, Kannada, Hindi and Malayalam films. He is widely considered one ‘of the greatest Indian singers of all time. Balasubrahmanyam has won six National Film Awards for ‘Best Male Playback Singer for his works in four different languages – Telugu, Tamil, Kannada and Hindi; 25 Andhra Pradesh state Nandi Awards for his work in Telugu cinema; and numerous other state awards from Karnataka and Tamil Nadu.

In addition, he won the Filmfare Award and six Filmfare Awards South. According to some sources, he holds the Guinness World Record for recording the highest number of songs by a singer with over 40,000 songs. He recorded 21 songs in Kannada for the composer Upendra Kumar in Bengaluru from 9 am to 9 pm on 8 February 1981. In addition, he recorded 19 songs in Tamil and 16 songs in Hindi in a day, which has also been a record. In 2012, he received the state NTR National Award for his contributions to Indian cinema.

In 2016, he was honoured with the Silver Peacock Medal as Indian Film Personality of the Year. He was a recipient of the Padma Shri (2001), Padma Bhushan (2011) and Padma Vibhushan (Posthumously) (2021) from the Government of India. He was a recipient of the Harivarasanam Award from the Government of Kerala. On 25 September 2020, S. P. Balasubrahmanyam died in Chennai after being hospitalized for over a month for complications due to COVID-19
Answer:
SP BALU-THE SAGA
Sripathi Panditaradhyula Balasubrahmanyam
A) Career
Singer, tv presenter, music director, actor, producer.

B) Language worked in
Telugu, Tamil, Kannada, Malayalarn and Hindi.

C) Awards

  • National Film Awards – Best Male Playback Singer in four languages 4 25 AP Nandi Awards
  • Numerous Awards from Karnataka, Tamil Nadu, Kerala 4- Filmfare Awards 4 NTR National Award 4 Silver Peacock Medal
  • the Padma Shri (2001) and Padma Shushan (2011) and Padma Vibhushan (2021) (posthumously- after death)
  • Harivarasanam Award from Kerala Government

D) Records

  • Guinness World Record – over 40,000 songs -recorded
  • 21 songs recorded in one day (9AM – 9PM – 8 – Feb, 1981 – Kannada)
  • 19 songs in Tamil, 16 songs in Hindi – in one day – each.

E) The End

  • on 25 September 2020 -C0VID-19 complications

TS Inter 2nd Year English Grammar Note Making

Question 2.
It is observed that most educational institutions believe online classes as the only solution during this pandemic. In contrast, researcher Eric Bettinger Susanna Loeb’s work Promises and Pitfalls of Online Education shows, that online teaching may raise dropouts at primary and upper primary levels. It is observed from the survey report that online classes are suggestible for classes 8 and above.

It is beneficial to the one who can afford, but detrimental to the one who can ill afford, it. This reflects adversely for primary classes. Most of the rural and BPL parents may not. afford mobile phones, network charges, computers and even TV sets. This may lead to discrimination. Parents are not educated on cyber security and it may create a mess for parents as well as students. Our education system exists on the same planet as we are and affected by the conditions around us as we are. Primary victims of Online classes are rural students, particularly in the public sector. Most of the government school students from rural and interior areas can neither afford technology nor have parental support. It is the misfortune of these innocent kids. The system has to be considerate to them.
Answer:
ONLINE EDUCATION PROMISES & PITFALLS

Eric Bettinger Susanna Loeb’s Findings:

ONLINE EDUCATION

S.No PROMISES PITFALLS
1. advisable for classes above 8 Dropouts will increase in classes below 8
2. benefits only the rich discourages the poor discrimination increases
3. Educated parents can take of cybersecurity Uneducated parents leave children to their fate
4. Favours private sector Punishes public sector
5. Suits urban areas not suitable to rural and remote areas

Question 3.
Progress in life depends a good deal on crossing one threshold after another. Some time ago a man watched his little nephew trying to write his name. It was hard work, very hard work. The little boy had arrived at an effort to clear a threshold. Today he writes his name with comparative ease. Some people make the mistake of steering clear of thresholds. Anything that requires genuine thinking and use of energy, they avoid.

Some middle-aged and elderly people greatly enrich their lives by continuing to cross thresholds. One man went into an entirely new business when he was past middle life and made a success of it. De Morgan didn’t start to write novels until he was past sixty. Psychologists have discovered that man can continue to learn throughout life. And it is undoubtedly better to try and fail, than not to try at all.

Then, one can be placed in the category of the Swiss mountaineer of whom it was said, “He died climbing.” When a new difficulty raises to obstruct your path, do not complain. Accept the challenge. Determine to cross this threshold as you have crossed numerous other”thresholds in your past life. In the words of the poet, do not rest but strive to pass from dream to dream.
Answer:
STRIVE REST NOT CROSS THRESHOLDS

  1. Cross thresholds – achieve progress.
  2. Try and fail- stop not striving.
  3. Ready to think genuinely and use energy.
  4. Can start at any age – 60,70 or 80 too.
  5. Rest not – pass on from dream to dream

TS Inter 2nd Year English Grammar Note Making

Question 4.
Many religions existed in India in the Middle Age. The most widely prevalent were, of course, Hinduism and Islam But there were other religions too, like Buddhism, Jainism and Christianity. The outlook of the people, whether they were . Hindus or Muslims, was the same. They believed that the world was a vale of sorrow, and the only way to escape from it and the attainment of true happiness were by turning their hearts away from temptations of the senses and taking refuge in complete surrender to the will of God.

Whose unlimited grace alone could save man. It was, therefore, necessary to place oneself under the control of a spiritual guide and preceptor, and to follow the path of inner discipline which led to the goal of realization of God. Both among the Hindus and the Muslims, there were many orders that saintly preceptors had established. The heads of these orders ministered to the needs of their disciples. Kabir, Nanak and others among the Hindus had founded such orders.
Answer:
Surrender to God – The Secret of Life

  1. Many religions in India
  2. The outlook same – There is sorrow – to overcome it one needs to surrender to the will of God:
  3. Spiritual guides needed for inner discipline and realization of God
  4. Many order to guide – in India

TS Inter 2nd Year English Grammar Note Making

Question 5.
Lizzie, a medical intern, arrived at the hospital promptly at 8.00 a.m every morning. She said, “I began at once to prepare for the dressings by spreading the different ointments, preparing lint, lotion, poultices, bandages, etc. While I am doing that at a side table, the sister is going round and examining all wounds. The simpler case she leaves entirely to me very often, but the more difficult ones, such as ‘cancer, she dresses while I look on.” The time this took varied constantly depending on the number and nature of the cases, but she generally had time to go upstairs and visit the patients in two medical wards before joining the house surgeon, Thomas, in his eleven o’clock rounds.

After the doctor and surgeon finished their rounds, Lizzie gave patients their medicines as prescribed. Lunch was a fortifying meal of mutton chops and ale, which Lizzie ate alone in the hospital canteen. At 1.00 p.m, she returned to the surgical ward to accompany any visiting surgeons. Lizzie arrived back at home by 4.30, where she rested for half an hour, talking to Louie and James and playing with their children. After changing her clothes into something more dainty, she did algebra till teatime at seven o’clock. To close out her day, she wrote letters to friends and family by the fire or practised Latin.
Answer:
LIZZIE

  1. a medical intern
  2. promptly arrives at hospital at 8 am
  3. prepares dressings, lotions etc
  4. looks after simpler cases on her own
  5. gives medicines to patients as prescribed
  6. takes lunch alone in canteen
  7. accompanies visiting doctors from 1 pm to 4 pm-
  8. Back home at 4.30 pm
  9. rest for a while talking to Louie, James and their children
  10. does algebra till tea at 7 pm till
  11. letters to friends or practising Latin ends the day

TS Inter 2nd Year English Grammar Note Making

Question 6.
“Thanks to the internet, women can become entrepreneurs. In the last four years between 2012 and 2015, the number of new women-owned small and medium business Pages on Facebook has increased six-fold,” said Ankhi. “Kalpana Rajesh, a woman from India, was inspired to start her own business making bridal hair accessories after having done so for years for friends. She started her business in 2012 with three people – herself, her domestic worker and her friend.

Today, she employs more than 200 women, working across thirty-six branches from Delhi to Tuticorin, with multiple product lines. She says that without Facebook, she estimates it would have taken her fifteen-twenty years to grow her business to the same size it is today. Not only has Kalpana made a difference to her own life, but she has also made a telling difference to the lives of more than 200 women who are now earning their livelihood, thanks to Kalpana.”
Answer:
WOMEN ENTERPRENEURS – ROLE OF INTEREST

  1. Crucial role of internet in growing entrepreneurship Ankhi’s study – six-fold increase in Facebook pages of women-owned businesses
  2. Kalpana Rajesh – started her “business – bridal hair aceessories – in 2012 with just three women (including herself)
  3. Now (2022) she has thirty-six branches – all over India with 200 + employees – multiple products
  4. Connectivity made possible by Facebook
  5. helping herself and over 200 women ………………….

Question 7.
It is not enough to prepare well for examinations. Success in the exams depends also on your mental state of mind during the exam, proper time management, neat presentation of answers and other small details. Sleep well on the night before the exam and resist the temptation of last minute cramming. You should be well rested and relaxed.

On the morning of the exam, have a light breakfast and set out. Reach the examination hall well in time, particularly on the first day. Once you get the question paper, read it carefully. Remain calm as any silly mistake you may make in understanding the questions can have damaging consequences. Spend at least five minutes going through the different sections of the paper. It is advisable to start with those questions you are confident with, instead of wasting time with, the difficult ones.

Do not panic if you get stuck with a question. Leave it incomplete and move on to the other questions. After completing the easier questions move on to the next level of difficulty. Save the toughest questions for the end. All the ‘bits’ pertaining to a question should be answered in a sequence and at one place. Keep numbering the papers as you proceed. Draw all diagrams neatly and colour them, if possible, to make them more attractive. After you complete the paper, tie up the sheets properly. You should then revise the answer paper at least twice before handing it.
Answer:
WOMEN ENTREPRENEURS. ROLE OF INTERNET.

  • Apart from learning answers, physical preparedness and mental state contribute for success in examinations.
  • Identifying examination centre, making transport arrangements, getting stationery ready, etc. are important.
  • Sufficient sleep, light food, calm mind are important
  • Reach centre in time, read question paper slowly, think of questions you can answer well, leave the difficult ones for last half an hour draw figures where necessary, revise answers – success is yours.

TS Inter 2nd Year English Grammar Note Making

Question 8.
The brain has three main divisions, each having its own particular function. The. cerebrum is the largest and best-developed section of the brain. It is made up of many areas containing cells that control various parts of the body. Some areas perform the function of directing muscular activity. They allow the head to be turned, for example, other areas are responsible for sight, hearing and speech. The cerebrum is also the centre of intelligence and it enables human beings to reason and remember.

The cerebellum is a small section of the brain below the cerebrum its function is to coordinate the movement of limbs and also to control balance. The medulla oblongata is an enlarged area that connects the brain to the spinal cord. It serves to regulate the activities of the internal organs. It controls the beating of the heart and regulates all involuntary muscles. The parts of the brain are highly specialized. Together they make u the complex organ that controls the nervous system. [Model Question Paper]
Answer:
Brain – Parts
TS Inter 2nd Year English Grammar Note Making 2

TS Inter 2nd Year English Grammar Letter Writing

Telangana TSBIE TS Inter 2nd Year English Study Material Grammar Letter Writing Exercise Questions and Answers.

TS Inter 2nd Year English Grammar Letter Writing

Q.No.17 (4 Marks)

Letter writing is both an art and science. It requires scientific precision and artistic creation. The frame work or the layout is a science. But the writing of the body is an art.

Letters are broadly of two types : Private or personal and public or official or business. There is only a slight difference between the two kinds in regard to the framework. But the main body of one type is much different from the other.

Careful cultivation of this art called letter writing opens greener avenues for the young learners. Negligence of this valuable art results in gloomy future. This art can create miracles or mar one’s future.

Letters of great personalities have acquired the status of literary masterpieces and continue to thrill the readers with fresh fragrance even after centuries since their writing. That is the power of letter writing!

A letter has five parts. They are :

1. The heading: It consists of station arid date. It should be written on the right -hand top comer of the letter.
Eg. Santhinagar,
Kothagudem.
10-4-2022.

2. Salutation or Greeting: It is the addressing part.
Eg. Dear father, Madam,
Dear Sister, Sirs,
Sir, My dear brother,
Gentlemen, Dear Murali,

TS Inter 2nd Year English Grammar Letter Writing

3. Body of the letter: It should be precise. It may be divided into paragraphs as per need.

4. Complimentary note or leave taking: It should be on the right side under the last line of the body of the letter.
Eg. Yours faithfully,
Ever yours, Your loving son,
(Don’t put an apostrophe in yours)

5. Address: You have to write this at the beginning above Salutation in official and business letters. In letters to the members of your family or friends, the address should be written on the left after the body of the letter.
Eg.
Mr. R. Venkata Rao
C/o Dr. R.Madhusudhana Rao,
H.No. 209/C, Y.T. Road,
Suryapet.

SOME HELPFUL EXPRESSIONS

1. Beginning:
I have just received your letter.
I “hope that you are keeping well.
It was most kind of you to remember me.
It is a long time since I heard from you.
Your letter was indeed a great surprise to me.

2. Ending:
Please convey my regards to your parents.
With best wishes.
Hope to see you soon.
We look forward to hearing from you.
With all love and affection.

3. letters of congratulations:
Congratulations on your success.
Let me congratulate you On..
My hearty congratulations on your winning the match.
We send you our greetings on.

TS Inter 2nd Year English Grammar Letter Writing

4. letters of sympathy:
I am sorry to hear about..
It grieved me a lot to know..
It is indeed a matter of great sorrow..
I offer you my deepest sympathy..
God’s ways are strange.

5. Letters of complaint:
I regret to’ inform that..
I am sorry to bring to your notice..
It gives me pain to write that..
Even after repeated requests, I find that..

6. Applications:
I came to know that..
Having come to know that
In response to your advertisement.. the dailies speak…
Points to ponder over for the purpose of Public ExamlnadOn: I

Format of the letter is important.

  • Write each part at its proper place.
  • Use punctuation marks appropriately.
  • Better use fictitious names and places.

Body of the letter

  • Use the style relevant to the type of the letter. Formal style in official and informal in personal.
  • Divide body into paragraphs, if necessary.
  • See that all the hints given in the question are thoroughly covered.

See that there are no mistakes in spellings or sentence construction.

There are broadly three different formats. The one given above is known as ‘Indented Format’. Of late, it has been losing its importance. The other two types are a) Blocked Format and b) Fully Blocked Format. In Blocked or Semi Blocked Format every line of the letter including signature except date begins from the left margin. All the models and exercise answers in this material use Fully Blocked Format. In Blocked and Fully Blocked Formats punctuation makrs are used only in the body, not in the layout, of the letter. Any Format will be treated as correct in the Public Examination.

TS Inter 2nd Year English Grammar Letter Writing

Formal Letters

Let’s take a look at the format of a formal letter.

Formats:
Comparison
TS Inter 2nd Year English Grammar Letter Writing 1
Examine the Model Letters given below carefully.

1. A letter of complaint to the police commissioner about the mess caused by the video games centre in your locality and seeking help to control them.

Flat No: 35
Park Avenue Enclave
Kompally Hyderabad
23rd May, 2020

The Commissioner of Police
Police Commissioner ate
Malkajgiri
Hyderabad

Sir

Sub: Seeking help to control nuisance created by. Video game centers – reg.

I am a resident of Malkajgiri and a college student. I would like to bring to your kind notice that there are some serious problems created by the recently-opened video games centre on the main road, which has become the main attraction in the region. The centre is attracting many college and school going students. They have deviated from their studies and extracurricular activities. Most of my friends in this area as well as from the surroundings are more interested in sitting in the video game parlour than in the library or study room. Though parents do try to control, the children are being a bit too uneasy with them as the centre is open even late at the night.

I would like to request you to make the owner keep some kind of restrictions regarding the age group and timings.

I am sure you will kindly take necessary action at the earliest.

Thanks and regards
Yours sincerely
Signature
(R.RAJANI)

TS Inter 2nd Year English Grammar Letter Writing

2. A letter to the editor of a leading local newspaper, pointing to the need to save children from the pressure in schools.

Flat No: 329/1
Rajini Residency
Street N0.6
Boduppal
Hyderabad
16th April, 2022

To
The Editor
The Times of India
Banjara Hills
Hyderabad

Sir’

Sub: Need to save children from stress

I would be grateful if you allow me to express my views and grievances in the columns of your esteemed daily about the missing childhood these days.

Undoubtedly, childhood is the most important stage of everyone’s life. But it is often found missing these days. Their childhood is confined to an enclosed world of online classes, homework, tests and video games. What are we actually aiming at? Are we educating them or making them as machines?

The elders of the society need to recollect and realise the reasons for the success they are enjoying today. It’s a well- known fact that their childhood was liberal and creative with fun. Friends and family played a great role in their life. But, do the younger generation enjoy the same way? It’s high time to rethink. Every child should have an idea of life and how to modulate it. For that, they should get into some realities of life. Parents need to take the initiative for this. We should encourage children to socialize, go out and play in the open and develop wholesome personalities.

Yours truly
Signature
(S. Ram Prasad)
Loco Pilot

TS Inter 2nd Year English Grammar Letter Writing

3. A letter to the principal of your college requesting to issue your transfer, bonafide and conduct certificates as you completed your intermediate course and you are about to join a medical college.

‘Nandini Ramagiri
6/2 – Temple Street
Suddala
Mancherial 505303
2nd June, 2022

The Principal
Prerana College
Ram Nagar
Mancherial

Dear sir

Sub: Request for certificates

I was a student of your college in the academic years 2020- 2022. My optional subjects were Biology, Physics and Chemistry. My roll number was 2022126.1 am proud to inform you that I have secured the 201st rank in the NEET examination. This was possible only due to the excellent coaching provided by the lecturers of this college. Your inspirational words during assembly and study hours played a significant role in my success. I would like to thank you all wholeheartedly.

As you are aware, we need to submit transfer, bonafide and conduct certificates in the medical college during counselling. Therefore, may I request you to instruct the office to arrange the necessary certificates at the earliest? I have already submitted the “No Due Certificate”.

An early response will be very helpful.

Thanks and Regards

Yours faithfully
Signature
Nandini Ramagiri

TS Inter 2nd Year English Grammar Letter Writing

4. Drunken driving is a serious issue. Here is a letter from Swamy requesting the traffic police to control drunken driving.

Flat No: 12/A-3
RNS Colony
Himayatnagar
Hyderabad
6th April, 2022

The Sub Inspector
Traffic Police Station
Himayatnagar
Hyderabad

Sir

Sub: Request to control drunken driving

I would like to bring to your kind notice the serious issue in our area. The problem is caused by drunken drivers. The late evenings are .always troubling times for the residents of RNS Colony, Himayatnagar, as there is uncontrolled traffic and sometimes even minor accidents occur involving at least one drunken driver.

We are really tired of these issues daily. It’s irritating, but there is no way to control it, as the drivers are not in a position to get convinced. It would be kind of you if you can post some constables in our area, to check the drunken drivers so that we will be able to live in peace.

Thank you
Yours faithfully
Ram Prasad

TS Inter 2nd Year English Grammar Letter Writing

5. Here is a letter written by Mahesh wari, who is applying for the post of Assistant Teacher in a school.

C-5
Padmavathi Enclave
Warangal
Telangana
25th March, 2022

The Principal
Little Flower School
Survey of India
Uppal

Sir

Sub: Application for the post of Assistant Teacher

I wish to apply for the position of Assistant Teacher, advertised in today’s “The Hindustan Times”. I am twenty- two years old and have just passed the university examination from Osmania University, Hyderabad. I have also done a course in teaching children with special needs from the NIMH, Hyderabad.

I have enclosed the required testimonials for further reference.

If I am given an opportunity, I can assure you I will do my best to fulfil my duties to the best of my capabilities. I shall look forward to a positive response from your end.

Thank you

Yours faithfully
Maheshwari

Enclosures:

  1. Graduation Certificate & Certificates for teaching special children.
  2. Residence Certificate

TS Inter 2nd Year English Grammar Letter Writing

Exercises

Question 1.
Write a letter to the CEO of the Chemical Industry in your locality, highlighting the pollution causedby them to the nearby river. Request him/her to take necessary steps to control it
Answer:
Letter to CEO

M. Ramana
Pedavuru Of
Kondapalli (M)
Karimnagar (Dt)
14.06.2022

The CEO
Manisha Chemical Industry
Industrial Area
Karimnagar

Sir

Sub: pollution – your Industry – Remedial Measures – Req

I am to bring to your notice the pollution your unit is resulting into the adjoining river and atmosphere. Effluents – untreated – in huge quantities are discharged directly and secretly into the river. Strong and harmful chemicals are causing loss of lives in the river directly and harm to people and crops around indirectly.

People in India treat river as sacred and offer prayers to them. And rivers are lifelines to human civilizations. It is the responsibility of every citizen to protect rivers in all respects.

Money is undoubtedly important. But, lives are more precious.

It is hoped that you initiate immediate remedial measures to avoid any further pollution with immediate effect.

Thank you.
Yours truly

Pradyumn

TS Inter 2nd Year English Grammar Letter Writing

Question 2.
Write a letter to the editor of a reputed National Daily highlighting the need to spread the message the Statue, of Equality seeks to promote.

HINTS: Its importance – Dedicated to humanity by the Prime Minister – First Pooja offered by the President of India – Recorded in the World Book of Records, London
Answer:
Letter to Editor

Pravallika .M
12-85 Hydershakote
Hyderabad
12.03.2022

The Editor
News Herald
Hyderabad

Sir

I find pleasure in writing to you about the need to spread the message the Statue of Equality seeks to propagate. The 216-feet, golden-hued Panchaloha Statue of Bhagavad Ramanujacharya is not just a monument; it is a symbol. It is a movement for equality. The eleventh century Vaishnavite preacher Bhagavad Ramanuja practised equality. He broke all barriers of very rigid customs of those times.

He allowed even the downtrodden not only to enter temples but also to take part in all temple services. Realising the relevance and value of this principle of equality, Sri Sri Sri Tridandi Chinna Ramanuja Jeeyar Swami conceived this 1000 crore rupee mega project in 2014 and materialised it in 2022. The missionary zeal that went into the project needs to be followed by every citizen in promoting the great quality of equality. The importance of the project and its message can be gazed from these facts.

It was dedicated to HUMANITY on 5th February, 2022 by the Prime Mihister of India. First pooja to Samatha Moorthy inside the temple was per-format in the presence of President of India on 14 February 2022. The World Book of Records,
London recognised it as one of the wonders of the world. Let’s spread the message.

Yours
Pravallika

TS Inter 2nd Year English Grammar Letter Writing

Question 3.
You would like to know the procedure you have to follow if you lost a library book. Write an enquiry letter to the. Librarian requesting for information. [Model Question Paper]
Answer:
LETTER TO LIBRARIAN

Rajini. Ch
Second B.Com
National College
Devarakonda
10.02.2022

The Librarian
National College

Sir

I deeply regret to inform you that I lost the book ‘Accountancy Practices’ I borrowed from the library last week. While I am ashamed of myself, I feel it my immediate responsibility to rectify my mistake.

I would love to pay you the price of the book along with any other charges if that is permissible or else, I am ready to buy new copy of the same book and hand it over to you.

Please guide me in this regard so that I can relieve myself from the feeling of shame and guilt at the earliest. Moreover, it is- examination time and I should not deprive other students of the chance to use the book.

Seeking your directions.

Yours sincerely
Rajini Ch

TS Inter 2nd Year English Grammar Letter Writing

Question 4.
Write a letter to the Collector of your area requesting him/her to be the chief guest of an inter colony sports fest your society is organising.
Answer:
LETTER TO COLLECTOR

Sindhu G
12-4 Sai Nagar
Kama Reddy
10.06.2022

The Collector
Kama Reddy
Madam

I feel it our privilege to invite you as our chief guest at our Inter-Colony Sport Fest on 02.07.2022 at SPM. We, a small group of women, have been relentlessly working for the cause of women empowerment.

As part of this noble mission, we plan to organise this-Fest. We all know that you are a real model of empowered women.

Your message will go a long way in inspiring women in our area.

We eagerly look forward to listening to your captivating words.

Thank you Madam.

Yours sincerely
Sindhu G

Question 5.
Write a letter to your Manager requesting him to grant casual leave for five days.
Answer:
LETTER TO COLLECTOR

Raveendra
R/7, Seven Hills
Manasa nagar
Manchiryal
17 May 2022

James Bridge
HRManager
Lifeline Solutions
Nacharam
Hyderabad

Dear Sir

I am writing to you to inform you that I may not be able to attend office for five days from tomorrow i.e., from 18 May to 22 May, as I am down with flu. I have been advised by the doctor to take absolute rest for recovery. I regret the inconvenience caused to the firm because of my illness.

However, I am glad I could meet the deadline set to me for the report of Handles Agency. I have sent it to you for your approval. I am willing to put in extra efforts to clear the pending work, if any, once I am back from my leave.

Thanks and regards,

Yours sincerely
Raveendra

TS Inter 2nd Year English Grammar Letter Writing

Question 6.
Write a letter to the Sarpanch and concerned officer requesting them to take up necessary measures to improve sanitary conditions of your village.
Answer:
Gangadhar M
Gundlapalem
Gadwal (dist)
15.06.2022

The Sarpanch
Gundapalem
Madam

I regret to inform you that sanitary conditions in our village are really in a miserable condition.

It pains the villagers to see dirt and garbage accumulating at every possible place. With a woman at the helm of affairs and another woman as the sanitary inspector, the village should have been much cleaner than ever It is better late than neVer. It is high time you initiated corrective measures at once. Monsoon season is notorious for spreading diseases. If the sanitary condition here continues to be in the same state, lives would be at great risk.

Hope you understand the gravity of the situation.
Expecting early action.

Yours ever
Gangadhar M

Question 7.
You are disappointed to know that you have not been selected to represent your college in the under 19 cricket tournaments. Write a letter to the Coach requesting him to reconsider his decision and offer you one more chance to prove yourself .
Answer:
LETTER TO COACH

Sita S
Senior Intermediate
Geetanjali Junior College
15.07.2022

The PD and Cricket Coach
Geetanjali Junior College

Sir

I find it extremely difficult to accept the fact that I have not been selected to represent our college in Under-19 Cricket tournaments. I kept cool and thought repeatedly about the possible reasons for my rejection. I could find none. Throughout my past track record, my performance has been flawless. And in every success we recorded, my contribution has been considerable.

I don’t want to blame anyone. But, my sporting career is at stake. I very humbly request you to reconsider your decision. If there is a need, put me to any kind of test. But ensure my inclusion in the team. I guarantee you higher success rates for our college.

Thank you sir in anticipation of a positive decision.

Yours sincerely
Sita

TS Inter 2nd Year English Grammar Letter Writing

Question 8.
Write a letter to the Editor of a reputed newspaper about the ill effects of media, television and movies on your generation his decision and offer you one more chance to prove yourself
Answer:
LETTER TO EDITOR

Praveena. S
Narayana Peta
13.06.2022

The Editor
News Herald
Hyderabad

Sir

I wish to bring to the notice of the authorities the ill effects of negative and demotivating content in both print and electronic media and entertainment industry.

Young and impressionable minds fall easy prey to misleading and demoralising content. Media and cinema industry are more concerned about their commercial interests than their social responsibility.

In good olden days cinema and media used to offer healthy and personality- developing messages.

But today ‘good’ is to be searched for closely while ‘bad’ overflows and overwhelms.

It is time that controlling authorities exercised their powers and set things right at the earliest.

Yours
Praveena. S

TS Inter 2nd Year English Grammar Letter Writing

Question 9.
Write a letter of complaint to the Su b-Inspector of Police of your area about the theft of your mobile in your hostel. [REVISION TEST – III]
Answer:
Letter of Complaint:

Room 12
Godavari Hostel
New Wings Jr. College
Peddapalli
16.09.2021

Sub-Inspector
Peddapalli Police Station

Dear Sir

I am Madhavi of second MPC. I stay in Room 10. This morning while going to classes I kept my mobile in my cupboard as usual. But, to my shock and surprise, I found it missing this evening.

I request you to look into the issue and see that my phone is restored to me at the earliest.

Thank you Sir,
Yours sincerely
Sai Kumar P

Personal (Informal) Letters

Personal Letters : An informal letter is perhaps the most common of letters. Such letters are written from time to time to deliver good news to people, to convey festival greetings or to enquire about the health of family members and friends or even simply to maintain some contact with a person. These letters are very friendly and casual in their tone. These rely a lot on memories, shared secrets and humorous moments of the past.

Now, let’s go through some informal letters. You can notice the slight difference in the format too.

Question 1.
Read the letter written by Rahul Reddy to his friend describing the camp against child labour arranged in his school by an NGO called Sishukshema.
Answer:
B-102/1A
Buruguda
Asifabad
21st May, 2022

Dear Aravind

I hope you are doing well. I strongly believe you are doing well in your studies as it is in my case. I have a special reason to write this letter.

It is all about a camp called Sishukshema organised by an NGO, in our school, last week. Child labour was spotlighted. It was illustrated in a lively way. They discussed cases of children who were not allowed to go to school and made to work in factories, hotels and agricultural fields. We did really feel pity for them.

We are fortunate that we don’t have to face such situations. But the organization pointed out the need for our help and care for those who are not fortunate. So, we have decided to help them by providing them with books and fees. A special committee was formed in our school to raise funds for this, and I am the secretary of it.

I do hope that the students of your school also could definitely contribute to such a noble cause. Please share this with your friends and try to collect funds. Convey my regards to uncle and aunt.

Yours lovingly
Rahul reddy

Aravind
H.NO.5-10-125/A
Chikkadpally
Hyderabad – 500020

TS Inter 2nd Year English Grammar Letter Writing

Question 2.
Read this letter in which a student is expressing gratitude to the teacher who helped her in preparing for the board examination
Answer:
21-8/8
Chaithanyapuri
Dilshuknagar
Hyderabad
12th May, 2022

Dear Ms Kalyani

I would like to wholeheartedly express my gratitude for the help extended by you during my board  examination preparation. I was struggling to make out the grammar part of the paper. But your support and efforts made it a cakewalk. Thanks a lot, Miss, for your assistance and affection. You spent your valuable time with me to get me out of this trouble. I owe you a lot for that. You have been a great support in my life.

Now, I am confident that I can pass’ any competitive examination. I am sure, if you stand with me, I can be successful in my career. I’ll always be obliged to you for your generosity.

Thanks a lot

Yours affectionately
Srivani

Kalyani
H.No. 1-5-692
Ramnagar, Ambedkar Circle
Hanumakonda – 506001

Question 3.
Read the condolence letter written by Anurag to his friend Vinay on his friend’s death.
Answer:
12-6/1
Gandhi Street
Karimnagar
21st Feb, 2022

Dear Vinay

I was so sorry to hear about your friend, Raghu Ram’s death. I know how close you both were. You were more than friends. He was one of your family. Please accept my deep sympathies on. this irreplaceable loss.

Raghu Ram was very active and courageous. He took part in most of our community activities. He inspired me a lot. Many can take him as an inspiration. But he neglected his health, it seems. He should have been a bit careful regarding his health. I know, his death is a great loss in your life. Don’t hesitate to call me. I’m always here to help you.

May God bless you and Raghu Ram’s family with the strength to sail through this tough time. 11 op . to meet you this week. Please take care of your health and accept my sincere condolences.

With deep sympathies,

Yours truly
Anurag

Vinay
# 306, Anurag Enclave
Sripuram Township
Khammam – 507002

TS Inter 2nd Year English Grammar Letter Writing

Question 4.
This is a letter written by a son to his father asking him to send Rs. 15000.
Answer:
231-A/1
Prerana College
Ram Nagar
Karimnagar
10th Sep, 2021

Dear father

Hope you are doing well. I am sure that all our family members are fine. I am studying well in all subjects. I’m proud to have lovely parents like you and mom.

Now, it’s difficult to express the purpose of this letter, but it’s a must. You know, it’s time to pay the college term fee of Rs.15000. It would be helpful to me if you could send the money immediately. The principal has instructed me to pay the amount by 21st September without fail.

Hope Lakshman is studying well. Convey my regards to mom and granny.

Yours affectionately
Ram Prasad

Krishna Prasad
Khileshapuram Village
Raghunathapalli Mandal
Jangaon District

TS Inter 2nd Year English Grammar Letter Writing

Question 5.
Read a thanking letter written by Vijay to his uncle for the birthday gift.
Answer:
Flat No.: 35
Green Wood
Kukatpally
Hyderabad

24th April, 2022

Dear uncle

Thank you so much for the wonderful gift that I received from you today. You know my tastes well. That’s why you gifted me a beautiful marble statue of Lord Budha.

I was rather disappointed to know that you are not attending my birthday party. But the statue of Buddha brought back a smile to my face. You are such a wonderful man. You are so careful and thoughtful in selecting an appropriate gift! Your gift symbolised your intention of preparing me mentally and physically to face the challenges of life.

I promise you that I’ll follow your guidance and put all my efforts to make you proud of me. Convey my regards to aunt and Kittu.

Looking forward to meeting you soon.

Yours affectionately
Vijay

Gopal Rao
# 5-65, New City Road
Bhadrachalam
Bhadradri Kothagudem District

Exercises

Question 1.
Write a letter to your friend telling him/her about the new college you joined recently [Model Question Paper]
Answer:
LETTER TO A FRIEND ABOUT YOUR COLLEGE

13-12 Hamsa Veedhi
KoilSagar
16.06.2022

Dear Santhi

I am very happy to write to you about the college I joined here. It is Mother Teresa Junior college for Girls. True to its name, it is really service oriented. Sprawling campus with lush green trees greet students every day. Spacious and well- ventilated classrooms, labs, library and study rooms offer us cool comfort. The principal is an inspiring personality with smiling looks and affectionate approach.

All the lecturers are friendly with us. They explain every topic clearly and in simple terms. Focus is on self-learning and self-assessing techniques. Games, cultural events, quizzes, debates etc are regular features. Learning here is a fun-filled activity. Creativity is encouraged. Slow learners are taken care of personally.

I am blessed to have joined this college. I wish you to visit our college at the earliest. Convey my regards to aunt and uncle. Good wishes to Pinky. Looking forward to seeing you.

Yours lovingly,
MadhanManohar

Shanti. K
Krsihna Enclave
Street No 10
Vikas Nagar

TS Inter 2nd Year English Grammar Letter Writing

Question 2.
We all witnessed COVID 19 deaths recently. You have witnessed the death of your neighbour due to COVID*19. Write a. letter to your friend in the U.S. A describing the incident and how you felt about it.
Answer:
LETTER TO A FRIEND – COVID DEATH

11- A Sainikpuri
Secunderabad

Dear Avinash

With a heavy heart that I do write to you about the tragic death of our neighbour – our uncle – Seetha Rama Chandra Murthy. The end had been very painful. COXID-19 infection, detected rather late. Best efforts from expert doctors failed to save uncle. Uncle was so dynamic, so friendly, so helpful that there was not a single soul in the village that did not bid a tearful farewell to that noble soul.

The saving grace is that uncle’s son and daughter are comfortably settled in our own village. They willingly and lovingly come forward to take care of aunt.

Yet the pain resulting from that sudden and sad demise needs quite a long time to ^subside. Yet, none can alter our fate except accepting it gracefully.

How are your children doing?
Any plans to visit India?
Regards to all of us there.

Yours lovingly
Raja Rao

Avinash Kumar. K
13 New Extension
Broad Way
New Jersey

TS Inter 2nd Year English Grammar Letter Writing

Question 3.
Imagine you have received information from the Ministry of Education that you have secured the 5th place in Innovative’ Challenges Competitions. Write a letter to your friend describing your success.
Answer:
LETTER TO A FRIEND – SUCCESS

A1 Apartments
Vivekananda Nagar
Amaravaram
18.06.2022

Dear Basha

I am just thrilled to tell you that I have secured the fifth position at the national level Innovative Challenge Competitions.

The Ministry of Human Resources conducted this competition in the last month with a view to encouraging young minds to take up creative research. As you know well, I have a keen bent of mind for innovation. I crave for fresh and new ideas.

The moment I saw the notification for this competition in February, I decided to participate in it. Systematic and scientific smart work with the active support from our physics lecturer saw to it that I achieved this distinction.

This honour encourages me to take up creative research as my full-time career. I see immense potential in the field.

What’s up there at your end ?

Let us meet soon.

Yours affectionately,
Syed Nasseruddin

Basheer
Flat No. 205
Nalanda Heights
Near New Mosque
Nayeem Nagar

TS Inter 2nd Year English Grammar Letter Writing

Question 4.
Write a thanksgiving letter to the lecturer who guided you through the Innovative Challenge Competition.
Answer:
LETTER TO LECTURER – THANKSGIVING

24-8B Church Road
Nadinetta Palem
Sanga Reddy (Dt)
15.06.2022

Dear Sir

I am very happy to have secured the 5th position at national level in the Innovative Challenge Competition. But I am even happier to say that it’s because of your active support that I achieved this success. The way you monitored my work and the way you offered directions wherever corrections were necessary decided my destiny. But for your measured guidance, I wouldn’t have attained this position. I will be grateful to you sir, for this invaluable assistance. I hope to do better in my future endeavours with your help and blessings.

Thank you sir.

Yours sincerely
Daniel Sekhar

N. Prasanna
Lecturer in Physics
Sanga Reddy Academy of Sciences
SangaReddy

Question 5.
Write a letter to your younger sister explaining the importance of reading books.
Answer:
LETTER TO SISTER-READING BOOKS

08-A1, Knowledge Hub
VivekNagar
Wisdompur
08.07.2022

Dear Vahini

How are you all there? Hope you are doing well there in your studies.

From mom I understand that you have been burning midnight oil. Mom adds that you are not really happy with your scores. She affirms that your work, and the outcomes are out of proportion.

It is here I feel like putting in a word or two. What I understand is your toil is missing the right direction. Hard work is always important. But smart work really matters. I advise you to read books beyond your syllabus. You may think you don’t find time for ‘other’ books. If you have a will, you will find a way. “Reading maketh a full man,” (a woman too, of course!) said Francis Bacon.

This is more relevant in the modem knowledge-driven society. A good book first relieves you of the worry you suffer from. Then it shows you the way to perform better as you become a FULL WOMAN. Once you taste the fruit of reading, you cannot stop yourself from reading life¬changing books. This will sure change your attitude positively.

Bye for now

Your loving brother
Avinash. K

Vaishnavi. K
10-A Madhura Nagar
Gopala Patnam
Adilabad (dt)

TS Inter 2nd Year English Grammar Letter Writing

Question 6.
Write a letter to your younger sister explaining the importance of reading books.
Answer:
LETTER TO SISTER – READING BOOKS

6-3 Dwaraka Nagar
Thimmapuram
16.06.2022

Dear Manu

Sorry for the delay in replying to your letter.

For the past twenty days we have been very busy with the arrangements for our College Silver Jubilee celebrations. At last the programme ended on grand note the day before yesterday. Elaborate arrangements began a month earlier. As the Secretary of our college students union; I had to be responsible for quite a number of activities like cultural and sports competitions. Everything went off well. The concluding cultural extravaganza was the highlight. Group dances, solo folk performance, patriotic songs touched everyone’s heart. The chief guest’s inspiring speech drew loud applause from one and all.

Each student remembers the event for life.

By the way, how are you doing in your studies?
Let’s meet this weekend.

Yours lovingly
Dwivedi M

Manu. M
18/6-A Humayun Nagar
Pandy Bazaar
Chennai

TS Inter 2nd Year English Grammar Letter Writing

Question 7.
Write a letter to the front line warriors of your local hospital expressing gratitude for their services during the pandemic.
Answer:
LETTER TO FRONT LINE WARRIORS

1-2/3B Ramnagar Enclave
Main Road
Chanda Nagar
11.02.2022

Dear Doctor

It is highly admirable that you and your team have been relentlessly working to save people from COVID-19 related complication. While the world dreads to just hear the word COVID, you have been reaching out to the infected persons and rendering medical services, knowing well the risks the work involves.

It is here that you and your team deserve our heartfelt gratitude. It is worth ‘ mentioning that our village stands out in the entire state with zero fatality rate in COVID -19 cases. Credit goes to you all.

May God bless you all with more and more energetic enthusiasm. *

Yours gratefully
Shyam Kumar

Dr. Prem Kumar
Govt. Primary Health Center
Chanda Nagar

Question 8.
You are the president of a voluntary organization. You are going to conduct a blood donation camp on behalf of the Red Cross. Write a letter to your uncle requesting him to assist you.
Answer:
Letter to Uncle:

r12-14 Ashram Veedhi
Vedaranya Puri
Medak(dt)
10.05.2022

Dear uncle

Our ‘Friends Club’ is organising a massive blood donation camp on the 20th of this month. The collection arrangements are being taken care of by the Red Cross Society. We, the volunteers have given a wide publicity to the camp and response to our call to donate blood is really encouraging. Our modest estimates show not less than 200 persons are going to donate blood on that day.

As a doctor with commitment to common man’s cause, you have won a unique reputation. I have drawn inspiration from you in social service. You have always been great support and encouragement to me. Now I request for your active guidance and support for this massive blood donation camp. As that day happens to be a Sunday, please do come, help us and encourage us.

Mom and dad also want to see you, for it is long since you visited us.

Looking forward to seeing you,

Your loving nephew
Srikanth P

Dr. Madhusudhana Rao
People’s Clinic
Siddipet

TS Inter 2nd Year English Grammar Letter Writing

Question 9.
Write a letter to your uncle describing your feelings about monootonous academic work.
Answer:
Letter to Uncle – Monotonous Academic Work:

10, Tagore Hostel
Ideal College
Ravindra Nagar
13.05.2022

Dear uncle

How are you all there? I’m fine here.

I write this to relieve myself of the stress resulting from our monotonous academic activity. Right from 5 in the morning to 10 in the evening, work, work and nothing else. And that too all mechanical mugging up tasks. No scope for thinking. No room for creativity. Play, exercise, entertainment are strangers in the campus. I am fed up totally.

I crave for a change. I pray for wisdom to dawn on the administrators. I know you understand me well. I felt like unburdening myself.
Hope to see you this weekend.

Lovingly yours
Praveen Kumar
Vivek K

12 Bhagyanagar Towers
Vallabh Nagar
Vaisali

TS Inter Second Year Maths 2A Measures of Dispersion Important Questions Long Answer Type

Students must practice these Maths 2A Important Questions TS Inter Second Year Maths 2A Measures of Dispersion Important Questions Long Answer Type to help strengthen their preparations for exams.

TS Inter Second Year Maths 2A Measures of Dispersion Important Questions Long Answer Type

Question 1.
Find the mean deviation about the mean for the following continuous distribution. [AP – Mar. 2015]

TS Inter Second Year Maths 2A Measures of Dispersion Important Questions Long Answer Type 1

Solution:

TS Inter Second Year Maths 2A Measures of Dispersion Important Questions Long Answer Type 2

Here, Σfi = 100
Σfixi = 7100
∴ Mean \(\frac{\sum_{\mathrm{i}=1}^{\mathrm{n}} \mathrm{f}_{\mathrm{i}} \mathrm{x}_{\mathrm{i}}}{\mathrm{N}}=\frac{7100}{100}\) = 71
∴ Mean deviation about mean is M.D = \(\frac{\Sigma \mathrm{f}_{\mathrm{i}}\left|\mathrm{x}_{\mathrm{i}}-\overline{\mathrm{x}}\right|}{\mathrm{N}}=\frac{1040}{100}\) = 10.4.

Question 2.
Find the mean deviation about the mean for the following continuous distribution.

TS Inter Second Year Maths 2A Measures of Dispersion Important Questions Long Answer Type 3

Solution:
We can form the following table from the given data :

TS Inter Second Year Maths 2A Measures of Dispersion Important Questions Long Answer Type 4

Here, N = Σfi = 100
Σfixi = 12530
∴ Mean, \(\bar{x}=\frac{\sum_{i=1}^n f_i x_i}{N}=\frac{12530}{100}\) = 125.3
∴ Mean deviation about mean is M.D = \(\frac{\Sigma \mathrm{f}_{\mathrm{i}}\left|\mathrm{x}_{\mathrm{i}}-\overline{\mathrm{x}}\right|}{\mathrm{N}}\)
= \(\frac{1128.8}{100}\)
= 11.288 = 11.28.

TS Inter Second Year Maths 2A Measures of Dispersion Important Questions Long Answer Type

Question 3.
Find the mean deviation from the mean of the following data, using the step deviation method. [AP – Mar. ’18; TS – Mar. 2016]

TS Inter Second Year Maths 2A Measures of Dispersion Important Questions Long Answer Type 5

Solution:
We can form the following table from the given data :

TS Inter Second Year Maths 2A Measures of Dispersion Important Questions Long Answer Type 6

Let the assumed mean be A = 35
Here, C = 10
N = Σfi = 50
Mean, \(\bar{x}=A+\frac{\sum_{i=1}^n f_i d_i}{N} \times C\)
= \(A+\frac{\sum_{i=1}^7 f_i d_i}{N} \times C\)
= 35 + \(\frac{(-8)}{50}\) × 10
= 35 – 1.6 = 33.4
∴ Mean deviation about mean is M.D = \(\frac{\Sigma f_{\mathrm{i}}\left|\mathrm{x}_{\mathrm{i}}-\overline{\mathrm{x}}\right|}{\mathrm{N}}=\frac{659.2}{50}\) = 13.185.

Question 4.
Find the mean deviation about the mean for the given data using step deviation method. [AP – Mar. ’17, ’16, AP – May 2015] [TS – Mar. ’18, May ’16]

TS Inter Second Year Maths 2A Measures of Dispersion Important Questions Long Answer Type 7

Solution:
We can form the following table from the given data:

TS Inter Second Year Maths 2A Measures of Dispersion Important Questions Long Answer Type 8

Let the assumed mean be A = 25
Here, C = 10
N = Σfi = 50
\(\bar{x}=A+\frac{\sum_{i=1}^n f_i d_i}{N} \times C\)
= \(\mathrm{A}+\frac{\sum_{\mathrm{i}=1}^5 \mathrm{f}_{\mathrm{i}} \mathrm{d}_{\mathrm{i}}}{\mathrm{N}} \times \mathrm{C}\)
= 25 + \(\frac{10}{50}\) × 10 = 27
∴ Mean deviation about mean is M.D = \(\frac{\Sigma \mathrm{f}_{\mathrm{i}}\left|\mathrm{x}_{\mathrm{i}}-\overline{\mathrm{x}}\right|}{\mathrm{N}}=\frac{472}{50}\) = 9.44.

TS Inter Second Year Maths 2A Measures of Dispersion Important Questions Long Answer Type

Question 5.
Find the mean deviation about the median for the following continuous distribution.

TS Inter Second Year Maths 2A Measures of Dispersion Important Questions Long Answer Type 9

Solution:

TS Inter Second Year Maths 2A Measures of Dispersion Important Questions Long Answer Type 10

Median class = Class containing \(\frac{N}{2}^{\text {th }}\) item
= \(\frac{50}{2}\) = 25 item
= 20 – 30 class
Here, l = 20, C = 10, f = 14, m = 14, N = 50
∴ Median, M = l + \(\frac{\frac{N}{2}-m}{f}\) × C
= 20 + \(\frac{25-14}{14}\) × 10
= 20 + 7.86 = 27.86
∴ Mean deviation about median is M.D = \(\frac{\Sigma \mathrm{f}_{\mathrm{i}}\left|\mathrm{x}_{\mathrm{i}}-\mathrm{M}\right|}{\mathrm{N}}\)
= \(\frac{517.16}{50}\) = 10.34

Question 6.
Find the mean deviation about median for the following data.

TS Inter Second Year Maths 2A Measures of Dispersion Important Questions Long Answer Type 11

Solution:

TS Inter Second Year Maths 2A Measures of Dispersion Important Questions Long Answer Type 12

Median class = Class containing \(\frac{\mathrm{N}^{\text {th }}}{2}\) item
= \(\frac{1000}{2}\) = 500th item = 35 – 40 class
Here, l = 35, C = 5, f = 160, m = 420, N = 1000
∴ Median, M = l + \(\frac{\frac{N}{2}-m}{f}\) × C
= 35 + \(\frac{500-420}{160}\) × 5
= 35 + 2.5 = 37.5
∴ Mean deviation about median is M.D = \(\frac{\Sigma \mathrm{f}_{\mathrm{i}}\left|\mathrm{x}_{\mathrm{i}}-\mathrm{M}\right|}{\mathrm{N}}=\frac{8175}{1000}\) = 8.175.

TS Inter Second Year Maths 2A Measures of Dispersion Important Questions Long Answer Type

Question 7.
Calculate the variance and standard deviaon,of the following continuous frequency distribution.
[AP – May 2016; TS – Mar. 2017; Mar. ‘14, Board Paper]

TS Inter Second Year Maths 2A Measures of Dispersion Important Questions Long Answer Type 13

Solution:
We can form the following table from the given data:

TS Inter Second Year Maths 2A Measures of Dispersion Important Questions Long Answer Type 17

∴ Mean, \(\bar{x}=\frac{1}{N} \sum_{i=1}^7 f_i x_i=\frac{3100}{50}\) = 62
Variance, σ2 = \(\frac{1}{N} \sum_{i=1}^7 f_i\left(x_i-\bar{x}\right)^2\)
= \(\frac{1}{50}\) (10050) = 201
Standard deviation, σ = \(\sqrt{\frac{1}{N} \sum_{i=1}^7 f_i\left(x_i-\bar{x}\right)^2}\)
= \(\sqrt{\text { variance }}=\sqrt{201}\)= 14.17 (approximately).

Question 8.
The following table gives the daily wages of workers in a factory. Compute the standard deviation and the coefficient of variation of the wages of the workers.

TS Inter Second Year Maths 2A Measures of Dispersion Important Questions Long Answer Type 15

Solution:
We shall solve this problem using the step deviation method, since the midpoints of the class intervals are numerically large.

TS Inter Second Year Maths 2A Measures of Dispersion Important Questions Long Answer Type 16

From the table, N = \(\sum_{i=1}^9\) fi = 72
Let the assumed mean, A = 300
Here, C = 50
From the table, \(\sum_{i=1}^9\) fidi = – 31
Mean, \(\bar{x}=A+\frac{\sum_{i=1}^9 f_i d_i}{N}\) × C
= 300 + \(\frac{-31}{72}\) × 50
= 300 – \(\frac{1550}{72}\)
= 278.5 (approximately)

TS Inter Second Year Maths 2A Measures of Dispersion Important Questions Long Answer Type 17

TS Inter Second Year Maths 2A Measures of Dispersion Important Questions Long Answer Type

Question 9.
The scores of two cricketers A and B in 10 innings are given below. Find who is a better run getter and who is a more consistent player.

TS Inter Second Year Maths 2A Measures of Dispersion Important Questions Long Answer Type 18

Solution:
For cricketer A : Scores of A are 40, 25, 19. 80, 38, 8, 67, 121, 66, 76
∴ Mean, \(\overline{\mathrm{x}}_{\mathrm{A}}=\frac{\text { Sum of the scores }}{\text { No. of innings }}\)
= \(\frac{40+25+19+80+38+8+67+121+66+76}{10}\)
= \(\frac{540}{10}\) = 54
The deviations of the respective observations from the mean i.e., xi – \(\overline{\mathrm{x}}\) are: – 14, – 29, – 35, 26, – 16, -46, 13, 67, 12, 22
Variance, σ2 = \(\frac{1}{n} \sum_{i=1}^{10}\left(x_i-\bar{x}\right)^2\)
= \(\frac{196+841+1225+676+256+2116+169+4489+144+484}{10}\)
= \(\frac{10596}{10}\) = 1059.6
Standard deviation, σA = \(\sqrt{1059.6}\) = 32.55
C.V of A = \(\frac{\sigma_{\mathrm{A}}}{\overline{\mathrm{x}}_{\mathrm{A}}}\) × 100
= \(\frac{32.55}{54}\) × 100 = 60.28.

For cricketer B:
Scores of B are 28, 70, 31, 0, 14, 111, 66, 31, 25, 4
Mean \(\overline{\mathrm{x}}_{\mathrm{B}}=\frac{\text { Sum of the scores }}{\text { No. of innings }}\)
= \(\frac{28+70+31+0+14+111+66+31+25+4}{10}=\frac{380}{10}\)
= 38

The deviations of the respective observations from mean i.e., (xi – \(\overline{\mathbf{x}}\)) are: – 10, 32, – 7, – 38, – 24, 73, 28, – 7, – 13, – 34
Variance, σB2 = \(\frac{1}{n} \sum_{i=1}^{10}\left(x_i-\bar{x}\right)^2\)
= \(\frac{100+1024+49+1444+576+5329+784+49+169+1156}{10}\)
= \(\frac{10680}{10}\) = 1068
Standard deviation. σB = \(\sqrt{1068}\) = 32.68
C.V of B = \(\frac{\sigma_B}{\bar{x}_B}\) × 100
= \(\frac{32.68}{38}\) × 100 = 86
Since, \(\overline{\mathbf{x}}_{\mathrm{A}}\) is greater than \(\overline{\mathbf{x}}_{\mathrm{B}}\) then cricketer A is better run getter (scorer).
Since, C.V of A is less than C.V of B then cricketer ¡s also a more consistent player.

Question 10.
From the prices of shares X and Y given below, for 10 days of trading, find out which share is more stable?

TS Inter Second Year Maths 2A Measures of Dispersion Important Questions Long Answer Type 19

Solution:
Share X:
Prices of share X are 35, 54, 52, 53, 56, 58, 52, 50, 51, 49
Mean, \(\overline{\mathrm{x}}_{\mathrm{X}}=\frac{1}{\mathrm{~m}} \sum_{\mathrm{i}=1}^{10} \mathrm{x}_{\mathrm{i}}\)
= \(\frac{510}{10}\) = 51
The deviations of the respective observations from mean i.e., (xi – \(\overline{\mathrm{x}}\))2 are: – 16, 3, 1, 5, 7, 1, – 10, – 2
Variance, σX2 = \(\frac{1}{n} \sum_{i=1}^{10}\left(x_i-\bar{x}\right)^2\)
= \(\frac{256+9+1+25+49+1+1+0+4}{10}\)
= \(\frac{350}{10}\) = 35
Standard deviation, σx = √35 = 5.9 (approximately)
C.V of X = \(\frac{\sigma_X}{\bar{x}_X}\) × 100
= \(\frac{5.9}{51}\) × 100 = 11.5 (approximately)

Share Y:
Prices of share Y are 108, 107, 105. 105, 106, 107, 104, 103, 104, 101
Mean, \(\overline{\mathrm{x}}_{\mathrm{Y}}=\frac{1}{\mathrm{n}} \sum_{\mathrm{i}=1}^{10} \mathrm{x}_{\mathrm{i}}\)
= \(\frac{1050}{10}\) = 105
The deviations of the respective observations from mean i.e.. (xi – \(\overline{\mathrm{x}}\)) are 3, 2, 0, 0, 1, 2, – 1, – 2, – 1, – 4
Variance, σY2 = \(\frac{1}{n} \sum_{\mathrm{i}=1}^{10}\left(\mathrm{x}_{\mathrm{i}}-\overline{\mathrm{x}}\right)^2\)
= \(\frac{9+4+0+0+1+4+1+4+1+16}{10}\)
= \(\frac{40}{10}\) = 4
Standard deviation, σY = √4 = 2
C.V. of Y = \(\frac{\sigma_Y}{\bar{x}_Y}\) x 100
= \(\frac{2 \times 100}{105}\) x 100 = 1.904
Since, C.V of X is greater than C.V of Y then the share of Y is more consistent (stable).

TS Inter Second Year Maths 2A Measures of Dispersion Important Questions Long Answer Type

Question 11.
Find the mean and variance using the step deviation method of the following tabular data, giving the age distribution of 542 members.

TS Inter Second Year Maths 2A Measures of Dispersion Important Questions Long Answer Type 20

Solution:
We form the following table From the given data:

TS Inter Second Year Maths 2A Measures of Dispersion Important Questions Long Answer Type 21

Let the assumed mean, A = 55
Here, C = 10

TS Inter Second Year Maths 2A Measures of Dispersion Important Questions Long Answer Type 22

Some More Maths 2A Measures of Dispersion Important Questions

Question 12.
Students of two sections A and B of a class show the following performance in a test (conducted 100 marks).

TS Inter Second Year Maths 2A Measures of Dispersion Important Questions Long Answer Type 23

Which section of students has greater variability In performance?
Solution:
Given that,

TS Inter Second Year Maths 2A Measures of Dispersion Important Questions Long Answer Type 24

The variance of distribution of marks of section A is σ12 = 64
∴ The standard deviation of distribution of marks of section A is σ1 = 8
The variance of distribution of marks of section B is σ22 = 81
∴ The standard deviation of distribution of marks of section B is σ2 = 9
The average marks in the test of section A is \(\bar{x}_1\) = 45
The average marks in the test of section B is \(\bar{x}_2\) = 45
∵ The average marks in the test of both sections of students is the same i.e., 45.
The standard deviation of the distribution of marks in section B is greater than the standard deviation of (he distribution of marks in section A.
Hence, the section B has greater variability in the performance.

TS Inter Second Year Maths 2A Measures of Dispersion Important Questions Long Answer Type

Question 13.
Find the variance and standard deviation of the following frequency distribution.

TS Inter Second Year Maths 2A Measures of Dispersion Important Questions Long Answer Type 25

Solution:
From the given data, we can form the following table:

TS Inter Second Year Maths 2A Measures of Dispersion Important Questions Long Answer Type 26

Mean of the given data is (\(\overline{\mathrm{x}}\)) = \(\frac{1}{N} \sum_{i=1}^7 f_i x_i\)
= \(\frac{760}{40}\) = 19
Variance, σ2 = \(\frac{1}{N} \sum_{i=1}^7 f_i\left(x_i-\bar{x}\right)^2\)
= \(\frac{1}{40}\) (1736) = 43.4
Standard deviation, σ = \(\sqrt{\text { variance }}\)
= \(\sqrt{43.4}\) = 6.58 (approximately).

Question 14.
Calculate the variance and standard deviation for a discrete frequency distribution.

TS Inter Second Year Maths 2A Measures of Dispersion Important Questions Long Answer Type 27

Solution:
From the given data, we can form the following table:

TS Inter Second Year Maths 2A Measures of Dispersion Important Questions Long Answer Type 28

Mean of the given data is (\(\overline{\mathrm{x}}\)) = \(\frac{1}{N} \sum_{i=1}^n f_i x_i\)
= \(\frac{1}{N} \sum_{i=1}^7 f_i x_i=\frac{420}{30}\) = 14
Variance, σ2 = \(\frac{1}{N} \sum_{i=1}^7 f_i\left(x_i-\bar{x}\right)^2\)
= \(\frac{1}{30}\) (1374) = 45.8
Standard deviation, σ =\(\sqrt{\text { variance }}\)
= \(\sqrt{45.8}\) = 6.76 (approximately).

TS Inter Second Year Maths 2A Measures of Dispersion Important Questions Long Answer Type

Question 15.
Find the mean deviation about the median for the following data.

TS Inter Second Year Maths 2A Measures of Dispersion Important Questions Long Answer Type 29

Solution:
We can form the following table from the given data:

TS Inter Second Year Maths 2A Measures of Dispersion Important Questions Long Answer Type 30

Median class = Class containing \(\frac{N^{t h}}{2}\) item
= \(\frac{100}{2}\) = 50th item = 40 – 50 class
Here, l = 40, f = 28, m = 32, C = 10, N = 100
∴ Median, M = l + \(\frac{\frac{\dot{N}}{2}-\mathrm{m}}{\mathrm{f}}\) × C
= 40 + \(\frac{50-32}{28}\) × 10
= 40 + \(\frac{180}{28}\)
= 40 + 6.42 = 46.42
∴ Mean deviation about median is M.D = \(\frac{\Sigma \mathrm{f}_{\mathrm{i}}\left|\mathrm{x}_{\mathrm{i}}-\mathrm{M}\right|}{\mathrm{N}}=\frac{1428.4}{100}\) = 14.284

Question 16.
Lives of two models of refrigerators A and B obtained ¡n a survey are given below.

TS Inter Second Year Maths 2A Measures of Dispersion Important Questions Long Answer Type 31

From the above data suggest which model to purchase.
Solution:
Model – A:
To find the mean and variance of lives of model A refrigerators, we shall construct the following table:

TS Inter Second Year Maths 2A Measures of Dispersion Important Questions Long Answer Type 32

From the table, N = \(\sum_{\mathbf{i}=1}^5\) fi = 46, \(\sum_{\mathbf{i}=1}^5\) fixi = 212
Mean, \(\bar{x}_A=\frac{1}{N} \sum_{i=1}^5 f_i x_i\)
= \(\frac{212}{46}\) = 4.6
From the table, \(\sum_{i=1}^5 f_i\left(x_i-\bar{x}\right)^2\) = 244.96
Variance, σA2 = \(\frac{1}{N} \sum_{i=1}^5 f_i\left(x_i-\bar{x}\right)^2\)
= \(\frac{244.96}{46}\) = 5.32
Standard deviation, σA = \(\sqrt{5.32}\)
= 2.3 (approximately)
Coefficient of variation of model A = \(\frac{\sigma_{\mathrm{A}}}{\mathrm{x}_{\mathrm{A}}}\) × 100
= \(\frac{2.3}{4.6}\) × 100
= 50 (approximately).

TS Inter Second Year Maths 2A Measures of Dispersion Important Questions Long Answer Type

Model B:
To find the mean and variance of lives of model B refrigerators, we shall construct the following table:

TS Inter Second Year Maths 2A Measures of Dispersion Important Questions Long Answer Type 33

From the table, N = \(\sum_{i=1}^5\) fi = 49
\(\sum_{i=1}^5\) fixi = 297
Mean, \(\bar{x}_B=\frac{1}{N} \sum_{i=1}^5 f_i x_i\)
= \(\frac{297}{49}\) = 6.06
From the table, \(\) = 224.8164
Variance, σB2 = \(\frac{1}{N} \sum_{i=1}^5 f_i\left(x_i-\bar{x}\right)^2\)
= \(\frac{224.8164}{49}\) = 4.58 (approximately)
Standard deviation, σB = \(\sqrt{4.58}\)
= 2.1 (approximately)
Coefficient of variation of model B = \(\frac{\sigma_B}{x_B}\) × 100
= \(\frac{2.1}{6.06}\) × 100 = 34.65 (approximately)
Since C.V. of model B is less than C.V. of model A then the model B is more consistent than the model A with regard to life in years.
Hence, we suggest model B for purchase.

TS Inter 2nd Year English Grammar Writing Descriptions

Telangana TSBIE TS Inter 2nd Year English Study Material Grammar Writing Descriptions Exercise Questions and Answers.

TS Inter 2nd Year English Grammar Writing Descriptions

Q.No.16 (4 Marks)

Students learning a language go ahead step by step-sounds/letters → words → sentences → composition. “Writing Descriptions” is a kind of composition. Here, we try to learn how to describe a person, a place, a thing or a process. One should first be clear about the points (content) that are to be included.

Then, one should try t. present those points in correct language and in a systematic order. Keen obse ation of suitable models first and regular practice in writing descriptions nex nelp one master this art. Constant assessment of one’s own performance and necesaryremedial measures go a long way in enhancing this competency.

I. DESCRIBING A PERSON:

While describing a person we include details like the person’s appearance, qualities, nature, typical traits, etc.

Now, see a model.

The person I always remember most is the principal of my college. He is not very tall, but he is well-built in his physique. He has grey hair and wears spectacles but only while reading. While he speaks to us, at the assembly, he has the habit of pushing his spectacles to the top of his head. He rarely smiles and always looks stern. However, he is really very kind and always treats the students in a friendly manner. When a student is in trouble, he always tries to help him. All the students and teachers respect our principal.

Examine another model.
This disheartening introspection was interrupted by the waiting-room door opening. An old man stood on the threshold, looking at me silently. He wore a heavy black jacket buttoned high in the chest, narrow trousers, and a two-inch collar. In his hand, he held a pair of gold-rimmed pince-nez, which were attached to his right lapel by a thick black silk ribbon.

TS Inter 2nd Year English Grammar Writing Descriptions

He was so thin, so old, so pale, and so slow he could have taken his place in the near-by post-mortem room without attracting attention. He clipped his glasses on to his nose with a slow, shaky movement and inspected me more carefully. I leapt to my feet and faced him.
(From the short story ‘An Interview’)

Exercise

Question 1.
Describe your mother using the hints given below.

tall and thin – black hair – important person in life – wake up at 5 am – prepares us for college – takes care of father, grandparents too – works without complaining – emotionally strong – want to be like her – symbol of love and sacrifice
Answer:
MY MOTHER

Of all persons on this earth, I love my mother most. She is my first and best teacher. I love to be like her and if I can, I will be the blessed one. With her tall and slim appearance, she looks impressive at once. Her thick dark hair is an added attraction. She wakes up at five in the morning and works hard till late in the evening with a never fading smile. She gets ready for us everything we need, takes care of father’s and grandparents’ needs. She is very strong both physically and emotionally. If someone is looking for a true symbol of love, sacrifice and contentment, my mother stands as that symbol!

Question 2.
Describe your best friend Deepthi using the hints given below.

fair and tall – 165 ems – aged 25 – slim – thick hair – large, expressive eyes – wears western clothes – sari on special occasions – practises yoga – a good athlete – hardworking – honest – helpful – my best friend
Answer:
DEEPTHI- MY REST FRIEND

Deepthi – the name rings music in my ears! She is my most beloved friend. She fits perfectly into the definition of a true friend – as offered by Khalil Gibran. She is. twenty-five. She looks fair. And she is tall indeed and very slim. With her thick black hair and ever-present smile, she impresses everyone. She practises Yoga. She is fond of athletics. She prefers modem western clothes. Yet, she puts on traditional Indian costumes on special occasions. She is honest to the core and loves hard but smark work. I am proud to be her friend!

TS Inter 2nd Year English Grammar Writing Descriptions

II. DESCRIBING A PLACE:

The description of a place intludes in it details like its location, special features, Significance, people, crops, landmarks and so on.

Examine the model given under carefully.
Yadagirigutta is a small town in the Yadadri Bhuvanagiri District of Telangana State. It is 60 KMs from Hyderabad city. The famous Hindu Temple, Sri Lakshmi Narasimha Swamy Temple is situated on a hillock in the town. It is a unique pleasant hillock that enjoys moderate climate in allseasons. The place is visited by an average of five thousand to eight thousand pilgrims every day. After the formation of Telangana State, the Hon’ble Chief Minister Sri Kalvakuntla Chandra shekhar Rao has been personally supervising the development of the temple to make it one of the famous tourist attractions not only in India but also all over the world.

Exercise

Question 1.
Describe the famous tourist place, Ooty using the hints given below.

town – hill station – Tamil Nadu – 265 KMs from Bangalore – located in the Nilgiris – 7500 ft above sea level – cool and a pleasant summer destination – lakhs of tourists – – coffee plantations – top boarding schools – Queen of the Hill Stations
Answer:
OOTY THE QUEEN OF HILL. STATIONS

Ooty or Udhagamandalam is rightly and deservedly regarded as the Queen of Hill Sta-tions. Situated in the Western. Ghats at an elevation of7500 feet in Nilgiris district of Tamil Nadu, Ooty is one of the most preferred tourist destinations in India. Nature’s, bounty, pleasant climate, hill slopes, waterfalls, lakes, churches, temples, Botanical and Rose Gardens, hill railways are some of the prominent Sights that mesmerise the visitors. Travel up the Ghat road or rail track itself is an experience to cherish for life time. It is, therefore, no wonder that the English people loved to spend here most of their time. (Before India became independent.)

TS Inter 2nd Year English Grammar Writing Descriptions

Question 2.
Describe your own village or town based on your knowledge and understanding in not more than 100 words.
Answer:
MY VILLAGE

My village is away from the bustle of modern urban societies. With green-covered hill ridges on two sides and a stream on another side, our village is endowed with rich natural beauty. Climate round the year is pleasant. Villagers grow a variety of crops twice a year. All homes have at least one milching animal each. People lead peaceful, comfortable and contented lives. Maintaining cleanliness and greenery is a collective responsibility. Basic amenities like roads, drains are maintained well. A school and a hospital meet villagers’ educational and health needs. Our village is a model one.

III. DESCRIBING A THING :

In the descriptions of things, the particulars involved are the appearance, make up, uses and any other relevant details of the thing described. Observe the sample description that follows.

The National Flag of India is a horizontal tricolourof deep saffron at the top, white in the middle and dark green at the bottom in equal proportion. The ratio of width of the flag to its length is two is to three (2:3). In the centre of the white band is a navy-blue colour wheel with twenty-four spokes known as the Ashoka Chakra. This is taken from I he famous Ashoka Sthupa (pillar) of Saranath. Each spoke symbolises one principle of life and also the twenty-four hours In the day, which is why it is called the wheel of time.

Exercise

Question 1.
Describe about the Charminar using the hints given below.

monument location 1591 AD four minarets height materials used commein orate the end of deadly plague prime tourist attraction
Answer:
THE CHARMINAR

The Charminar has for long been the symbol of Hyderabad and the emblem of Telangana. Founded in 1591 by Muhammad Quli Qutb Shah, this 48.7 meter high monument has been the centre of attraction of tourists from across the globe. With Indo-Islamic architectual styles and rich ornate designs, its appearance is a feast to eyes. Situated on the eastern bank of the Musi River in the old city area, this tourist centre also serves as a religious centre on all important festive occasions. A very busy market place surrounds the landmark where a wide range of articles are sold at a’ reasonable price. The Charminar (four minarets – pillars) is a place to visit.

TS Inter 2nd Year English Grammar Writing Descriptions

Question 2.
Describe about the Statue of Equality using the hints given below.

the statue -location – imposing size – posture – materials used – wide eyes – overflowing with mercy huge ears eager to listen – broad shoulders ready to take up respon sibilities – folded hands – appealing for Equality – for service to society – Supreme Being [Model Question Paper]
Answer:
THE STATUE OF EQUALITY

The latest feather in Telangana’s cap is the 216 – feet, golden-hued Panch aloha (five metals) Staute of Equality Situated on a sprawling 50-acre site at Muchintal, near Hyderabad, the statue stands for the image and preachings of the eleventh century Vaishnavite Shri Bhagavad Ramanuja charya. Bhagavad Ramanujacharya put his heart and soul to practise and propagate equality among all.

The statue is not just a monument; it is a symbol; it is a movement. The imposing statue in sitting posture has wide eyes that overflow with mercy. Huge ears stand for eagerness to listen and learn. Broad shoulders express readiness to take up responsibilities. Folded hands appeal for equality. A visit to the place is bound to bring in transformation!

Question 3.
Describe about the Telangana Martyrs Memorial using the hints given below.

monument – location – designer – materials used – height – completion date – dedicated to – symbol for
Answer:
TELANGANA MARlYRS MEMORIAL

Telangana Martyrs Memorial is situated near Public Gardens, Saifabad, Hyderabad. It is a 25-feet tall black and red granite monument. It was designed by professor of architecture Aekka Yadagiri Rao. It was commissioned in 1974. It commemorates the sacrifices of more than three hundred and sixty youngsters who faced bullets for the cause of separate Telangana in the 1969 movement. A white lily flower, atop the Memorial pays rich tributes to those martyrs. After Telangana became a separate state, it was decided to observe June 2nd every year as the Martyrs’ Memorial Day officially.

TS Inter 2nd Year English Grammar Writing Descriptions

IV. DESCRIBING A PROCESS:

Presenting various steps involved in a relatively simple activity is called ‘Describing a Process’. It requires the knowledge of necessary items and the method of doing that ‘activity’, It also demands the capacity to put that knowl-edge into a neat and properly organised paragraph. Observing as many descriptions of processes as possible is definitely of great help. You come across a number of examples in books on chemistry and cookery, for instance. All the flow charts serve as good examples. After observing sufficient number of examples, start writing on your own.

Points to ponder over for the purpose of Public Examination?

  • Use the Simple Present Tense, as the ‘actions’ are universal.
  • Imperative sentences are commonly used,
    eg: Take a glass of water. Then put it.
  • Passive sentences are also used,
    eg: A spoonful of salt is added.
  • The use of linkers (markers) like first, then, after that is very important.A list of linkers is given here
    TS Inter 2nd Year English Grammar Writing Descriptions 1
  • Give the list of ingredients, if necessary. (Generally given in the case of recipes).
  • The given activity may require about 6 to 8 steps for completion. So your answer may have 6 to 8 sentences.
  • The entire process can also be presented in the form of a FLOWCHART.
  • Give a HEADING.

Examples:

1. Preparing potato fry

Given below is a description of how a beginner can make Aloo fry. Read the recipe and try it out at home! Observe the concise, numbered instructions, the list of ingredients, as also the preparation and cooking time, making it easy for a person to decide whether to attempt the dish or not.

Recipe for potato fry
Preparation time: 5 min, Cooking Time: 20 min, Serves: 2
Ingredients

  • 4 Potatoes – 2, large, washed, peeled’ and cubed 4
  • Oil – 2 tbsps 4
  • Turmeric powder – 1- 2 tsp
  • Chilli powder -1 tsp
  • 4 Salt to taste Method
  1. Heat oil in a heavy bottomed vessel.
  2. Add the diced potatoes and cook on medium flame for 4 to 5 minutes, tossing the cubed potatoes frequently.
  3. Reduce flame, add turmeric powder and mix. Place lid and cook on low flame for 10 minutes.
  4. Remove lid, add salt. Allow the potatoes to reach a nice brown shade. It may take another 5-6 minutes.
  5. Add chilli powder: and mix well. The potato fry is ready.

TS Inter 2nd Year English Grammar Writing Descriptions

2. Sending a letter by Registered Post

When a letter is sent by registered post, the postman personally hands over the letter to the recipient and takes his signature, instead of simply leaving it in the recipient’s letter box. If the sender wants the proof of the letter having been delivered, he can attach an acknowledgement card to the letter. Registered post is, therefore, a safe way of sending important letters and documents. Given below is a paragraph about the process of sending a letter by registered post.

Observe the use of the passive voice.

Registered post is a safe way of sending important letters and documents. The letter is placed in an envelope and the words “By Registered Post” are inscribed on the top. The address of both the recipient as well as the sender must be written. The cover is then taken to the post office. It should be handed over the clerk at the Registration counter.

The clerk weighs it and informs us about the value of the stamps that should be affixed on the cover. The minimum charges are Rs. 25. The stamps should be bought and affixed accordingly and, once again, the cover is handed to the registration clerk. A receipt is given by the clerk and this should be kept safely till we come to know that the letter has reached the recipient.

3. Applying for a passport

A passport is an official document issued by the government, certifying the identity and citizenship of the person and entitling him to travel to foreign countries and return. The process of getting a passport was quite difficult till a few years ago but it has become considerably easy now. Given below is the process that must be followed * by Indian citizens to get a passport.

TS Inter 2nd Year English Grammar Writing Descriptions

Applying for a passport online

Applying for a passport is difficult offline but is easy online. The applicant should go to the Passport Seva Website first. He/She should fill the User Registration Form carefully and click on ‘Register’. The applicant will then reach Applicant Home page. He should click on the link Apply for a Fresh Passport.

The form contains details of name; place and date of birth, gender, marital status, educational qualifications, identification marks, Aadhaar Card Number and so on. An ARN (Acquirer Reference Number) is generated when the form is submitted Next, the applicant must book an appointment at the Passport Seva Kendra depending on the availability of dates. A fee of Rs. 1500 is charged for booking an appointment.

On the appointed day the applicant must go to the Passport office with all original documents, self attested Photostat (Xerox) documents and the passport form with a photo pasted on it. The original documents are checked. A photograph is taken and biometric information taken. The person will be interviewed briefly. An acknowledgement slip is given. Within a day or two, police verification takes place at the address given. In a few days the applicant receives the passport.

Exercise

Question 1.
Describe how Sandbya drew Rs. 500 from an ATM.
Answer:
Drawing Money from ATM

Sandhya first went to the nearest ATM. After entering the ATM room, she inserted the card in the slot. Then from the displayed options she selected banking. Later she entered her 4 digit pin. After that she selected withdrawal from the choices. Next she clicked on Savings- account. And then she entered the amount. Then she opted for a printed advice by clicking on yes. As the machine then rolled out cash first and printed note later, she collected both, picked up her ATM card arid left the chamber.

TS Inter 2nd Year English Grammar Writing Descriptions

Question 2.
Describe how you and your friends made arrangements for the College Day Function. (Hints: date, chief guest, programme, speeches, cultural items, invitations, stage arrangements, catering)
Answer:
How We Made Arrangements for the College Day

The moment our Principal announced proposals for college day, we Intermediate second year students) met in the students’ counsel room with our English lecturer in the chair. We discussed and decided upon the most convenient date. Later we thought of a guest who could really inspire us through his talk. We all decided-unanimously – our Collector to be our guest.

Then we chalked out the programme sheet. What first, what next, etc. We selected speakers to represent all sections, classes, groups, categories also. Then the talks dealt with cultural programmes. After that invitation cards, stage arrangement, food needs, etc. occupied our attention. Committees were formed for each activity. With the approval of our Principal and support and guidance of our lecturers we went ahead with our plans and made our College Day a grand success.

Question 3.
Describe how your elder brother got a Driving license.
(Hints : Learner’s License – Road signs, general rules – application – documents to be attached – Practice – Test driving after 30 days – Getting permanent license)
Answer:
GETTING A DRIVER’S LICENSE

First, my brother started learning how to drive. He also improved his knowledge of the symbols and signs on road sides and in driving. Then he filled in the prescribed form and submitted it in the Local RTA (Road Transport Authority) or MVI (Motor Vehicle Inspector) office along with the payment details of necessary fee. Then, he took a vision (eye- sight) test and a written test. He cleared both of them and got a Learner’s License. Then, he went on practising driving on roads. After a month, he took a test in actual driving. He got through it too. After that, he was issued the Driving License.

TS Inter 2nd Year English Grammar Writing Descriptions

TS Inter 1st Year Maths 1A Ratios up to Transformations Important Questions Short Answer Type

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

TS Inter 1st Year Maths 1A Ratios up to Transformations Important Questions Short Answer Type

Question 1.
Prove that \(\frac{\tan \theta+\sec \theta-1}{\tan \theta-\sec \theta+1}=\frac{1+\sin \theta}{\cos \theta}\). [Mar. ’14]
Answer:
TS Inter First Year Maths 1A Trigonometric Ratios up to Transformations Important Questions Short Answer Type 1

Question 2.
If A + B = \(\frac{\pi}{4}\), then prove that i) (1 + tan A) (1 + tan B) = 2. ii) (cot A – 1) (cot B -1) = 2. [Mar. 61′(TS), ’07 Ma
Answer:
(i) Given that A + B = 45°
⇒ tan (A + B) = tan 45°
⇒ \(\frac{\tan A+\tan B}{1-\tan A \tan B}\) = 1
⇒ tan A + tan B = 1 – tan A . tan B
⇒ tan A + tan B + tan A tan B = 1

L.H.S = (1 + tan A) (1 + tan B)
= 1 + tan B + tan A + tan A tan B
= 1 + (tan A + tan B + tan A tan B)
= 1 + 1 = 2 = RHS.
∴ (1 + tan A) (1 + tan B) = 2

(ii) Given that A + B = 45°
⇒ cot (A + B) = cot 45°
⇒ \(\frac{\cot A \cot B-1}{\cot B+\cot A}\) = 1
⇒ cot A. cot B – 1 = cot A + cot B
⇒ cot A cot B – cot A – cot B = 1
L.H.S = (cot A – 1) (cot B – 1)
= cot A cot B – cot A – cot B + 1 = (cot A cot B – cot A – cot B) + 1 = 1 + 1=2 = RHS.
∴ (cot A – 1) (cot B – 1) = 2

TS Inter First Year Maths 1A Ratios up to Transformations Important Questions Short Answer Type

Question 3.
Prove that sin2θ + sin2(θ + \(\frac{\pi}{3}\)) + sin2(θ – \(\frac{\pi}{3}\)) = \(\frac{\pi}{3}\)
Answer:
TS Inter First Year Maths 1A Trigonometric Ratios up to Transformations Important Questions Short Answer Type 2

Question 4.
If A, B, C are the angles of a triangle and if none of them is equal to \(\frac{\pi}{2}\) then prove that tan A + tan B + tan C = tan A tan B tan C.
Sol. If A, B, C are the angles of a triangle then
A + B + C = 180°
⇒ A + B = 180 0 – C
⇒ tan (A + B) = tan (180° – C)
⇒ \(\frac{\tan A+\tan B}{1-\tan A \tan B}\) = – tan C
⇒ tan A + tan B = – tan C (1 – tan A tan B)
⇒ tan A + tan B = – tan C + tan A tan B tan C
⇒ tan A + tan B + tan C = tan A tan B tan C

Question 5.
If 0 < A < B < \(\frac{\pi}{4}\) and sin(A +B) = \(\frac{24}{25}\) and cos(A – B) = \(\frac{4}{5}\), then find the value of tan 2a.
Answer:
0 < A < \(\frac{\pi}{4}\) and 0 < B < \(\frac{\pi}{4}\) ⇒ 0 < A < B < \(\frac{\pi}{4}\)
∴ (A + B) lies in first quadrant.
TS Inter First Year Maths 1A Trigonometric Ratios up to Transformations Important Questions Short Answer Type 3

Question 6.
If tan α – tan β = m and cot α – cot β = n, then prove that cot(α – β) = \(\frac{1}{m}-\frac{1}{n}\)
Answer:
We have tan α – tan β = m
TS Inter First Year Maths 1A Trigonometric Ratios up to Transformations Important Questions Short Answer Type 4

Question 7.
If \(\frac{\sin (\alpha+\beta)}{\sin (\alpha-\beta)}=\frac{a+b}{a-b}\) then prove that a tan β = b
Answer:
Given \(\frac{\sin (\alpha+\beta)}{\sin (\alpha-\beta)}=\frac{a+b}{a-b}\)
By using componendo and dividendo, we get
TS Inter First Year Maths 1A Trigonometric Ratios up to Transformations Important Questions Short Answer Type 5

Question 8.
If A + B + C = \(\frac{\pi}{2}\) and and if none of A, B, Cs an odd multiple of then prove that cot A + cot B + cot C = cot A cot B cot C.
Answer:
Given A + B + C = \(\frac{\pi}{2}\) ⇒ A + B = \(\frac{\pi}{2}\) – C
∴ cot(A + B) = c(\(\frac{\pi}{2}\) – C) = tanC = \(\frac{1}{\cot C}\)
⇒ \(\frac{\cot A \cot B-1}{\cot B+\cot A}=\frac{1}{\cot C}\)
⇒ cot A + cot B + cot C = cot A cot B cot C

Question 9.
Prove that sin 18° = \(\frac{\sqrt{5}-1}{4}\). [May ’10]
Answer:
Let A = 18°
5A = 90°
2A + 3A = 90°
2A = 90° – 3A
sin 2A = sin (90° – 3A)
sin 2A = cos 3A
2 sin A cos A = 4 cos3A – 3 cos A
2 sin A cos A = cos A (4 cos2A – 3)
2 sin A = 4 cos2A – 3
2 sin A = 4 (1 – sin2A) – 3
2 sin A = 4 – 4 sin2A – 3
2 sin A = 1 – 4 sin2A
4 sin2A + 2 sin A – 1 = 0
This is a quadratic equation in sin A.
Here a = 4,b = 2, c = -1
TS Inter First Year Maths 1A Trigonometric Ratios up to Transformations Important Questions Short Answer Type 6
Since A = 18°, it lies in first quadrant and hence sin A > 0.
sin A = \(\frac{-1+\sqrt{5}}{4}\) ⇒ sin A = \(\frac{\sqrt{5}-1}{4}\)
∴ sin 18° = \(\frac{\sqrt{5}-1}{4}\)

TS Inter First Year Maths 1A Ratios up to Transformations Important Questions Short Answer Type

Question 10.
If A is not an integral multiple of \(\frac{\pi}{2}\), prove that
(i) tan A + cot A = 2 cosec 2A,
(ii) cot A – tan A = 2 cot 2A. [B.P] [Mar. ’18(AP)]
Answer:
TS Inter First Year Maths 1A Trigonometric Ratios up to Transformations Important Questions Short Answer Type 7

Question 11.
If θ is not an integral multiple of \(\frac{\pi}{2}\), prove that tan θ + 2 tan 2θ + 4 tan 4θ + 8 cot 8θ = cot θ. [Mar. ’19(AP); May ’01]
Answer:
We know that cot A – tan A = 2 cot 2A
TS Inter First Year Maths 1A Trigonometric Ratios up to Transformations Important Questions Short Answer Type 8
cot A – tan A = 2 cot 2A
tan A = cot A – 2 cot 2A …………………(1)
Put A = 0 in (1)
tan θ = cot θ – 2 cot 2θ

Put A = 20 in (1)
tan 2θ = cot 2θ – 2 cot 4θ

Put A = 40 in (1)
tan 4θ = cot 4θ – 2 cot 8θ

L.H.S = tan θ + 2 tan 2θ + 4 tan 4θ + 8 cot 8θ = (cot θ – 2 cot 2θ) + 2 (cot 2θ – 2 cot 4θ) + 4 (cot 4θ – 2 cot 8θ) + 8 cot 8θ
= cot θ – 2 cot 2θ + 2 cot 2θ – 4 cot 4θ + 4 cot 4θ – 8 cot 8θ + 8 cot 8θ = cot θ = R.H.S
∴ tan θ + 2 tan 2θ + 4 tan 4θ + 8 cot 8θ = cot θ

Question 12.
Prove that sin A. sin(\(\frac{\pi}{3}\) + A) sin (\(\frac{\pi}{3}\) – A) = \(\frac{1}{4}\) sin 3A and hence deduce that sin 20°. sin 40°. sin 60°. sin 80° = \(\frac{3}{16}\). [May ’97, ’93]
Answer:
TS Inter First Year Maths 1A Trigonometric Ratios up to Transformations Important Questions Short Answer Type 9
Let A = 20° ⇒ sin 20°. sin (60° + 20°) sin (60° – 20°)
= \(\frac{1}{4}\) sin 3 (20°)
⇒ sin 20° . sin 80°. sin 40° = \(\frac{1}{4}\) sin 60°

Multiply with sin 60° on both sides then we get
sin 20° . sin 40° . sin 60° . sin 80°
= \(\frac{1}{4}\)sin 60 – \(\frac{1}{4} \cdot\left(\frac{\sqrt{3}}{2}\right)^2=\frac{1}{4} \cdot \frac{3}{4}=\frac{3}{16}\)

Question 13.
Prove that sin4\(\frac{\pi}{8}\) + sin4\(\frac{5 \pi}{8}\) + sin4\(\frac{5 \pi}{8}\) + sin4\(\frac{7 \pi}{8}=\frac{3}{2}\). [Mar ’13; Mar. ’00]
Answer:
TS Inter First Year Maths 1A Trigonometric Ratios up to Transformations Important Questions Short Answer Type 10

Question 14.
Show that sin A = \(\frac{\sin 3 A}{1+2 \cos 2 A}\). Hence find the value of sin 15°.
Answer:
TS Inter First Year Maths 1A Trigonometric Ratios up to Transformations Important Questions Short Answer Type 11

Prove that tan α = \(\frac{\sin 2 \alpha}{1+\cos 2 \alpha}\) and hence deduce the values of tan 15° and tan 22\(\frac{1}{2}\)°
Answer:
2 – √3, √2 – 1

TS Inter First Year Maths 1A Ratios up to Transformations Important Questions Short Answer Type

Question 15.
Prove that tan 9° – tan 27° – cot 27° + cot 9° = 4.
Answer:
We have tan A + cot A
= \(\frac{\sin A}{\cos A}+\frac{\cos A}{\sin A}=\frac{1}{\sin A \cos A}\) = 2 cosec 2A
Put A = 9°, we have tan 9° + cot 9° = 2 cosec 18°
Put A = 27°, we have tan 27° + cot 27° = 2 cosec 54°
L.H.S = tan 9° – tan 27° + cot 9° – cot 27° = 2 (cosec 17° – cosec 54°)
TS Inter First Year Maths 1A Trigonometric Ratios up to Transformations Important Questions Short Answer Type 12

Question 16.
Prove that cos2\(\frac{\pi}{8}\) + cos2\(\frac{3 \pi}{8}\) + cos2\(\frac{5 \pi}{8}\) + cos2\(\frac{7 \pi}{8}\) = 2.
Answer:
TS Inter First Year Maths 1A Trigonometric Ratios up to Transformations Important Questions Short Answer Type 13

Question 17.
Prove that sin\(\frac{\pi}{5}\). sin\(\frac{2 \pi}{8}\).sin\(\frac{3 \pi}{8}\).sin\(\frac{4 \pi}{5}=\frac{5}{16}\). [Mar. ’13]
Answer:
L.H.S = sin\(\frac{\pi}{5}\). sin\(\frac{2 \pi}{8}\).sin\(\frac{3 \pi}{8}\).sin\(\frac{4 \pi}{5}\)
= sin 36° . sin 72°. sin 108°. sin 144°
= sin 36° . sin 72°. sin (90° + 18°) sin (180° – 36°)
= sin 36° . sin (90° -18°). sin (90° +18°). sin (180° – 36°)
= sin 36° . cos 18°. cos 18°. sin 36°
= sin236° . cos218°
= \(\left(\frac{10-2 \sqrt{5}}{16}\right)\left(\frac{10+2 \sqrt{5}}{16}\right)\)
= \(\frac{100-20}{256}=\frac{80}{256}=\frac{5}{16}\)

Question 18.
Prove that \(\frac{1-\sec 8 \alpha}{1-\sec 4 \alpha}=\frac{\tan 8 \alpha}{\tan 2 \alpha}\).
Answer:
TS Inter First Year Maths 1A Trigonometric Ratios up to Transformations Important Questions Short Answer Type 14

Question 19.
Prove that [Mar. ’19 (AP) & TS]
(1 + cos\(\frac{\pi}{10}\))(1 + cos\(\frac{3 \pi}{8}\))(1 + cos \(\frac{7 \pi}{8}\))(1 + cos\(\frac{9 \pi}{8}\)) = \(\frac{1}{16}\)
Answer:
LHS = (1 + cos\(\frac{\pi}{10}\))(1 + cos\(\frac{3 \pi}{8}\))(1 + cos \(\frac{7 \pi}{8}\))(1 + cos\(\frac{9 \pi}{8}\)
(1 + cosl8) (1 + cos 54) (1 + cos 126) (1 + cos 162)
= (1 + cos 18) (1 + sin 36) (1 – sin 36) (1 – cos 18)
= (1 + cos 18) (1 – cos 18) (1 + sin 36) (1 – sin 36)
= (1 – cos218°) (1 – sin2 36°)
= sin218° cos236° = \(\left(\frac{\sqrt{5}-1}{4}\right)^2\left(\frac{\sqrt{5}+1}{4}\right)^2\)
= \(\frac{(5-1)^2}{256}=\frac{16}{256}=\frac{1}{16}\)

Question 20.
If A is not an integral multiple of t, prove that cos A. cos 2A. cos 4A . cos 8A = \(\frac{\sin 16 A}{16 \sin A}\) and hence deduce that cos\(\frac{2 \pi}{15}\).cos\(\frac{4 \pi}{15}\).cos\(\frac{8 \pi}{15}\).cos\(\frac{16 \pi}{15}=\frac{1}{16}\).
Answer:
L.H.S = cos A. cos 2A. cos 4A . cos 8A
TS Inter First Year Maths 1A Trigonometric Ratios up to Transformations Important Questions Short Answer Type 15

Question 21.
If \(\frac{\sin (\alpha+\beta)}{\cos (\alpha-\beta)}=\frac{1-m}{1+m}\), then prove that tan(\(\frac{\pi}{4}\) – α) = m tan(\(\frac{\pi}{4}\) + β). [Mar. ’95, ’83, ’82, ’81]
Answer:
Given \(\frac{\sin (\alpha+\beta)}{\cos (\alpha-\beta)}=\frac{1-m}{1+m}\)
By using componendo and dividendo we get
TS Inter First Year Maths 1A Trigonometric Ratios up to Transformations Important Questions Short Answer Type 16

TS Inter First Year Maths 1A Ratios up to Transformations Important Questions Short Answer Type

Question 22.
If sec (θ + α) + sec (θ – α) = 2 sec θ and cos α ≠ 1, then show that cos θ = ± √2 cos \(\frac{α}{2}\).
Answer:
Given sec (θ + α) + sec (θ – α) = 2 sec θ
TS Inter First Year Maths 1A Trigonometric Ratios up to Transformations Important Questions Short Answer Type 17
⇒ cos2θ cos α = cos2θ – sin2α
⇒ sin2α = cos2θ – cos2θ cos α
⇒ sin2α = cos2θ (1 – cos α)
⇒ 1 – cos2α = cos2θ (1 – cos α)
⇒ (1 – cos α) (1 + cos α) = cos2θ (1 – cos α)
⇒ cos2θ = 1 cos α ⇒ cos2θ = 2 cos2\(\frac{\alpha}{2}\)
⇒ cos θ = ± √2 cos \(\frac{α}{2}\)

Question 23.
If m sin B = n sin (2A + B), then prove that (m + n)tan A = (m – n)tan (A + B). [Apr. ’85]
Answer:
Given m sin B = n sin (2A + B)
⇒ \(\frac{m}{n}=\frac{\sin (2 A+B)}{\sin B}\)
By using componendo and dividendo we get
TS Inter First Year Maths 1A Trigonometric Ratios up to Transformations Important Questions Short Answer Type 18

TS Inter 2nd Year English Grammar Curriculum Vitae

Telangana TSBIE TS Inter 2nd Year English Study Material Grammar Curriculum Vitae Exercise Questions and Answers.

TS Inter 2nd Year English Grammar Curriculum Vitae

Q.No.15  (1 ×4 = 4 Marks)

Curriculum Vitae (CV) presents the personal and academic details of an individual to the prospective employer in a systematically organised form. Slight variations in the format entitle this account to be called ‘Resume’ / ‘rezjumei /( ‘Biodata’ or ‘Academic Vitae’. Whatever be the title, presenting it properly paves the way for a prosperous future, for it initiates the process of selection of candidates. Hence, it is very important, from the real life point of view’, for the students to learn to prepare the CV as impressively as possible.

It is equally important from the examination point of view too, for the student can score all the allotted five marks with a little bit of care and practice. The question may be asked in two different ways. You may be asked to respond to a job notification. Then, you will have to ‘imagine’ the information required for the notified job and prepare the CV with that information. This is a little demanding.

The other way is to ask you to prepare the CV with the information provided byway of hints. This is relatively easier. Either way, you must know the format well. Any format, written correctly, fetches you. full marks. Choose the one you feel comfortable with.

Examine the following model carefully.
RESUME OF VASUDEVARAO MANNEM
VASUDEVARAO MANNEM
1-1-32, New World Colony,
Happy Society, Gandhi marg,
Hyderabad 512345
Mobile: 91-9999223444
[email protected]

TS Inter 2nd Year English Grammar Curriculum Vitae

OBJECTIVE
A position as Project Manager in the information technology Industry.

2006-2010
B.Tech in Electronics and Communication Engineering ABC Engineering College, Karimnagar, 78% aggregate.

2004-2006
Intermediate Board of Intermediate Education.
DFE College, Karimnagar. 73.4% aggregate.

2004
SSC. Board of Secondary Education.
GIH School, Karimnagar,76% aggregate.

TECHNICAL SKILLS
Language : C, C++
DBMS Packages : Oracle 8i
Operating System : MS DOS, Windows 98, NT, 2000, XP, 7
Web Designing : JAVA, HTML, XML

PROFILE

  • Higly energetic, growth oriented individual seeking to establisha career in the Information Technology industry.
  • Ability to take on challenges, work under pressure dedication towards work.

STRENGTHS

  • Good Communicator
  • Team Player
  • Problem solver

ADDITION AI INFORMATION

Language Known : English, Telugu and Hindi
Interest : Listening to Music, Playing Chess
Age : 22 years
Father’s name : Sri. Mannem Ramarao
References : Available on Request

TS Inter 2nd Year English Grammar Curriculum Vitae

I. Here is a Sample Resume written by Sunil Kumar Yemula.

SUNIL KUMAR VEMULA
ADDRESS : H.No. 2-1-446/2A, Sharma Apartments,
New Nallakunta, Hyderabad – 500044
Ph: 9999955555
E-mail: [email protected]

CAREER OBJECTIVE
To be a professional who can make a qualitative difference with an esteemed organization, where high competence and skill is rewarded.

EDUCATION

  • Discontinued Bachelor of Commerce from Masterminds College affiliated to Nagarjuna University, Guntur, in March 2021 due to Covid pandemic
  • Discontinued C A from Masterminds College affiliated to Nagarjuna University, Guntur, in March 2021 due to Covid pandemic
  • Intermediate (Mathematics, Economics, Commerce), Board of Intermediate Education, GJC, Kacheguda, TS in March 2020
  • SSC, Board of Secondary Education from GNR Model School, Malakpet, 2018

TECHNICAL. OTHER KEY SKILLS

  • Working knowledge of computers
  • Quick learner – Learn things very quickly and adopt it in understandable manners
  • Quick Driven – Focus more on quality of work and strive very hard to achieve it.
  • Logical thinker – Always solve the problem with a best logical solution
  • Communication Skills – Fluency in English and Telugu logical solution

HOBBIES :

  • Singing – Won awards in singing competition during schooling
  • Modern arts – Earn money by modern arts (by using discarded material)

LANGUAGES KNOWN : English and Telugu
PERSONAL PROFILE : Will be provided on request
REFERENCES : Will be provided on request

Place : HYDERABAD
Sunil Kumar Vemula

TS Inter 2nd Year English Grammar Curriculum Vitae

II. Look at the call for News Anchor for a television channel advertised in job search portal https://in.indeed.com. Prepare a CV in response.

NEWS ANCHOR
Nakshatra Media
Hyderabad, Telangana.
₹ 9,678 – ₹ 27,947 a month

A. Apply securely with Resume

  • Responsive employer
  • Organizing the breaking news in a way that it presentsd the most interesting aspects first.
  • Meeting up the reporters, news directors and fellow news anchors to..

Here is a CV prepared by Manoja in response to the advertisement.

III. Here is a CV prepared by Manoja in response to the advertisement.

MANOJA KSSP
ADDRESS : Flat no. 402, Nagarjuna Apartments, Ramalayam Road,
Ramgiri, Nalgonda. Telangana- 508001
New Nallakunta, Hyderabad – 500044
Ph: 9XXXXXXXX8
E-mail: [email protected]

CAREER OBJECTIVE
To be a professional who can make a qualitative difference with an esteemed organization, where high competence and skill is rewarded.

EDUCATION:

Course College University / Board Year of Passing CGPA Grade
B.A (History, Pol Sc., Journalism) GDC(W), Nalgonda M.G. University 2022 – I year Pursuing
Intermediate Bi.P.C Vivekananda Junior College, Nalgonda TSBIE, TS 2021 B+
Class X Triveni High School,Nalgonda ICSE 2019 B+

TECHNICAL SKILLS

  • Telugu Typing, Computer skills
  • Communication Skills – Fluency in English and Telugu.

WORK EXPERIENCE:

  • Worked as News presenter for City Cable Nalgonda, Summer 2021
  • Covered Covid hit areas and interviewed officialsand did live coverage

HOBBIES:

  • Singing – Won awards in singing competition during schooling
  • Making short films – on mobile

Languages Known : Telugu, Hindi and English
Personal Profile : Will be provided on request
References : 1. Dr. Ghanshyam, Principal, GDC(W) Nalgonda
2. Venu Madhavi, Program Executive, City Cable, Nalgonda.

Place : HYDERABAD
KSSP Manoja

TS Inter 2nd Year English Grammar Curriculum Vitae

IV. Let’s look at a job advertisement that was published in a newspaper.

Join Swiggy family as a Part-Time or Full-Time Food Delivery Executive Who can be an ideal Rider/Driver/Delivery Boy/Logistics/Admin/Delivery Executive for Swiggy?

Urgently hiring-Multiple vacancies – Weekends/Weekday options
Freshers also can apply. Prefer candidate above 18 years of age and can ridea two¬wheeler, 10th, 10th Pass, 12th Pass, students/candidates looking to work part-time, in shifts can visit our website and post your resume for the following positions:

  • Delivery rider, Delivery Boys / Delivery Executive, * Back Office Executive, * Loading, Unloading, * Delivery Operations,
  • Call Centre Executive, Collection agents, * Office Assistants, * Data Entry, * Field Sales Job, * Logistics *Helper * Night Shift Partime Helper

Here is a Resume prepared by Senthil Mammutty in response to the advertisement.

Senthil Mammutty
134 Swagath Hotel Street
S.D road, Secunderabad, T.S
(040)2xxxxx42
[email protected]

OBJECTIVE
To obtain an operations executive position in food retail industry

EDUCATION
NIFT, B.Des (Bachelor of Design), Madapur, Discontinued in fisal year.

EXPERIENCE
Food Service Worker, McDonald’s Restaurant 2020-Present, Madapur, Hyderabad.
Responsibilities: To provide excellent customer service, operate cash registers, maintain the work area clean and neat, prepare food and refill lobby items as necessary

AWARDS
Best Delivery executive 4.5 star ratings 2021

ACTIVITIES
Debates, Theatre at Junior College 2018-19
Participated in local and state level debate/drama competitions Won ThirdPrize in the District level debate conference, November 2018

VOLUNTEER
Red Ribbon Club, Red Cross Centre- Summer 2021 Banjara Hills, Hyderabad Performed office work such as data processing, filling, and answering phones; provided child-care services and general help as necessary.

REFERENCES
Available upon request

Place: SECUNDERABAD
Senthil Mammutty

TS Inter 2nd Year English Grammar Curriculum Vitae

V. Look at this advetisement on the job portal https://naukri.com.

Wanted Social Media Manager for “Swecchha” NGO. We are hiring Full time / Permanent / Part time social media managers, who will be managing all social media platforms of the organization Facebook, Instagram, twitter, Iinkedln, YouTube etc. The person will be responsible for all end to end social media actioities. Any Graduate can apply.

Key Skills required: Social Media, Social Networking, Social Media Content Marketing NGO Management, Digital Marketing, Social Media Marketing, Marketing, Social Service.
Here is a functional CV that Vaishnav has prepared.

Gottumukkala Vaishnav
ADDRESS: Flat #108, VImala Nivas, Opp. Community Hall,
Huzurabad, Karimnagar
Ph : +91 70 XXXXXXX
E-mail id : [email protected]

CAREER OBJECTS
To work in an organization that provides challenges and provides learning opportunities to hone amy skills and gives scope for serving society.

EDUCATION
Pursuing Masters in Social Work (Distance Mode)
Year of completion of Degree 2024 completed BBA from GDC, Warangal, KU with CGPA 7.5, Grade A 2022

TECHINAL SKILLS
‘Networking-Multimedia’ course, Bengaluru 2023 Web Programming, web designing, multimedia tools

WORK EXPERIENCE
Handled GDC Warangal official website, social media admin of Facebook, Instagram, Twitter, Telegram, WhatsApp You-Tube Channel, Blog sites.

WORK EXPERIENCE
Workship Resource person to Tharuni’ NGO to train girl students in developing self confidence 2019-20. Conducted workshops for Ru jroo’s Agaaz-e-Baatcheet, an Interfaith programme for College students sponsored by The British Deputy High Commission, India 2018 -2020 Associated with MAVA (Men Against Violence Against Women) for their awareness campaigns in colleges 2018 – 2019 Have been an admin of social media campaigns of Sneha, Mitr.

Additonal Information

Languages known : English, Telugu, Hindi and French
Interests : Rock Climbing. Rappelling, Photography
References :

  1. Dr. Mamatha Raghveer, Founder Tharuni Warangal
  2. Principal, GDC, Warangal

Excercise

Preparea Curriculum Vitae/Resume/Bio data in response to the advertisements published in Posters. News papers and College groups.

Question 1.
TS Inter 2nd Year English Grammar Curriculum Vitae 1
Answer:
For the post of Asst. Professor: Global Institute of Engineering & Technology Chilkur
CV of Ramarao Kokkiragadda

OBJECTIVE
Looking for a position that provides opportunities to mould budding geniuses into flowering personalities of Mother India.

DETAILS

NAME : Ramarao Kokkiragadda
FATHER : Vijay Kumar K
DATE OF BIRTH : 17. 08.1996
ADDRESS : 3-2-19-A, Masjid Street, Vaheb Nagar Armoor – 503224, Nizamabad (dt)
Mobile: 9986786324
Mail Id: [email protected]

EDUCATIONAL QUALIFICATIONS:

SI. No. Name of the Course Name of the Institution Years of Study % of Marks
1. PGDTE EFLU, Hyderabad 2019-20 71%
2. B.Ed SCRK Educational College, Bodhan 2018-19 82%
3. M.A (Eng.Lit) OU Campus, Hyderabad 2016-18 69%
4. B.A. (ECO. Socio. EL) MAM Degree College, Kamareddy 2013-16 76%
5. Intermediate(HEC) National Junior College, Nizamabad 2011-13 64%
6. SSC MHLK High School, Nizamabad 2011 67%

Technical Skills
PPT Designer Certificate

Work Experience
Lab (English Language) Incharge – One year JNTU Campus, Hyderabad

Languages Known : Urdu, Hindi, Telugu, English

References

  1. Prof. Isaac Saqueria
    – Dept, of ELT. OU Campus
  2. Prof. Anwar Pasha
    – Dept, of English JNTU, Hyderabad

10.06.2021
Armoor
Signature

TS Inter 2nd Year English Grammar Curriculum Vitae

Question 2.
TS Inter 2nd Year English Grammar Curriculum Vitae 2
Answer:
BIO-DATA of Gongati Deepak
Name  :  CHARAN GANTA
Father’s Name  : VENKATESWARA RAO GANTA
Date of Birth and Age  :  17.11.1995, Age 27 years
Full Address  :  11/C, Sri Ramakrishna Complex,
Vidyanagar Colony, Adilabad – 504001
+919848546666
//[email protected]//

Academic Qualifications

Name of the Course Name of the Institution Years of Study % of Marks
M.B.A Indian Business School, Hyderabad 2016 – 2018 78%
B.Com Government Degree College, Adilabad 2013 – 2016 80%
Intermediate M.EC Group Government Junior College, (Boys) Adilabad 2011 – 2013 91%
SSC ZPHS Thamsi 2011 92%

Experience
5 years as Co-ordinator, Sales and Marketing Dept., Solar Industries limited

Language known
English, Hindi, Urdu, Telugu and French

Place: Adilabad
Date : 14 May 2022

Signature

TS Inter 2nd Year English Grammar Curriculum Vitae

Question 3.
TS Inter 2nd Year English Grammar Curriculum Vitae 3
Answer:
A. BIO DATA of SRIMUKHI B

Name  :  SRI LAKSHMI BADETI
Father’s Name  :  KRISHNA RAO
Date of Birth and Age  :  26.11.1995
Full Address  : H.No. 3114/5/2-A CHRUCH ROAD
Near Post Office, Siddipet, Medak (Dist)
+91 9848486854
email id: [email protected]

Academic Qualifications

SI.

No.

Name of the Course Name of the Institution Years of Study % of Marks
1. M.A. (Psychology) O.U. Campus College 2016-2018 61%
2. B.Ed Govt. Edn. College Siddipet 2015-2016 74%
3. B.A Govt. Junior Degree College, Siddipet 2012 – 2015 64%
4. Intermediate(HEC) Govt. Junior College Siddipet 2010 – 2012 69%
5. SSC ZPHS for Girls, Siddipet 2009 – 2010 76%

Experience : Three years part-time – a private school.

Language known : Teiugu, English, Hindi

Place: Siddipet
Date : 14 May 2022

Signature

TS Inter 2nd Year English Grammar Curriculum Vitae

Question 4.
TS Inter 2nd Year English Grammar Curriculum Vitae 4
Answer:
For the post of Graphic Designer
ATMAKURI RADHAKRISHNA
F/o A. Srinivas
DOB : 16.08.1998
H.No.: 14-11-A-Z
Main Road
MAHABUBABAD – 506101
MOBILE : 91 – 8323435678
Mail ID : [email protected]

Objective
A POSITION that opens greener avenues for enchanting graphics for ad and entertainment industry

Experience
One year – Graphic Designer Creative Commercials

Education Qualifications

SI. No. Name of the Course Name of the Institution Years of Study % of Marks
1. Certificate Course in Graphic Designing NIIT Warangal 2019-2020 A+
2. B.Tech (CSE) Vignan Engineering College for Women Hanumakonda 2015-2019 72%
3. Intermediate(MPC) St. Anns Junior College for Girls, Mahabubabad 2013 – 2015 93%
4. SSC Savitri Memorial High School, Mahabubabad 2012 – 2013 86%

Technical Skills
C++, PYTHON, JAVA

Languages Known
Telugu, English, Hindi

Place : Mahabubabad
Date: 29-06-2021

Signature

TS Inter 2nd Year English Grammar Curriculum Vitae

Question 5.
TS Inter 2nd Year English Grammar Curriculum Vitae 5
Answer:
For the post of Radio Jockey in an eminent Entertainment Service Provider Firm
Resume of ALTAF MD

ALTAF MD
F/o. Md. Jani
DOB: 06.07.1998
H.No.: 13-14-27
Muzaphar Street
Tirumalagiri – 508202
Suryapet (Dt)

Objective
Aspiring to join a firm that enhances my confidence and skills to be able to sell icecream on Mount Everest and water heaters in That Desert.

Experience
Part time PRO of Corporate colleges 3 years with excellent record for my communication skills

Educational Qualifications :

SI. No. Name of the Course Name of the Institution Years of Study % of Marks
1. MBA M.K.M. College of Management Nalgonda 2018-2020 81%
2. B.Sc (MPC) Anwarloom Degree College for Women, Devarakonda 2015-2018 86%
3. Intermediate(MPC) Medha Junior College for Girls, Suryapet 2013 – 2015 92%
4. SSC ZPHS High School, for Girls, Tirumalagiri 2012 – 2013  78%

Technical Skills
Capable of creating educational games software, entertainment with musical voice

Languages Known
Urdu, Hindi, Telugu, English

Place: Tirumalagiri
Date: 24-04-2021

Signature

TS Inter 2nd Year English Grammar Curriculum Vitae

Question 6.
TS Inter 2nd Year English Grammar Curriculum Vitae 6
Answer:
Bio- data of M. Praveen

Name : M PRAVEEN
Father’s Name : VENKATA PRASAD
Date of Birth and Age : 13. 06.1998, Age 24 years
Full Address : 12-83, Kali Temple Road
Near Market Yard, Narayanpet
Mahabubnagar Dt.
7842614856
[email protected]

Academic Qualifications

SI. No. Name of the Course Name of the Institution Years of Study % of Marks
1. Diploma in Interiors Hafeez Contractor’s Architecture Academy 2020 – 2021 ‘A’ Grade
2. MBA Business Skills Institute of Management Mahabubnagar 2018 – 2020 74%
3. B.Com Govt. Degree College, Mahabubnagar 2015 – 2018 81%
4. Intermediate(CEC) Govt. Junior College Narayanapet 2013 – 2015 81%
5. SSC Arya Samaj High School-Narayanapet 2012 – 2013 90%

Experience
2 years Interior Designer Dhruva Architects Allied Book Services, Mahabubnagar

Language known
Telugu, English,Hindi Urdu, Kannada

Place: Narayanapet
Date: 13.06.2022

Signature

TS Inter 2nd Year English Grammar Curriculum Vitae

Question 7.
TS Inter 2nd Year English Grammar Curriculum Vitae 7
Answer:
CV of Jani Mohammad
Objective: A POSITION IN IT
DETAILS:

Name : JANI MOHAMMAD
Father’s Name : IBRAHIM MOHAMMAD
Date of Birth and Age : 22.11.1998,
Full Address : H.No. 22/14-2/A
Bakal wadi, Old Town,
NIZAMABAD ‘
Mobile: 9785631257
e-mail:[email protected]

Academic Qualifications

SI. No. Name of the Course Name of the Institution Years of Study % of Marks
1. M.Tech (IT) O.U. Campus Eng. College, Hyderabad 2019 – 2021 73%
2. B.Tech (IT) Paramitha College of Technology, Karimnagar 2015 – 2019 71%
3. Intermediate Brilliant Junior College Nizamabad 2013 – 2015 92%
4. SSC SJ Joseph’s Grammar School Nizamabad 2013 89%

Experience
Two years – IT Professional (wireless) Softech Solutions – Hyderabad

Language known
Telugu, English,Hindi

Place: Nizamabad
Date : 05.07.2022

Signature

TS Inter Second Year Maths 2B Differential Equations Important Questions Long Answer Type

Students must practice these Maths 2B Important Questions TS Inter Second Year Maths 2B Differential Equations Important Questions Long Answer Type to help strengthen their preparations for exams.

TS Inter Second Year Maths 2B Differential Equations Important Questions Long Answer Type

Model III – Problems on non-homogeneous D.E

Question 1.
Solve (2x + y + 1) dx + (4x + 2y – 1) dy = 0. [(TS) Mar. ’15]
Solution:
TS Inter Second Year Maths 2B Differential Equations Important Questions Long Answer Type L1 Q1
TS Inter Second Year Maths 2B Differential Equations Important Questions Long Answer Type L1 Q1.1

Question 2.
Solve the differential equation \(\frac{d y}{d x}=\frac{x+2 y+1}{2 x+4 y+3}\). [Mar. ’19 (TS)]
Solution:
Given differential equation is \(\frac{d y}{d x}=\frac{x+2 y+1}{2 x+4 y+3}\) ……(1)
TS Inter Second Year Maths 2B Differential Equations Important Questions Long Answer Type L1 Q2
4v + log (4v + 5) = 8x + 8c
4(x + 2y) – 8x + log [4(x + 2y) + 5] = c
4x + 8y – 8x + log(4x + 8y + 5) = c
8y – 4x + log (4x + 8y + 5) = c

TS Inter Second Year Maths 2B Differential Equations Important Questions Long Answer Type

Question 3.
Solve \(\frac{\mathrm{dy}}{\mathrm{dx}}=\frac{\mathrm{x}-\mathrm{y}+3}{2 \mathrm{x}-2 \mathrm{y}+5}\). [(AP) May ’15]
Solution:
TS Inter Second Year Maths 2B Differential Equations Important Questions Long Answer Type L1 Q3
TS Inter Second Year Maths 2B Differential Equations Important Questions Long Answer Type L1 Q3.1

Question 4.
Solve \(\frac{d y}{d x}=\frac{4 x+6 y+5}{3 y+2 x+4}\). [(TS) May ’19]
Solution:
TS Inter Second Year Maths 2B Differential Equations Important Questions Long Answer Type L1 Q4
TS Inter Second Year Maths 2B Differential Equations Important Questions Long Answer Type L1 Q4.1
TS Inter Second Year Maths 2B Differential Equations Important Questions Long Answer Type L1 Q4.2
8z + 9 log|8z + 23| = 64x + c
8(2x + 3y) + 9 log|8(2x + 3y) + 23| = 64x + c
24y + 9 log|16x + 24y + 23| = 48x + c
Which is the required solution.

Question 5.
Solve \(\frac{d y}{d x}=\frac{3 y-7 x+7}{3 x-7 y-3}\)
Solution:
TS Inter Second Year Maths 2B Differential Equations Important Questions Long Answer Type L1 Q5
TS Inter Second Year Maths 2B Differential Equations Important Questions Long Answer Type L1 Q5.1
TS Inter Second Year Maths 2B Differential Equations Important Questions Long Answer Type L1 Q5.2
TS Inter Second Year Maths 2B Differential Equations Important Questions Long Answer Type L1 Q5.3

TS Inter Second Year Maths 2B Differential Equations Important Questions Long Answer Type

Question 6.
Solve \(\frac{d y}{d x}=\frac{x+2 y+3}{2 x+3 y+4}\)
Solution:
TS Inter Second Year Maths 2B Differential Equations Important Questions Long Answer Type L1 Q6
TS Inter Second Year Maths 2B Differential Equations Important Questions Long Answer Type L1 Q6.1
TS Inter Second Year Maths 2B Differential Equations Important Questions Long Answer Type L1 Q6.2
TS Inter Second Year Maths 2B Differential Equations Important Questions Long Answer Type L1 Q6.3

Question 7.
Solve the differential equation (x – y) dy = (x + y + 1) dx. [Mar. ’17 (TS)]
Solution:
TS Inter Second Year Maths 2B Differential Equations Important Questions Long Answer Type L1 Q7
TS Inter Second Year Maths 2B Differential Equations Important Questions Long Answer Type L1 Q7.1
TS Inter Second Year Maths 2B Differential Equations Important Questions Long Answer Type L1 Q7.2

Question 8.
Solve (2x + y + 3) dx = (2y + x + 1) dy
Solution:
TS Inter Second Year Maths 2B Differential Equations Important Questions Long Answer Type L2 Q1
TS Inter Second Year Maths 2B Differential Equations Important Questions Long Answer Type L2 Q1.1
TS Inter Second Year Maths 2B Differential Equations Important Questions Long Answer Type L2 Q1.2

TS Inter Second Year Maths 2B Differential Equations Important Questions Long Answer Type

Question 9.
Solve \(\frac{d y}{d x}=\frac{6 x+5 y-7}{2 x+18 y-14}\)
Solution:
TS Inter Second Year Maths 2B Differential Equations Important Questions Long Answer Type L2 Q2
TS Inter Second Year Maths 2B Differential Equations Important Questions Long Answer Type L2 Q2.1
TS Inter Second Year Maths 2B Differential Equations Important Questions Long Answer Type L2 Q2.2
TS Inter Second Year Maths 2B Differential Equations Important Questions Long Answer Type L2 Q2.3

Question 10.
Find the solution of the equation x(x – 2) \(\frac{\mathrm{dy}}{\mathrm{dx}}\) = 2(x – 1)y = x3(x – 2), which satisfies the condition that y = 9, when x = 3. [(TS) May ’17]
Solution:
TS Inter Second Year Maths 2B Differential Equations Important Questions Long Answer Type L2 Q3
TS Inter Second Year Maths 2B Differential Equations Important Questions Long Answer Type L2 Q3.1
TS Inter Second Year Maths 2B Differential Equations Important Questions Long Answer Type L2 Q3.2

Question 11.
Form the differential equation corresponding to the family of circles of radius r given by (x – a)2 + (y – b)2 = r2, where ‘a’ and ‘b’ are parameters.
Solution:
Given equation is (x – a)2 + (y – b)2 = r2 ………(1)
a, b are parameters.
differentiating (1) w.r.t. ‘x’ on both sides we get
2(x – a)(1 – 0) + 2(y – b)(\(\frac{\mathrm{dy}}{\mathrm{dx}}\) – 0) = 0
(x – a) + (y – b)(\(\frac{\mathrm{dy}}{\mathrm{dx}}\)) = 0 ……..(2)
Again differentiating (2) w.r.t ‘x’ on both sides, we get
TS Inter Second Year Maths 2B Differential Equations Important Questions Long Answer Type L3 Q1
TS Inter Second Year Maths 2B Differential Equations Important Questions Long Answer Type L3 Q1.1
TS Inter Second Year Maths 2B Differential Equations Important Questions Long Answer Type L3 Q1.2
Which is the required differential equation.

TS Inter Second Year Maths 2B Differential Equations Important Questions Long Answer Type

Question 12.
Form the differential equation from y = c(x – c)2, where ‘c’ is an arbitrary constant. [(TS) Mar. ’16]
Solution:
Given y = c(x – c)2 ………(1)
(where ‘c’ is an arbitrary constant)
Diff. with respect to x on both sides
TS Inter Second Year Maths 2B Differential Equations Important Questions Long Answer Type L3 Q2

TS Inter 2nd Year English Grammar Filling in Forms

Telangana TSBIE TS Inter 2nd Year English Study Material Grammar Filling in Forms Exercise Questions and Answers.

TS Inter 2nd Year English Grammar Filling in Forms

Q.No. 14 (8 × 1/2 = 4 Marks)

In our day to day life, we need to fill in various kinds of forms. Before filling in a particular form, one must go through the relevant instructions carefully. Forms should be filled in very carefully in legible hand writing. To fill in forms correctly, one must first know what information is required to be filled in a given blank. To understand this one must carefully read what is given before a blank, and sometimes, what is given after a blank too. In the Public Examination question paper, the blanks in the given form are numbered. The student can write the relevant information against those numbers. It is not necessary to copy down the entire form

Now study the following examples carefully

I. Depositing Money in a Bank:

When we deposit money in the Savings Bank Account, we fill in the Savings Bank Account Pay-in-SUp and enter the details. The slip has two parts. The longer one is retained with the bank while the smaller one, called counter foil, is returned to us after the required particulars are entered. First observe how the form was filled in and then attempt the exercise that follows.
TS Inter 2nd Year English Grammar Filling in Forms 1

Exercise

Question 1.
Mr. L. Srinivas wants to deposit an amount of Rs. 9600/- on 22.05.2022 in his Savings Account with the SBI, Asifabad branch. His account number is 63217569982. He carries the amount in the denomination of Rs. 500 notes 18 and the remaining are Rs. 200 notes. His mobile number is 9848123456. Fill the details in the following voucher to deposit the amount.
TS Inter 2nd Year English Grammar Filling in Forms 2
Answer:
1) Asifabad
2) 22.05.2022
3) 63217569982
4) L. Srinivas
5) 9848123456
6) 9600/-
7) Nine thousand and six hundred
8) 500 × 8 18 ; 200 × 3
9) 9600
10) L. Srinivas

TS Inter 2nd Year English Grammar Filling in Forms

Question 2.
You are M. Venkateswarlu Your Savings Bank Account number is 12545635489 in the SBi Branch of Shamsnabad, Your mobile number is 7502012543. Deposit an amount of Rs. 8000/- into your account today. And the donornlnation is 3 notes of Rs. 2000 and the remaining are Rs. 500 notes.
TS Inter 2nd Year English Grammar Filling in Forms 3
Answer:
1) Shamshabad
2) 20.04.2022
3) 12545635489
4) M. Venkateswrarlu
5) 7502012543
6) 8000/-
7) Eight thousand only
8) 2000 × 3; 500 × 4
9) 8000
10) M. Venkateswarlu

Question 3.
You are Ch. Krishna. Your Account Number is 56218561932. Deposit an amount of Rs. 9,300/- into your Savings Bank Account with the SBI, Punjagutta Branch. Your mobile number is 8374373612. The amount is the denomination of Rs. 500 notes 18 and the remaining are Rs. 100 notes.
TS Inter 2nd Year English Grammar Filling in Forms 4
Answers:
1) Panjagutta
2) 14.06.2022
3) 56218561932
4) Ch. Krishna
5) 8374373612
6) 9300/-
7) Nine thousand and three hundred only
8) 500 × 18 ; 100 × 3
9) 9300
10) Ch. Krishna

TS Inter 2nd Year English Grammar Filling in Forms

II. Depositing Money in a Bank:

Observe how the Withdrawal form was filled before you attempt the exercise.
TS Inter 2nd Year English Grammar Filling in Forms 5

Exercise

Question 1.
You are Laxmi. You want to withdraw an amount of Rs. 14500/- from your account in the SBI, Mancherial Branch on 02.06.2022. Your account number is 52178999999 and PAN is CNPCKI234N. Fill the following withdrawal form.
TS Inter 2nd Year English Grammar Filling in Forms 6
Answer:
1) Macherial
2) 02.06.2022
3) Laksmi
4) 52178999999
5) fourteen thousand and five hundred only
6) 14500/-
7) CNPCK1234N
8) 6384725109
9) Mancherial
10) Lakshmi

TS Inter 2nd Year English Grammar Filling in Forms

Question 2.
You are Ch. Gopi Krishna. You have a Savings Bank Account in the SBI Hanumakonda Main Branch, your account number is 52738963762 and PAN is BCKPC2356P. Withdraw an amount of Rs. 25000 – today by filling the Savings Bank Withdrawal Form .
TS Inter 2nd Year English Grammar Filling in Forms 7
Answer:
1) Hanumakonda Main
2) 06.05.2022
3) Ch. Gopi Krishna
4) 52738963762
5) Twenty five thousand only
6) 25000/-
7) BCKPC2356P
8) 8436271590
9) Hanumakonda Main
10) Ch. Gopi Krishna (Ch. Gopi Krishna)

III. Application for a Demand Draft / Banker’s Cheque

Demand draft is drawn in favour of a person or a firm. The particulars are to be filled in with utmost care. We should also mention in which branch the DD is to be realized. The commission charged by the bank for ‘th,e service is called exchange.

Now carefully go through the sample DD form and do the exercise which follows.
TS Inter 2nd Year English Grammar Filling in Forms 8

Exercise

Question 1.
You are K. Gangadhar residing at Warangal. You want to apply for EAMCET – 2O2. Apply for a DD’for Rs. 800/- in favour of The Convener, TS EAMCET-2022, JNTU, Hyderabad, in SB!, War an gal Main Branch. It should be payable on SBI, JNTU Branch, Hyderabad. The exchange to be paid is Rs. 35/-.
TS Inter 2nd Year English Grammar Filling in Forms 9
Answer:
1) Warangal Main
2) 05.06.2022
3) K. Gangadhar
4) The Convener, TS EAMCET-2022
5) Rs 800/-
6) Rs 35/-
7) Eight hundred and thirty five only
8) Not applicable
9) SBI JNTU Branch Hyderabad
10) 8642103579
11) K. Gangadhar

TS Inter 2nd Year English Grammar Filling in Forms

Question 2.
You are S, Srinivas, staying at Vidyanagar, Adilabad. You want to purchase some books from ‘Assorted Book Store’, Hanumakonda. Apply for a Demand Draft of Rs. 3,600/ today in favour of the book store payable at the SBI, Hanumakonda Main Branch. The exchange to be paid is Rs. 40/-
TS Inter 2nd Year English Grammar Filling in Forms 10
Answer:
1) Vidyanagar
2) 04.05.2022
3) S. Srinivas
4) Assorted Bookstore Hanumakonda
5) Rs 3600/-
6) Rs 40/-
7) Three thousand six hundred and forty only
8) Not applicable
9) Hanumakonda Main Branch
10) 9361485710
11) S. Srinivas

Question 3.
You are Murali Mohan. You want to get a Bankers Cheque for Rs.6500/- on Hanumakonda Main Branch of the State Bank of India in favour of ‘Nava Telangana Publishing House’. The exchangeis Rs. 45/-. Fill in the form given below. You are taking the Banker’s cheque at Jankapur Branch, Asifabad.
TS Inter 2nd Year English Grammar Filling in Forms 11
Answer:
1) Jankapur
2) 03.05.2022
3) Murali Mohan
4) Nava Telangana Publishing House
5) Rs 6500/-
6) Rs 45/-
7) Six thousand five hundred and forty five only
8) Not applicable
9) Hanumakonda Main Branch
10) 9210364587
11) Murali Mohan

TS Inter 2nd Year English Grammar Filling in Forms

IV. Depositing Cash in a Post Office Account

We can also avail ourselves of the banking services at various branches of Post offices. We can save our money at any branch of a post office. Given below is the Post Office Savings Bank form.

Study the form carefully and attempt the exercise that follows.
TS Inter 2nd Year English Grammar Filling in Forms 12

Exercise

Question 1.
You are K. Madhubala. Your account number Is 18975 in Bellampally Post office, Mancherial district. Deposit an amount of Rs. 25000/- into your account by filling in the Post Office Savings Account form.
TS Inter 2nd Year English Grammar Filling in Forms 13
Answer:
1) Bellampalli
2) 18975
3) 06.04.2022
4) K. Madhubala
5) Twenty five thousand
6) Rs 25000/-
7) Not applicable
8) K. Gangadhar

TS Inter 2nd Year English Grammar Filling in Forms

Question 2.
You are P. Neelaveni. Your Account Number is 1981 in Mahboobnagar Post Office. Deposit an amount of Rs. 6000/- into your account by filling in the Post Office Savings Bank form.
TS Inter 2nd Year English Grammar Filling in Forms 14
Answer:
1) Mahaboobnagar
2) 1981
3) 08.05.2022
4) P. Neelaveni
5) Six thousand
6) Rs 6000/-
7) Not applicable
8) P.Neealaveni

V. Withdrawing Cash from a Post Office Account

Withdrawing money from a Post Office is a simple transaction. Just fill in the Post Office Savings Bank Withdrawal form and submit it to the official concerned. The passbook must accompany the form. Now look at the Withdrawal form and do the exercise that follows.
TS Inter 2nd Year English Grammar Filling in Forms 15

Exercise

Question 1.
You are M. Dinakar having a savings account in the post office Narsampet, Warangal district. Withdraw an amount of Rs. 12000/- today by filling in the withdraw! form.
TS Inter 2nd Year English Grammar Filling in Forms 16
Answer:
1) Narsampet
2) 03.06.2022
3) Savings (SB)
4) 9816
5) 12000/-
6) Twelve thousand only
7) Not applicable
8) Dinakar.M

TS Inter 2nd Year English Grammar Filling in Forms

Question 2.
You are S. Swetha, Your Post Office Savings Bank Account Number is 56847 at Post Office of Godavarikhani, Peddapalli district. Withdraw an amount of Rs. 1200/- today by filling in the withdrawal form.
TS Inter 2nd Year English Grammar Filling in Forms 17
Answer:
1) Godavarikhani
2) 13.07.2022
3) Savings (SB)
4) 56847
5) 1200/-
6) Twelve hundred only
7) Not applicable
8) S. Suuetha

VI. Withdrawing Cash from a Post Office Account

If we plan to undertake a long railway journey it is advisable to reserve a berth in advance in a particular train and class so that we can travel comfortably. Look at the filled-in- form below and then fill in the blank form given after.
TS Inter 2nd Year English Grammar Filling in Forms 18

Exercise

Question 1.
You are Mr. D. Venkateswarlu, You want to go to Sirpur Kaghaznagar on 24.05.2022 from Warangal along with your father, Rama Rao, aged 55 and your mother, Janaki, aged 50 by the train number 12656, Navajeevan Express. Reserve three seats in advance for 2nd seating (2S) class by filling in the form given below
TS Inter 2nd Year English Grammar Filling in Forms 19
Answer:
1) 12656
2) Navjeevan Express
3) 24.5.2022
4) 2nd Seating (2S)
5) three (3)
6) Warangal
7) Sirpur Kaghaznagar
8) Warangal
9) Sirpur Kaghaznagar
10) 9848943545
11) D. Venkateswarlu : Ramarao Janaki
12) D. Venkateswarlu
13) 8-13, Gandhi Nagar, Warangal
14) D. Venkateswarlu
15) 9848943545
16) 15.04.2022
17) 4.15 PM

TS Inter 2nd Year English Grammar Filling in Forms

TS Inter 2nd Year English Grammar Idioms and Phrases

Telangana TSBIE TS Inter 2nd Year English Study Material Grammar Idioms and Phrases Exercise Questions and Answers.

TS Inter 2nd Year English Grammar Idioms and Phrases

Q.No. 12 (4 Marks)

Do you have any idea of what an idiom is?
Let us read this conversation.

Anitha  :  Hi, Akhila… seem to be over the moon!
Akhila  :  Yeah…Don’t you know? The Inter results are music to my ears. What about you?
Anitha  :  Ah! I had to eat humble pie.
Akhila  :  Why… ? You burnt the midnight oil… I think.
Anitha  :  Nevertheless, I failed in one subject.
Akhila  :  Don’t cry your eyes out. Pull up your socks. Prepare we for the next exam.
Anitha  :  It’s OK. But my father doesn’t have belief in my ability, often says, “Don’t tell me cock and bull stories”.
Akhila  :  Come on Anitha. Don’t cry over spilt milk. Keep bad company at bay. You will succeed. Cheer up…
Anitha  :  Thank you Akhila. You have been a pillar of support.
Akhila  :  It’s alright. See you

TS Inter 2nd Year English Grammar Idioms and Phrases

Have you gone through the groups of words in italics ? What do they mean? What can you get from the words in isolation? Don’t they sound strang Yes, they are called idioms.

What is an idiom ?
An idiom is an artistic expression whose meaning is unpredictable from the usual meaning of its component words. Use of idioms adds glamour to the language, and finds a place in everyday use of language as well.

Now, let’s look at some idiomatic expressions and their usage.

1. once in a blue moon: happen very rarely
He attends classes once in a blue moon.

2. an arm and a leg: very expensive
It cost me an arm and a leg to study in the USA.

3. a piece of the cake: very easy
Batting is a piece of cake for Virat these days.

4. a drop in the ocean: a tiny part of something much bigger
The small donation was just a drop in the ocean.

5. bite one’s tongue: want to say something but stop oneself
Sitara wanted to speak out about the unfair decision. But she bit her tongue.

TS Inter 2nd Year English Grammar Idioms and Phrases

6. go the extra mile: doing much more than required
My father always goes the extra mile to help the needy.

7. get ducks in a row: to get one’s affairs in order or organized
I can’t hope to do well at my job until I get my ducks in a row.

8. let the cat out of the bag: reveal a secret accidentally
Joel let the cat out of the bag about my surprise birthday party.

9. working against the clock: not having enough time to do something
I am really working against the clock now. I must hurry.

10. flogging a dead horse: attempting to continue with something that is over We are flogging a dead horse. Our present business is making no money.
So, let’s do something else.

11. on cloud nine: very happy
Rahul is on cloud nine since he got a good job.

12. bolt from the blue: something happened unexpectedly
The results of the recent polls were a bolt from the blue to many parties.

13. storm in a tea cup: making unnecessary fuss/ getting excited about something unimportant
There was a storm in a tea cup over who should be the Chief Guest on Hostel Day.

TS Inter 2nd Year English Grammar Idioms and Phrases

14. make hay while the sun shines : to take advantage of a good situation that may not last long
Our boss is on vacation. Let’s make hay while the sun shines and relax.

15. beat black and blue: covered with bruise marks caused by being hit
Kiran was beaten black and blue by the violent crowd.

16. fight an uphill battle: struggle against very unfavourable circumstances
The Kings XI Punjab must fight an uphill battle to win the IPL title.

17. donkey’s years: a long time .
I have been teaching grammar for donkey’s years.

18. at the eleventh hour: at the last possible moment
If you want to do your best, don’t do things at the eleventh hour.

19. bee in one’s bonnet: an idea that constantly occupies one’s thoughts
Our English teacher has a bee in her bonnet about correct pronunciation.

20. cook someone’s goose: spoil someone’s plans or chances of success
This year’s severe drought cooked Ramaiah’s goose.

21. feather in one’s cap: the achievement of which one can be proud of
Bahubali’s success is a feather in Rajamouli’s cap.

22. rags to riches: start offbeing very poor and become very rich and successful
Dhirubhai Ambani’s life is a story of rags to riches.

TS Inter 2nd Year English Grammar Idioms and Phrases

23. in the blink of an eye: happen fast and instantaneously
The announcement of intermediate results reached every come” in the blink of an eye.

24. in/by leaps and bounds: make rapid or spectacular progress
Our business flourished in leaps and bounds.

25. risk life and limb: in danger of death or severe injury
Don’t risk your life and limb by participating in reality shows.

26. save one’s neck/skin: escape from death, punishment, etc. especially by leaving others in an extremely difficult situation
Satish got his friends into trouble to save his skin.

27. birds of a feather flock together: similar in many ways, so spend time together
Arun and Varan are sports enthusiasts and are often found together. So, our friends usually speak of them as birds of a feather (flock together).

29. bite off more than you can chew: try to manage something too difficult
Actor Shireesh bit off more than he could chew in his debut movie.

30. take the bull by the horns: act decisively to deal with a complex problem
I want to take the bull by the horns by deciding to swim across the fiver.

31. leave no stone unturned: try everything possible to achieve something
President Kalam left no stone unturned to motivate the youth.

TS Inter 2nd Year English Grammar Idioms and Phrases

32. no spring chicken: one is quite old or well past one’s youth
I am no spring chicken, you know. How can I dance?

33. beyond wildest dreams: better than you imagined for
Last year’s rainfall was beyond our wildest dreams.

34. keep your nose to the grindstone: concentrate on working or studying hard (informal)
In the Intermediate class, my daughter has to keep her nose to the grindstone. No time for games or music.

35. paddle your own canoe: do something without the help of others
Sonu refused all help as he believed in paddling his owm canoe.

36. have a bone to pick: annoyed with somebody and talk to them about it
Lakshmi has a bone to pick with Revati as she was not invited to the marriage.

37. give a tongue-lashing: scold someone severely
The teacher gave the lazy boy a tongue-lashing when he called Rani a lazy girl.

38. dressed up to the nines: wearing bright or glamorous clothes
Actors often dress up to the nines for public functions.

39. make one’s ears burn: embarrassed by hearing something being said about you
The discussion about my childhood pranks made my ears burn.

TS Inter 2nd Year English Grammar Idioms and Phrases

40. turn a deaf ear: refuse to listen to somebody
Our boss turned a deaf ear to our request to change the meeting venue.

41. back to the salt mines: returning to work with some reluctance
After the vacation, the students had to go back to the salt mines.

42. nuts and bolts: detailed facts and the practical aspects (informal)
Unless I get to know the nuts and bolts of the business, I can’t venture into it.

43. step into someone’s shoes: take over a job / a position held by someone before you
When the manager retires, I’ll step into his shoes.

44. catch-22: a frustrating situation that will lead to further frustration
In big cities, if you don’t have a place to live in, you can’t get a job, and with no job, you can’t get a place to live in! Thus, it’s a catch-22 situation.

45. at the drop of a hat: do it immediately without hesitation
The wealthy socialite throws parties at the drop of a hat.

46. wild goose chase: a search for something that is impossible for you to find or that does not exist, that makes you waste a lot of time
Without a proper address or phone number, it would be a wild goose chase to locate someone in Hyderabad.

47. taste your own medicine: have the same bad treatment that you have given to others
The evil-minded will taste their own medicine sooner or later.

48. blow one’s horn: to praise oneself; to boast
People avoid her as she constantly blows her horn.

49. burn the midnight oil: to work very late into the night
I have to present this report by tomorrow. So, I must bum the midnight oil tonight.

TS Inter 2nd Year English Grammar Idioms and Phrases

50. thrilled to bits: extremely pleased about something
I was thrilled to bits when I received a fancy gift.

51. a bed of roses: something which is easy
Life is not always a bed of roses.

52. a white elephant: expensive but not that useful
His new car has become a white elephant.

53. hit the nail on the head: say something correctly
She hit the nail on the head with her response.

54. spill the beans: to reveal a secret
They were afraid he would spill the beans.

55. hot cakes: fastselling
The new model cars are selling like hot cakes.

56. face the music: accept unpleasant consequences
Having lost his character, he has to face the music.

57. judge a book by its cover: judge something primarily on appearance
You can’t judge a book by its cover. Just because he looks strange, that doesn’t mean . he is not a nice person.

58. Achilles heel: a weak (vulnerable) spot
Maths has always been my Achilles heel.

TS Inter 2nd Year English Grammar Idioms and Phrases

59. by a whisker: by a very small amount/margin
Finally, our team lost by a whisker and I was disappointed.

60. every cloud has a silver lining: every misfortune has some positive aspect
If we hadn’t missed the plane, we wouldn’t have met you. It is rightly said every cloud has a silver lining.

61. part and parcel: an essential or fundamental element
Don’t get disheartened at losing your form. It’s part and parcel of being a professional.

62. a thick skin: an ability to not be upset by criticism
A politician needs a thick skin.

63. a sea change: a complete change in someone’s attitude or behavior
There is a sea change in the behavior of the culprit after his release from the prison.

64. in a nutshell: briefly; in essence
Let me explain the proceedings in a nutshell.

65. get the nod: to receive permission from someone to start something
Rahul got the nod after a lengthy discussion among the members.

66. take the rap: to be blamed or punished, especially for something you have not done
She was prepared to take the rap for the shoplifting, though it had been her sister’s idea.

67. dark horse: one who is previously unknown and is now prominent
The Gujarat Titans has proved to be a dark horse in the recent IPL.

TS Inter 2nd Year English Grammar Idioms and Phrases

68. a hot potato: controversial and sensitive issue
Racism is currently a hot potato in the international cricket.

69. a square meal: a large, filling, nutritious meal
The soldiers are very tired. They haven’t had a square eat for four days.

70. by fair means or foul: by any possible method
They never gave up trying to recover their property by fair means or foul.

71. a labour of love: a task that you do for pleasure without expecting payment
Preparing this book is clearly a labour of love.

72. keep the pot boiling: keep going on actively
I threw in a question just to keep the pot boiling while my brain caught up.

73. tie the knot: to get married
The couple tied the knot last year.

74. from top to bottom: very thoroughly
I would clean my room from top to bottom every Sunday.

Exercises

I. Fill in the blanks ITI the following sentences with suitable idiomatic expressions given below. Make necessary changes in the idioms if needed.

take the rap
in a nut shell
a sea change
by a whisker
get the nod
a thick skin

1. Finally, our team lost _____________ and I was disappointed.
2. A politician needs _____________
3. There is _____________ in the behavior of the culprit after his release from the prison.
4. Let me explain the proceedings _____________
5. Rahul _____________ after a lengthy discussion among the members.
6. She was prepared to _____________ for the shoplifting, though it had been her sister’s idea.
Answers:
1. by a whisker
2. a thick skin
3. a sea change
4. in a nutshell
5. go the nod
6. take the rap

TS Inter 2nd Year English Grammar Idioms and Phrases

II. Fill in the blanks in the following sentences with suitable idiomatic expressions given below. Make necessary changes in the idioms if needed.

on cloud nine
tie the knot
go the extra mile
apiece of cake
turn a deaf ear
hot cakes

1. The new model cars are selling like _____________
2. My father always _____________ since he got a good job.
3. Rahul is _____________ for Virat these days.
4. The couple _____________ last year.
5. Our boss _____________ to our request to change the meeting venue.
Answers:
1. hot cakes
2. goes the extra mile
3. on cloud nine
4. a piece of cake
5. tied the knot
6. turned a deaf ear