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TS Polycet (Polytechnic) 2022 Previous Question Paper with Answers And Model Papers With Complete Analysis

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51)In the right angle △ABC, ∠B=90°, tanc= $\frac5{12}$ then the length of hypotenuse is

A) 16

B) 13

C) 21

D) 17

View Answer

B) 13
Explanation:tanC = 5/12 ⇒ opposite = 5, adjacent = 12 ⇒ hypotenuse = √(5² + 12²) = √169 = 13

52)If tan(A-B)= $\frac1{\sqrt3}$ , COS A= $\frac12$ then ∠B=

A) $\frac{2\mathrm\pi}3$

B) $\frac{\mathrm\pi}4$

C) $\frac{\mathrm\pi}6$

D) $\frac{\mathrm\pi}3$

View Answer

D) $\frac{\mathrm\pi}3$

Explanation:tan(A-B) = 1/√3 ⇒ A-B = 30°, also cosA = 1/2 ⇒ A = 60° ⇒ B = 30°

53)If A=45°, B=60°, then sinA + cosB

A) $\frac{2-\sqrt2}{2\sqrt2}$

B) $\frac{2+\sqrt2}2$

C) $\frac{2+\sqrt2}{\sqrt2}$

D) $\frac{2+\sqrt2}{2\sqrt2}$

View Answer

D) $\frac{2+\sqrt2}{2\sqrt2}$

Explanation:sin45° = 1/√2, cos60° = 1/2 ⇒ sinA + cosB = 1/√2 + 1/2 = (2 + √2)/2√2

54)The length of the shadow of a vertical pole is √3 times its original length. The angle of elevation to the sun is

A) 30°

B) 45°

C) 60°

D) 90°

View Answer

A) 30°
Explanation:tanθ = h/base = 1/√3 ⇒ angle = 30°

55)Find length of a kite string flying at 100m above the ground with the elevation 60°

A) $\frac{100}{\sqrt3}$

B) $\frac{50}{\sqrt3}$

C) $\frac{200}{\sqrt3}$

D) $\frac{25}{\sqrt3}$

View Answer

C) $\frac{200}{\sqrt3}$

Explanation:Height = 100 m, angle = 60° ⇒ sin60° = 100 / hypotenuse ⇒ hypotenuse = 100 / (√3/2) = 200/√3

56)If sinθ = cos(0∠θ∠90°) then tanθ

A) -1

B) 4

C) 2

D) 1

View Answer

D) 1
Explanation:If sinθ = cosθ ⇒ θ = 45° ⇒ tanθ = 1

57)The value of $\frac{\tan\left(\alpha\right)}{\sqrt{1+\tan^2\left(\alpha\right)}}$ is

A) cos α

B) sin α

C) cosec α

D) sec α

View Answer

B) sin α
Explanation: $\frac{\tan α}{\sqrt{1 + \tan^2 α}} = \sin α$

\[By identity]

58)The tops of the two poles are of height 20m and 14m are connected by a wire, if wire makes an angle 30° with the horizontal, then the length of the wire is

A) 11m

B) 12m

C) 13m

D) 10m

View Answer

B) 12m
Explanation:Height difference = 6 m, angle = 30° ⇒ sin30° = 6 / wire ⇒ wire = 6 / 0.5 = 12 m

59)Identify the correct statement

A) P(E)=-1

B) P(E)≥1

C) 0≤P(E)≤1

D) None

View Answer

C) 0≤P(E)≤1
Explanation:Probability of any event is always between 0 and 1

60)If sin (A-B)= $\frac12$ and cos(A+B)= $\frac12$ then ∠A, ∠B=?

A) 45°, 15°

B) 15°, 45°

C) 45°, 30°

D) 30°, 15°

View Answer

A) 45°, 15°
Explanation:sin(A-B) = 1/2 ⇒ A-B = 30°, cos(A+B) = 1/2 ⇒ A+B = 60°
Solving:
A – B = 30
A + B = 60 ⇒ Add: 2A = 90 ⇒ A = 45°, B = 15°

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