TS Polycet (Polytechnic) 2021 Previous Question Paper with Answers And Model Papers With Complete Analysis

56) If a two digit number is choosen at random then the probability that number choosen is a multiple of 3

A) $\frac12$
B) $\frac13$
C) $\frac14$
D) $\frac15$

View Answer

B) $\frac13$

Explanation:Two-digit numbers: 10 to 99 → Total = 90
Multiples of 3 in this range = from 12 to 99 = 12, 15, …, 99
This is an AP with a = 12, d = 3
Use formula: nth term = a + (n-1)d
99 = 12 + (n-1)×3 ⇒ n = 30
Probability = 30 / 90 = 1/3
Answer: $\frac13$

57) p(x)+P(“not x”)=

A) -1
B) -2
C) 1
D) 2

View Answer

C) 1

Explanation:P(x) + P(not x) = 1 (law of total probability)

58) If cotθ= $\frac ba$ then $\frac{\cos\theta+\sin\theta}{\cos\theta-\sin\theta}$ =

A) $\frac{b-a}{b+a}$
B) $\frac{b+a}{b-a}$
C) $\frac{a-b}{a+b}$
D) $\frac{a+b}{a-b}$

View Answer

B) $\frac{b+a}{b-a}$

Explanation:Given cotθ = b/a ⇒ cosθ = a/√(a² + b²), sinθ = b/√(a² + b²)
Then, $\frac{\cosθ + \sinθ}{\cosθ - \sinθ} = \frac{a + b}{a - b}$
Answer: $\frac{a + b}{a - b}$

59) The angle of elevation of the top of a tower, whose height is 100 m, at a pint whose distance from the base of the tower is 100 m is

A) 30°
B) 60°
C) 90°
D) 45°

View Answer

D) 45°

Explanation:Height = 100 m, Distance = 100 m
Right triangle ⇒ tan θ = 100/100 = 1 ⇒ θ = 45°

60) The value of $\frac{1-\tan^245^\circ}{1+\tan^245^\circ}$ = …….

A) 0
B) -1
C) 1
D) 2

View Answer

A) 0

Explanation: $\frac{1 - \tan^2 45°}{1 + \tan^2 45°} = \frac{1 - 1}{1 + 1} = \frac{0}{2} = 0$

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