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

51) The A.M. of 30 students is 42. Among them, two students got zero marks. Then A.M. of the remaining students is

A) 40

B) 45

C) 50

D) 55

View Answer

B) 45
Explanation:A.M. of 30 students is 42
⇒ Total marks = 30 × 42 = 1260
2 students got zero ⇒ remaining 28 students got 1260 – 0 – 0 = 1260
New A.M. = 1260 / 28 = 45Answer: B. 45

52) The median of 17, 31, 12, 27, 15, 19, 23 is

A) 19

B) 20

C) 21

D) 22

View Answer

A) 19
Explanation:Data: 17, 31, 12, 27, 15, 19, 23
Sorted: 12, 15, 17, 19, 23, 27, 31 → Median is the middle = 19

53) Mode of A, B, C, D ….. Z is

A) 20

B) 21

C) 22

D) No mode

View Answer

D) No mode
Explanation:Mode = Most frequent value
A to Z are all distinct letters
⇒ No repetition
⇒ No mode
Answer: No mode

54) The value of sinθ or cosθ never exceeds

A) -1

B) 1

C) 0

D) None of these

View Answer

B) 1
Explanation:Maximum value of sinθ or cosθ is 1

55) In the figure, the value of cosec A is

A) 12/13

B) 13/5

C) 13/12

D) 5/13

View Answer

C) 13/12
Explanation:From the figure: triangle with sides 5, 12, 13 → right-angled at B
cosec A = hypotenuse / opposite = 13 / 12
Answer: $\frac{13}{12}$

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

A) 1/2

B) 1/3

C) 1/4

D) 1/5

View Answer

B) 1/3
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: $\frac{1}{3}\$

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

A) A

B) B

C) C

D) D

View Answer

B) B
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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