SOLVED PAPER 2022 (CDS) (II) (Elementary Mathematics)

Total Questions: 100

51. (Questions 51 and 52) Consider the following for the next two questions that follow. Consider the equation

Correct Answer: (b)
Solution:

52. Consider the equation

Correct Answer: (d)
Solution:

53. (Questions 53-55) Consider the following information for the next three questions that follow.

A triangle ABC with sides AB = 15 cm, BC = 9 cm, CA = 12cm is inscribed in a circle.

What is cos²A + cos²B + cos²C equal to?

Correct Answer: (b) 1
Solution:

54. What is sin² A + sin² B + sin² C equal to?

Correct Answer: (a) 2
Solution:

55. What is the radius of the circle?

Correct Answer: (a) 4.5 cm
Solution:

So, radius of the circle OC is less than 5. According to option (a), 4.5 cm is radius circle.

56. (Questions 56 and 57) Consider the following for the next two questions that follow.

The angle of elevation of a cloud at C from a point (P), H m above the surface of a lake is 30°. The height of the cloud from the surface of the lake is 2H m. Let 0 be the angle of depression of the reflection of the cloud in the lake from the point P.

What is the value of θ ?

Correct Answer: (c) 60°
Solution:

57. What is PC equal to ?

Correct Answer: (d) 2 Hm
Solution:

58. (Questions 58-60) Consider the following data for the next three questions that follow.

A frequency distribution table is given below.

x012345
f46pq25105

Total frequency is 200 and mean of the distribution is 1.46.

What is the value of p?

Correct Answer: (c) 76
Solution:Table for given data,
xfᵢfᵢxᵢ
0460
1pp
2q2q
22575
41040
5525

59. What is the value of q?

Correct Answer: (d) 38
Solution:From Question 58, valid q = 38

60. What is the median of the distribution?

Correct Answer: (a) 1
Solution:Now table for given data,
xfᵢfᵢxᵢ
04646
176122
238160
225185
410195
55200