SOLVED PAPER 2020 (CDS) (II) (Elementary Mathematics)

Total Questions: 100

51. The difference between two angles is 15° and the sum of the angles in radian is 5π/12. The bigger angle is k times the smaller angle. What is k equal to?

Correct Answer: (b) 3/2
Solution:Let the angle be x and kx,

52. Consider the following statements :

Correct Answer: (b) only 2
Solution:We have,

53. A road curve is to be laid out on a circle. What radius should be used if the track is to change direction by 42° in distance of 44 m?

(Assume π = ²²⁄₇ )

Correct Answer: (a) 60 m
Solution:Given, θ = 42º

54. What is the maximum value of 3sin θ - 4 ?

Correct Answer: (b) -1
Solution:

55. If sin θ + cos θ = √2, then what is sin⁶θ + cos⁶θ + 6 sin²θ cos²θ equal to ?

Correct Answer: (d)
Solution:Given,

56. What is the least value of 9sin²θ +16 cos²θ ?

Correct Answer: (b) 9
Solution:We have,

57. If cos 47° + sin 47° = k then what is the value of cos² 47° - sin² 47° ?

Correct Answer: (a)
Solution:Given,

58. If cosec θ - sin θ = p³ and sec θ - cos θ = q³, then what is the value of tan θ ?

Correct Answer: (b)
Solution:We have,

59. If 0 ≤ α β ≤ 90° such that cos(α - β) = 1, then what is sin α - sin β + cos α - cos β equal to ?

Correct Answer: (b) 0
Solution:

60. Consider the following statements.

1. The value of cos 61° + sin 29° cannot exceed 1.
2. The value of tan 23° - cot 67° is less than 0.

Which of the above statements is/are correct?

Correct Answer: (a) only 1
Solution:We have,