SOLVED PAPER 2021 (CDS) (I) (Elementary Mathematics)

Total Questions: 100

51. Consider the following inequalities

1. sin 1° < cos 57°
2. cos 60° > sin 57°

Which of the above is/are correct?

Correct Answer: (a) 1 only
Solution:

As sin x is an increasing function in 1st quadrant, Statement 2 is incorrect.
Hence, only Statement 1 is true.

52. If p = secθ - tanθ and q = cosecθ + cotθ, then what is p + q(p - 1) equal to?

Correct Answer: (a) - 1
Solution:


53. If cosecθ - cotθ = m, then what is cosecθ equal to?

Correct Answer: (d)
Solution:

54. Let ABC be a triangle right angled at C, then what is tan A + tan B B equal to?

Correct Answer: (d)
Solution:

55. Let cos α + cos β = 2 and sin α + sin β = 0, where 0 ≤ α <= 90°, 0 ≤ β ≤ 90° What is the value of cos 2α - cos 2β ?

Correct Answer: (a) 0
Solution:


56. If sec θ + cos θ = ⁵⁄₂ , where 0 ≤ θ ≤ 90°, then what is the value of sin² θ ?

Correct Answer: (c) ¾
Solution:


57. What is (1 + cot θ - cosec θ) (1 + tan θ + sec θ) equal to ?

Correct Answer: (c) 2
Solution:

58. If 6 + 8 tan θ = sec θ and 8 - 6 tan θ = k sec θ then what is the value of k² ?

Correct Answer: (d) 99
Solution:

59. A pole on the ground leans at 60° with the vertical. At a point x metre away from the base of the pole on the ground, two halves of the pole subtend the same angle. If the pole and the point are in the same vertical plane, then what is the length of the pole?

Correct Answer: (b) √3x m
Solution:


60. A vertical tower standing at the corner of a rectangular field subtends angles of 60° and 45° at the two nearer corners. If θ is the angle that the tower subtends at the farthest corner, then what is cot θ equal to ?

Correct Answer: (c)
Solution: