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

Total Questions: 100

51. A wheel makes 360 revolutions in one minute. What is the number of radians it turns in one second?

Correct Answer: (c) 12π
Solution:60 sec = 360 revolutions
∴ 1 sec = 6 revolutions
= 6 × 2 π radians = 12 π radians

52. What is the least value of (25cosec²x + sec²x)?

Correct Answer: (b) 36
Solution:25cosec²x + sec²x

53. Simplify the question

Correct Answer: (a) α = 1
Solution:Given that,

54. Simplify the question

Correct Answer: (a)
Solution:Given, tan 6θ = cot 2θ

55. A tree of height 15 m is broken by wind in such a way that its top touches the ground and makes an angle 30° with the ground. What is the height from the ground to the point where tree is broken?

Correct Answer: (c) 5 m
Solution:


56. On a plane area there are two vertical towers separated by 100 feet apart. The shorter tower is 40 feet tall. A pole of length 6 feet stands on the line joining the base of two towers so that the tip of the towers and tip of the pole are also on the same line. If the distance of the pole from the shorter tower is 75 feet, then what is the height of the taller tower (approximately)?

Correct Answer: (a) 85 feet
Solution:


57. The angles of elevation of the top of a tower from two points at distances p and q from the base and on the same straight line are 27° and 63° respectively. What is the height of the tower?

Correct Answer: (b)
Solution:Let height of the towerCD be h.


58. Simplify the question

Correct Answer: (d) 8
Solution:

59. Simplify the question

Correct Answer: (b) sec θ
Solution:

60. Simplify the question

Correct Answer: (a) 0
Solution: