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

Total Questions: 100

41. What is log₁₀ 31⋅25 equal to?

Correct Answer: (a) 3 - 5log₁₀2
Solution:

42. Solve it ?

Correct Answer: (a)
Solution:

43. The sum of the reciprocals of two alternate natural numbers is 7/24. What is the sum of the numbers?

Correct Answer: (c) 14
Solution:

44. If n is any natural number, then 5²ⁿ - 1 is always divisible by how many natural number ?

Correct Answer: (d) Eight
Solution:

45. If 5ˣ⁻³ = 8, then what is x equal to ?

Correct Answer: (a)
Solution:


46. What is the least value of 3sin²θ + 4cos²θ ?

Correct Answer: (b) 4
Solution:Given, 3sin²θ + 4cos²θ
= 3sin²θ + 3cos²θ + cos²θ
= 3 + cos²θ
minimum value = 3 + 1
[∵ minimum value of cos θ = -1] = 4

47. If sinθ cosθ = k, where 0 ≤ θ ≤ π/2 then which one of the following is correct?

Correct Answer: (b) 0 ≤ k ≤ 0.5 only
Solution:

48. If p = sin²θ + cos⁴θ for 0 ≤ θ ≤ π/2, then consider the following statements.

1. p can be less than ¾ .
2. p can be more than 1.

Which of the above statements is/are correct?

Correct Answer: (d) Neither 1 nor 2
Solution:


49. What is the ratio of the greatest to the smallest value of 2 - 2sin x - sin²x, 0 ≤ x ≤ π/2 ?

Correct Answer: (a) -2
Solution:

50. If the equation x² + y² + 2xy sin²θ = 0 contains real solution for x and y, then

Correct Answer: (a) x = y
Solution: