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

Total Questions: 100

31. What is the minimum value of cos³θ + sec³θ where 0°≤ 90° ?

Correct Answer: (c) 2
Solution:

32. Solve it ?

Correct Answer: (a)
Solution:


33. Solve it ?

Correct Answer: (c) 2
Solution:


34. A ladder 10 m long reaches a point 10 m below the top of a vertical flagstaff. From foot of the ladder, the elevation of top of the flagstaff is 60°. What is the height of flagstaff ?

Correct Answer: (b) 15 m
Solution:



35. Solve it ?

Correct Answer: (a) 1
Solution:


36. From an aeroplane flying about a river at an altitude of 1200 m, it is observed that the angles of depression of opposite points on the two banks of a river are 30° and theta If the width of the river is 3000 m, then which one of the following is correct?

Correct Answer: (c) 45° < θ < 60°
Solution:


37. Solve it ?

Correct Answer: (a)
Solution:

38. Consider the following

1. sin⁴θ - sin²θ = cos⁴θ - cos²θ
2. sin⁴θ + cos⁴θ = 1 + 2sin²θ cos²θ
3. tan⁴θ + tan²θ = sec⁴θ - sec²θ

Which of the above are identities?

Correct Answer: (c) 1 and 3 only
Solution:


39. What is the value of sin 24° sin 66° - cos 24° cos 66° + tan 24° tan 66° - cot 24° cot 66° ?

Correct Answer: (a) 0
Solution:

40. If x = p sin A cos B, y = p sin A sin B and z = p cos A, then what is the value of x² + y² + z² ?

Correct Answer: (c) p²
Solution: