MATHEMATICS (NDA/NA SOLVED PAPER 2022-I) (01 to 50)

Total Questions: 50

31. If tanθ = - 5/12, then what can be the value of sinθ?

Correct Answer: (a) 5/13 but cannot be - 5/13
Solution:

32. What is the value of cos⁴ 7π/8 + cos⁴ 5π/8?

Correct Answer: (b) 3/4
Solution:

33. What is sin²(π/4 + θ) - sin² (π/4 - θ) equal to?

Correct Answer: (a) sin2θ
Solution:

34. A vertical tower stands on a horizontal plane and is surmounted by a vertical flagstaff of height h. At a point on the plane the angles of elevation of the bottom and top of the flagstaff are θ and 2θ respectively. What is the height of the tower?

Correct Answer: (c) hcos2θ
Solution:

35. The shadow of a tower becomes x metre longer, when the angle of elevation of sun changes from 60° to θ. If the height of the tower is √3x metre, then which one of the following is correct?

Correct Answer: (b) 30° <θ < 45°
Solution:

36. If tan⁻¹(1/2) + tan⁻¹(x/3) = π/4, where 0 < x < 6, then what is x equal to?

Correct Answer: (a) 1
Solution:

37. If 3sin⁻¹x + cos⁻¹x = π, then what is x equal to?

Correct Answer: (c) 1/√2
Solution:

38. If tan α + tan β = 1 - tan α . tan β, where then which of the following is one of the values of (α + β)?

Correct Answer: (b) π/4
Solution:

39. If (1 + tan θ) (1 + tan 9θ) = 2, then what is the value of tan(10 θ)?

Correct Answer: (b) 1
Solution:

40. What is the value of

sin 0° + sin 10° + sin 20° + sin 30° +_____+sin 360°?

Correct Answer: (b) 0
Solution: