(Mathematics) NDA/NA Solved Paper 2017-I

Total Questions: 50

41. From the top of a lighthouse, 100 m high, the angle of depression of a boat is tan⁻¹ (5/12). What is the distance between the boat and the lighthouse?

Correct Answer: (c) 240m
Solution:

42. Solve the following question:

Correct Answer: (a) π/12
Solution:

43. Solve the following question:

Correct Answer: (c) 1/8
Solution:

44. Solve the following question:


Correct Answer: (a)
Solution:

45. If sinθ = 3 sin (θ+ 2α), then the value of tan (θ+ α) + 2 tan α is equal to

Correct Answer: (b) 0
Solution:

46. What is the value of tan 18°?

Correct Answer: (a)
Solution:

47. Let x, y, z be positive real numbers such that x, y,zare in GP and tan⁻¹x, tan⁻¹y and tan⁻¹z are in AP. Then which one of the following is correct?

Correct Answer: (a) x=y=z
Solution:

48. If tan (α + β) = 2 and tan (α - β) = 1, then tan (2α) is equal to 

Correct Answer: (a) -3
Solution:

49. Consider the following for triangle ABC:


Which of the above are correct?

Correct Answer: (b) 1 and 2
Solution:

50. If secθ - cosecθ = 4/3, then what is (sinθ - cosθ) equal to ?

Correct Answer: (b) 1/2 only
Solution: