Mathematics NDA/NA SOLVED PAPER 2018 (I) (01 to 50)

Total Questions: 50

41. If x, x - y and x + y are the angles of a triangle (not an equilateral triangle) such that tan(x - y), tanx and tan(x + y) are in GP, then what is x equal to?

Correct Answer: (b) π/3
Solution:

42. ABC is a triangle inscribed in a circle with centre O. Letα = <BAC, where 45° < α <90°. Let β = ∠BOC. Which one of the following is correct?

Correct Answer: (a)
Solution:

We know that angle subtended by a chord at centre is always double the angle subtended by it at any other part of the circle.

43. If a flage-staff of 6 m height placed on the top of a tower throws a shadow of 2√3 m along the ground, then what is the angle that the sun makes with the ground?

Correct Answer: (a) 60°
Solution:

Let OB and BD be the tower and flag-staff respectively. OA and AC be the shadow of tower and flag-staff respectively.

44. What is tan⁻¹(1/4) + tan⁻¹(3/5) equal to?

Correct Answer: (b) π/4
Solution:

45. A spherical balloon of radius r subtends an angle α at the eye of an observer, while the angle of elevation of its centre is β. What is the height of the centre of the balloon (neglecting the height of the observer)?

Correct Answer: (a)
Solution:

Let O bet the centre of the balloon, P be the eye of the observer and <APB be the angle subtendd by the balloon at the eye of the observer.
<APB = α

46. Simplify the equation?

Correct Answer: (a)
Solution:

47. If sinα + sinβ = 0 = cosα + cosβ, where 0<β<α<2π, then which one of the following is correct?

Correct Answer: (b) α = π + β
Solution:

48. Suppose cosA is given. If only one value of cos(A/2) is possible, then A must be:

Correct Answer: (c) An odd multiple of 180°
Solution:

49. Simplify the question?

Correct Answer: (b) 3
Solution:

50. Simplify the equation?

Correct Answer: (a) π/20
Solution: