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

Total Questions: 50

41. The top of a hill observed from the top and bottom of a building of height h is at angles of elevation π/6 and π/3 respectively. What is the height of the hill?

Correct Answer: (b) 3h/2
Solution:

42. What is/are the solution (s) of the trigonometric equation cosec x + cot x = √3 where 0 < x < 2π?

Correct Answer: (b) π /3 only
Solution:

43. Simplify the equation?

Correct Answer: (b) 1
Solution:

44. If cosα and cosβ (0 < α < β < π) are the roots of the quadratic equation 4x² - 3 = 0, then what is the value of secα × secβ?

Correct Answer: (a) -4/3
Solution:

45. Consider the following values of x :

Correct Answer: (a) 3 only
Solution:

46. If the second term of a GP is 2 and the sum of its infinite terms is 8, then the GP is:

Correct Answer: (c)
Solution:

47. If a, b, c, are in AP or GP or HP, then a-b/b-c is equal to?

Correct Answer: (c)
Solution:

48. What is the sum of all three digit numbers that can be formed using all the digits 3, 4 and 5, when repetition of digits is not allowed?

Correct Answer: (a) 2664
Solution:

Three digit number. that can be formed using 3, 4 and 5 when repetition not allowed are 543, 534, 453, 435, 354, 345
Sum
= 543 + 534 + 453 + 435 + 354 + 345
= 2664

49. The ratio of roots of the equations ax² + bx + c = 0 and px² + qx + r = 0 are equal. If D₁ and D₂ are respective discriminants, then what is D₁/D₂ equal to?

Correct Answer: (b) b²/q²
Solution:

50. If A = sin²θ + cos⁴θ, then for all real θ, which one of the following is correct?

Correct Answer: (b)
Solution: