NDA/NA SOLVED PAPER 2015-I (MATHEMATICS)

Total Questions: 120

51. (x³ - 1) can be factorised as

Correct Answer: (b)
Solution:As we know that cube root of unity is 1, ω and ω²
∴ x³ - 1 = (x - 1) (x - ω) (x - ω²)
∴ Option (b) is correct.

52. What is

Correct Answer: (c) i
Solution:

53. Let

Correct Answer: (a)
Solution:


54. The value of

Correct Answer: (c) xy
Solution:

55. If A= {x : x is a multiple of 3} and

B = {x : x is a multiple of 4} and
C= {x : x is a multiple of 12},
then which one of the following is a null set?

Correct Answer: (d) ( A ∩ B) / C
Solution:

56. If (11101011)₂ is converted decimal system, then the resulting number is

Correct Answer: (a) 235
Solution:

57. What is the real part of (sin x + i cos x)³ where i = √-1 ?

Correct Answer: (b) - sin 3x
Solution:

58. Solve the following equation

Correct Answer: (c) E(α + β)
Solution:


59. Let A = {x, y, z} and B = {p, q, r, s} . What is the number of distinct relations from B to A?

Correct Answer: (a) 4096
Solution:

60. If 2p + 3q = 18 and 4p² + 4pq - 3q² - 36 = 0 then what is (2p + q) equal to?

Correct Answer: (c) 10
Solution: