# NDA 2021 (1) Mathematics Question Paper

The exam was conducted on 18 April, 2021. There are 120 objective-type questions.

6. The number of integer values of k, for which the equation 2 sin x = 2k +1 has a solution, is

• (a) zero
• (b) one
• (c) two
• (d) four

12. How many matrices of different orders are possible with elements comprising all prime numbers less than 30?

• (a) 2
• (b) 3
• (c) 4
• (d) 6

19. What is the value of the following?

tan 31º tan 33° tan 35º ... tan 57° tan 59°

• (a) -1
• (b) 0
• (c) 1
• (d) 2

34. What is the area of the triangle ABC with sides a = 10 cm, c = 4 cm and angle B = 30° ?

• (a) 16 cm2
• (b) 12 cm2
• (c) 10 cm2
• (d) 8 cm2

37. Let R be a relation defined as xRy if and only if 2x + 3y = 20, where x, y ∈ N. How many elements of the form (x, y) are there in R?

• (a) 2
• (b) 3
• (c) 4
• (d) 6

43. If one root of 5x2 +26x + k = 0 is reciprocal of the other, then what is the value of k ?

• (a) 2
• (b) 3
• (c) 5
• (d) 8

45. What is the coefficient of the middle term in the expansion of (1 + 4x + 4x2)5 ?

• (a) 8064
• (b) 4032
• (c) 2016
• (d) 1008

48. If the first term of an AP is 2 and the sum of the first five terms is equal to one-fourth of the sum of the next five terms, then what is the sum of the first ten terms?

• (a) -500
• (b) -250
• (c) 500
• (d) 250