NDA 2022 (1) Mathematics Questions

NDA Questions

9. If A is the identity matrix of order 3 and B is its transpose, then what is the value of the determinant of the matrix C = A + B?

(a) 1
(b) 2
(c) 4
(d) 8

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13. If C(3n, 2n) = C(3n, 2n - 7), then what is the value of C(n, n - 5) ?

(a) 42
(b) 35
(c) 28
(d) 21

15. How many odd numbers between 300 and 400 are there in which none of the digits is repeated ?

(a) 32
(b) 36
(c) 40
(d) 45

16. How many permutations are there of the letters of the word ‘TIGER’ in which the vowels should not occupy the even positions ?

(a) 72
(b) 36
(c) 18
(d) 12

19. If the roots of the equation x2 - ax - bx - cx + bc + ca = 0 are equal, then which one of the following is correct ?

(a) a + b + c = 0
(b) a - b + c = 0
(c) a + b - c = 0
(d) -a + b + c = 0

21. What is the maximum value of n such that 5n divides (30! + 35!), where n is a natural number ? 

(a) 4
(b) 6
(c) 7
(d) 8

26. What is value of cot215° + tan215° ?

(a) 12
(b) 14
(c) 8√3
(d) 4 

34. A vertical tower stands on a horizontal plane and is surmounted by a vertical flagstaff of height h. At a point on the plane the angles of elevation of the bottom and top of the flagstaff are θ and 2θ respectively. What is the height of the tower ?

(a) h cosθ
(b) h sinθ
(c) h cos2θ
(d) h sin2θ

40. What is the value of sin0° + sin10° + sin20° + sin30° + ... + sin360° ? 

(a) -1
(b) 0
(c) 1
(d) 2

41. Consider all the subsets of the set A= {1, 2, 3, 4}. How many of them are supersets of the set {4} ?

(a) 6
(b) 7
(c) 8
(d) 9

49. In how many ways can a team of 5 players be selected out of 9 players so as to exclude two particular players ?

(a) 14
(b) 21
(c) 35
(d) 42

51. If the sum of the first 9 terms of an AP is equal to sum of the first 11 terms, then what is the sum of the first 20 terms ?

(a) 20
(b) 10
(c) 2
(d) 0

53. What is (1110011)2 + (10111)2 equal to?

(a) (101)2
(b) (1001)2
(c) (111)2
(d) (1011)2

60. The area of the region bounded by the parabola y2 = 4kx, where k > 0 and its latus rectum is 24 square units. What is the value of k?

(a) 1
(b) 2
(c) 3
(d) 4 

79. If xy = 4225 where x, y are natural numbers, then what is the minimum value of x + y?

(a) 130
(b) 260
(c) 2113
(d) 4226

82. What is the equation of the straight line which passes through the point (1, -2) and cuts off equal intercepts from the axes ?

(a) x + y - 1 = 0
(b) x - y - 1 = 0
(c) x + y + 1 = 0
(d) x - y - 2 = 0

84. What is the equation of the parabola with focus (-3, 0) and directrix x - 3 = 0?

(a) y2 = 3x
(b) x2 = 12y
(c) y2 = 12x
(d) y2 = -12x

87. A straight line passes through the point of intersection of x + 2y + 2 = 0 and 2x - 3y - 3 = 0. It cuts equal intercepts in the fourth quadrant. What is the sum of the absolute values of the intercepts ?

(a) 2
(b) 3
(c) 4
(d) 6

89. What is the equation of the locus of the mid-point of the line segment obtained by cutting the line x + y = p, (where p is a real number) by the coordinate axes ?

(a) x - y = 0
(b) x + y = 0
(c) x - y = p
(d) x + y = p

93. What is the equation of the line through the origin and the centre of the sphere ?

(a) x = y = z
(b) 2x = 3y = 4z
(c) 6x = 3y = 4z
(d) 6x = 4y = 3z

95. If p, q and r are the intercepts made by the plane on the coordinate axes respectively, then what is (p + q + r) equal to ?

(a) 10
(b) 11
(c) 12
(d) 13

104. What is the arithmetic mean of 50 terms of an AP with first term 4 and common difference 4 ?

(a) 50
(b) 51
(c) 100
(d) 102