NDA 2021 (2) Mathematics Paper
NDA Questions2. Let 4sin2x = 3, where 0 ≤ x ≤ π. What is tan3x equal to?
A. -2
B. -1
C. 0
D. 1
3. Let p, q and 3 be respectively the first, third and fifth terms of an AP. Let d be the common difference. If the product (pq) is minimum, then what is the value of d?
A. 1
B. 3/8
C. 9/8
D. 9/4
8. Consider three sets X, Y and Z having 6, 5 and 4 elements respectively. All these 15 elements are distinct. Let S = (X - Y) ∪ Z. How many proper subsets does S have?
A. 255
B. 256
C. 1023
D. 1024
9. Consider the following statements in respect of relations and functions:
- All relations are functions but all functions are not relations.
- A relation from A to B is a subset of Cartesian product A x B
- A relation in A is a subset of Cartesian product A x A
Which of the above statements are correct?
A. 1 and 2 only
B. 2 and 3 only
C. 1 and 3 only
D. 1, 2 and 3
11. Let ABC be a triangle. If Cos2A + cos2B + cos2C = -1 then which one of the following is correct?
A. sinA sinB sinC = 0
B. sinA sinB cosC = 0
C. cosA sinB sinC = 0
D. cosA cosB cosC = 0
13. Suppose set A consists of first 250 natural numbers that are multiples of 3 and set B consist of first 200 even natural numbers. How many elements does have?
A. 324
B. 364
C. 384
D. 400
16. If x2 + x + 1 = 0, then what is the value of x199 + x200 + x201?
A. -1
B. 0
C. 1
D. 3
19. Let S = {2, 3, 4, 5, 6, 7, 9}. How many different 3-digit number (with all digits different) from S can be made which are less than 500?
A. 30
B. 49
C. 90
D. 147
23. If p and q are the non-zero roots of the equation x2 + px + q = 0, then how many possible values can q have?
A. Nil
B. One
C. Two
D. Three
31. Consider the digits 3, 5, 7, 9. What is the number of 5-digit numbers formed by these digits in which each of these four digits appears?
A. 240
B. 180
C. 120
D. 60
32. How many distinct matrices exist with all four entries taken from {1, 2}?
A. 16
B. 24
C. 32
D. 48
Direction: Consider the following for the next two (02) items that follow.
A circle is passing through the points (5, -8), (-2, 9) and (2, 1).
36. What are the coordinates of the centre of the circle?
A. (-2, -50)
B. (-50, -20)
C. (-24, -58)
D. (-58, -24)
37. If r is the radius of the circle, then which one of the following is correct?
A. r < 10
B. 10 < r < 30
C. 30 < r < 60
D. r > 60
47. In C(n, 4), C(n, 5) and C(n, 6) are in AP, then what is the value of n?
A. 7
B. 8
C. 9
D. 10
48. How many 4-letter words (with or without meaning) containing two vowels can be constructed using only the letters (without repetition) of the word 'LUCKNOW?
A. 240
B. 200
C. 150
D. 120
55. Consider a regular polygon with 10 sides. What is the number of triangles that can be formed by joining the vertices which have no common side with any of the sides of the polygon?
A. 25
B. 50
C. 75
D. 100
62. What is the maximum area of a rectangle that can be inscribed in a circle of radius 2 units?
A. 4 square units
B. 6 square units
C. 8 square units
D. 16 square units
65. What is the condition that f(x) = x3 + x2 + kx has no local extremum?
A. 4k < 1
B. 3k > 1
C. 3k < 1
D. 3k ≤ 1
73. When the measure of central tendency is available in the form of mean, which one of the following is the most reliable and accurate measure of variability?
A. Range
B. Mean deviation
C. Standard deviation
D. Quartile deviation
76. The locus of a point P(x, y, z) which moves in such a way that z = 7 is a
A. line parallel to x-axis
B. line parallel to y-axis
C. line parallel to z-axis
D. plane parallel to xy-plane
78. The xy-plane divides the line segment joining the points (-1, 3, 4) and (2, -5, 6)
A. internally in the ratio 2 : 3
B. internally in the ratio 3 : 2
C. externally in the ratio 2 : 3
D. externally in the ratio 2 : 1
79. The number of spheres of radius r touching the coordinate axes is
A. 4
B. 6
C. 8
D. infinite
97. The mean of 10 observation is 5.5. If each observation is multiplied by 4 and subtracted from 44, then what is the new mean?
A. 20
B. 22
C. 34
D. 44
99. If the harmonic mean of 60 and x is 48. Then what is the value of x?
A. 32
B. 36
C. 40
D. 44
100. What is the mean deviation of first 10 even natural numbers?
A. 5
B. 5.5
C. 10
D. 10.5