Mathematics Quiz - Competitive Exams NDA

Free practice quiz: Mathematics (Competitive Exams NDA). 63 multiple-choice questions with answers and explanations. Play online, no sign-up needed.

This Competitive Exams NDA practice quiz has 63 multiple-choice questions on Mathematics. Try the 5 sample questions below (tap an option to check yourself), then play the full quiz online. No sign-up needed.

Sample questions

1. What is the value of ∫₀¹ x² dx?

   1. 1/2
   2. 1/3
   3. 1
   4. 1/4
   Show answer

   Answer: B. 1/3

2. The value of the determinant | 1 2 3 | | 4 5 6 | | 7 8 9 | is:

   1. -1
   2. 1
   3. 0
   4. 2
   Show answer

   Answer: C. 0

3. The value of the definite integral ∫₀¹ (1 - x)ⁿ dx, where n is a positive integer, is:

   1. 1/(n+1)
   2. n/(n+1)
   3. 1/(n-1)
   4. 1/n
   Show answer

   Answer: A. 1/(n+1)

4. The value of the limit lim_{x→∞} (√(x² + x) - x) is:

   1. 0
   2. ∞
   3. 1/2
   4. 1
   Show answer

   Answer: C. 1/2

5. The value of cot(75°) is:

   1. 2 + √3
   2. √3 + 1
   3. 2 - √3
   4. √3 - 1
   Show answer

   Answer: C. 2 - √3

More questions in this quiz

Answers and explanations are in the full quiz.

1. The solution of the differential equation dy/dx = y is:
2. If A is a 3×3 matrix with determinant 5, what is det(2A)?
3. The value of sin 75° is:
4. The equation of the tangent to the circle x² + y² = 25 at point (3, 4) is:
5. The sum of the series 1 + 1/2 + 1/4 + 1/8 + ... is:
6. The maximum value of f(x) = x³ - 3x on [-1, 2] is:
7. If the roots of x² - 5x + k = 0 are in the ratio 2:3, then k is:
8. The distance between the lines 3x + 4y = 9 and 3x + 4y = 15 is:
9. The number of ways to arrange the letters of the word 'EXAM' is:
10. The value of tan⁻¹(1) + tan⁻¹(1/2) + tan⁻¹(1/3) is:
11. The number of real roots of the equation x³ - 3x + 1 = 0 is:
12. The eccentricity of the ellipse 9x² + 16y² = 144 is:
13. The value of ∫₀^{π/2} sin x dx is:
14. If z = 1 + i, then z² is:
15. The coefficient of x⁵ in the expansion of (1 + x)¹⁰ is:
16. The area of the triangle with vertices (0,0), (3,0), (0,4) is:
17. The derivative of sin⁻¹(x) with respect to x is:
18. The equation of the normal to the parabola y² = 4x at (1, 2) is:
19. The value of tan 15° is:
20. The value of lim_{x→0} (sin 5x)/x is:
21. The number of one-one functions from a set of 3 elements to a set of 4 elements is:
22. If the centroid of a triangle with vertices (1, 2), (3, 4), and (5, k) is (3, 3), then k equals:
23. The locus of a point whose distance from the origin is equal to its distance from the plane x = 2 is:
24. The order and degree of the differential equation (d²y/dx²)³ + (dy/dx)⁵ = 0 are respectively:
25. If A is a skew-symmetric matrix of odd order, then det(A) is:
26. The period of the function f(x) = |sin x| + |cos x| is:
27. The length of the latus rectum of the hyperbola x²/9 - y²/16 = 1 is:
28. The sum of the roots of the equation |x - 2|² + |x - 2| - 6 = 0 is:
29. The vector equation of the plane passing through the points (1,0,0), (0,1,0), and (0,0,1) is:
30. The interval in which the function f(x) = x² - 4x + 6 is strictly increasing is:
31. The value of the expression i⁹ + i¹⁰ + i¹¹ + i¹² is:
32. The area of the region bounded by the curve y = x², the x-axis, and the lines x = 1 and x = 2 is:
33. The number of distinct permutations of the letters of the word 'MATHEMATICS' is:
34. If the function f(x) = x³ + ax² + bx + c has a local maximum at x = -1 and a local minimum at x = 3, then the value of a is:
35. The equation of the circle passing through the points (0,0), (a,0), and (0,b) is:
36. The value of the integral ∫ (1/(x² + a²)) dx is:
37. The number of points of discontinuity of the function f(x) = [x] on the interval [0, 3], where [x] is the greatest integer function, is:
38. If the sum of the first n terms of an A.P. is given by Sₙ = 3n² + 5n, then its 10th term is:
39. The value of the integral ∫ (dx)/(x² + 4) is:
40. If |x - 1| < 3, then x lies in the interval:
41. If A is a 2×2 matrix with determinant 3, then det(adj A) is:
42. The number of solutions of the equation sin x = x/2 is:
43. The value of ∫ 1/(x² - 1) dx is:
44. The equation of the circle with center (2, -3) and radius 5 is:
45. The term independent of x in the expansion of (x - 2/x)⁶ is:
46. The slope of the tangent to the curve y = x³ - 3x² + 2x at x = 1 is:
47. The value of tan⁻¹(2/3) + tan⁻¹(3/2) is:
48. The sum of the first 20 terms of the A.P. 3, 7, 11, ... is:
49. If x follows a binomial distribution with n = 6 and p = 1/2, then the mean is:
50. The value of sin⁻¹(1/2) + cos⁻¹(1/2) is:
51. The coordinates of the focus of the parabola y² = 8x are:
52. The angle between the planes 2x - y + z = 1 and x + y + 2z = 3 is:
53. The maximum area of a rectangle inscribed in a circle of radius 2 is:
54. The modulus of the complex number (3 + 4i)/(4 - 3i) is:
55. If the function f(x) is continuous at x = 0 and f(0) = 2, then lim_{x→0} f(x) is:
56. The number of terms in the expansion of (1 + 2x)⁷ is:
57. The value of the determinant | 2 3 | | 4 5 | is:
58. If two events A and B are independent with P(A) = 0.4 and P(B) = 0.5, then P(A ∩ B) is:

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