Engineering Mathematics Quiz - Competitive Exams GATE

Free practice quiz: Engineering Mathematics (Competitive Exams GATE). 70 multiple-choice questions with answers and explanations. Play online, no sign-up needed.

This Competitive Exams GATE practice quiz has 70 multiple-choice questions on Engineering 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. If A is a 2x2 matrix with eigenvalues 2 and 3, what is the determinant of A?

   1. 1
   2. 6
   3. 5
   4. 0
   Show answer

   Answer: B. 6

2. The Laplace transform of t^2 is:

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

   Answer: A. 2/s^3

3. The value of ∫_C dz/z where C is the circle |z| = 2 traversed once counterclockwise is:

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

   Answer: C. 2πi

4. The Newton-Raphson method converges quadratically when:

   1. The root is simple and initial guess is sufficiently close
   2. The initial guess is far from the root
   3. The function is discontinuous
   4. The derivative is zero at the root
   Show answer

   Answer: A. The root is simple and initial guess is sufficiently close

5. The value of ∫_0^{π/2} sin^3 x dx is:

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

   Answer: D. 2/3

More questions in this quiz

Answers and explanations are in the full quiz.

1. What is lim (x→0) sin x / x ?
2. The order and degree of the differential equation d²y/dx² + (dy/dx)³ + y = 0 are respectively:
3. If f(z) = u(x,y) + i v(x,y) is analytic, which of the following is true?
4. If P(A) = 0.3, P(B) = 0.4, and P(A ∩ B) = 0.2, what is P(A|B)?
5. The Newton-Raphson method is used to find the root of the equation f(x)=0. The iteration formula is:
6. The rank of the matrix [[1,2,3],[2,4,6],[3,6,9]] is:
7. Evaluate ∫_0^1 x e^x dx.
8. The solution of the differential equation dy/dx + y = e^{-x} with y(0)=1 is:
9. The residue of f(z) = e^z / (z^2+1) at z = i is:
10. For a Poisson distribution with mean λ, the variance is:
11. The trapezoidal rule for numerical integration is exact for polynomials of degree at most:
12. The determinant of the matrix [[2,0,0],[0,3,0],[0,0,5]] is:
13. The function f(x) = x^3 - 3x^2 + 4 has a local minimum at:
14. The function f(z) = conjugate of z is:
15. For a standard normal distribution, the mean and variance are:
16. Simpson's 1/3 rule requires the interval to be divided into:
17. If A is an orthogonal matrix, then which of the following is true?
18. If u = x^2 y + y^2 z + z^2 x, then ∂u/∂x at (1,1,1) is:
19. The general solution of d²y/dx² - 4y = 0 is:
20. The number of zeros of f(z) = z^4 + 3z^2 + 1 inside the unit circle is:
21. If a fair coin is tossed 3 times, what is the probability of getting exactly 2 heads?
22. The order of convergence of the bisection method is:
23. The Cayley-Hamilton theorem states that every square matrix satisfies:
24. If A is a 3×3 matrix with eigenvalues 1, -1, and 2, then the trace of A² is:
25. The value of the double integral ∫₀¹∫₀¹ (x + y) dx dy is:
26. The direction in which the directional derivative of f(x,y) = x² + y² at (1,1) is maximum is:
27. The Fourier series of an odd periodic function contains:
28. The eigenvalues of the matrix [[0, 1], [-1, 0]] are:
29. For what value of λ is the matrix [[λ, 1], [1, λ]] singular?
30. Green's theorem relates a line integral around a simple closed curve to a:
31. The integrating factor of the differential equation dy/dx + y tan x = sec x is:
32. The partial differential equation ∂²u/∂x² + ∂²u/∂y² = 0 is classified as:
33. The value of the integral ∫_0^∞ e^{-x²} dx is:
34. The Cauchy-Riemann equations for an analytic function f(z) = u + iv are:
35. If X is a continuous random variable with probability density function f(x) = 2x for 0 ≤ x ≤ 1, then E[X] is:
36. The mean of a binomial distribution with n = 10 and p = 0.4 is:
37. The number of degrees of freedom for a chi-square test with a 3×4 contingency table is:
38. The Laplace transform of cos(at) is:
39. The inverse Laplace transform of 1/(s² + 4) is:
40. The approximate value of √25.1 using the first-order Taylor expansion around x = 25 is:
41. If A is a 2×3 matrix and B is a 3×2 matrix, then the rank of AB is at most:
42. The value of the line integral ∫_C (x dy - y dx) where C is the unit circle traversed counterclockwise is:
43. The function f(z) = 1/(z-1)(z-2) has poles at z = 1 and z = 2. The residue at z = 1 is:
44. The probability that a continuous random variable takes an exact value is:
45. The value of the line integral ∮_C (y dx + x dy) around the unit circle oriented counterclockwise is:
46. The complementary function of the differential equation (D^2 + 4)y = 0 is:
47. For the matrix A = [[2, 1], [1, 2]], which of the following is an eigenvector corresponding to eigenvalue 3?
48. If a random variable X has the moment generating function M_X(t) = e^{2t + 2t^2}, the variance of X is:
49. The truncation error of the trapezoidal rule with step size h is proportional to:
50. The curl of the vector field F = yz i + xz j + xy k is:
51. The value of the beta function B(2, 3) is:
52. A linear system Ax = b with 4 equations and 4 unknowns has a unique solution only if:
53. The order of the Runge-Kutta method of fourth order used to solve initial value problems is:
54. According to the mean value theorem, if f is continuous on [a, b] and differentiable on (a, b), there exists c in (a, b) such that f'(c) equals:
55. If the coefficient matrix of a homogeneous system of 3 linear equations in 3 unknowns has rank 2, the solution space has dimension:
56. The type of the partial differential equation u_xx + 2u_xy + u_yy = 0 is:
57. The value of the gamma function Γ(5/2) is:
58. The value of the sum of the eigenvalues of the matrix A = [[4, -2], [1, 1]] is:
59. The value of the Fourier coefficient a_0 for f(x) = x on [−π, π] is:
60. The maximum value of the function f(x, y) = xy subject to x + y = 10 is:

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