Free Test Engineering Mathematics – Enginee...

Q1: What is the Laplace Transform of f(t) = e^(2t)?

A. 1/(s - 2) B. s/(s + 2) C. 1/(s + 2) D. s/(s - 2)

Q2: Which of the following is a solution of the differential equation dy/dx = y?

A. y = x B. y = ln(x) C. y = e^x D. y = x^2

Q3: If A is a 2x2 matrix with eigenvalues 3 and 5, what is the determinant of A?

A. 15 B. 8 C. 0 D. 1

Q4: What is the rank of a zero matrix of size 3x4?

A. 0 B. 1 C. 3 D. 4

Q5: What is the Fourier series of a constant function?

A. Zero B. A constant C. A sine series D. A cosine series

Q6: If X and Y are independent, what is Cov(X, Y)?

A. 0 B. 1 C. XY D. E[X + Y]

Q7: What is the value of ∇.∇φ in vector calculus?

A. Gradient B. Laplacian C. Divergence D. Curl

Q8: Which of the following is not an orthogonal matrix?

A. Identity matrix B. Rotation matrix C. Scaling matrix D. Reflection matrix

Q9: What is the value of ∫₀^π sin(x) dx?

A. 0 B. 1 C. 2 D. 2

Q10: What does the eigenvalue equation represent?

A. Ax = λx B. Ax = x C. A + x = λ D. Ax = Aλ

Q11: If Z = X + iY, then |Z| is given by?

A. X + Y B. X - Y C. sqrt(X^2 + Y^2) D. X^2 + Y^2

Q12: What is the inverse Laplace of 1/s?

A. 1 B. t C. e^t D. sin(t)

Q13: If a function is even, which of the following is always true?

A. f(x) = f(-x) B. f(x) = -f(-x) C. f(0) = 0 D. f(x) = x

Q14: What is the gradient of a scalar field?

A. A vector field B. A scalar field C. A constant D. Zero

Q15: What is the probability of getting a 2 in one throw of a fair die?

A. 1/2 B. 1/4 C. 1/6 D. 1/8

Q16: Which of the following is a linear transformation?

A. T(x) = 2x B. T(x) = x^2 C. T(x) = sin(x) D. T(x) = log(x)

Q17: Which of the following is true for a symmetric matrix?

A. A = A^T B. A = -A^T C. A^2 = I D. A = A^-1

Q18: What is the variance of a constant random variable?

A. 1 B. 0 C. Infinity D. Undefined

Q19: If A is invertible, then which of the following is true?

A. det(A) = 0 B. det(A) ≠ 0 C. A is a zero matrix D. A is singular

Quiz for Engineering Mathematics