Gate Mathematics Electrical Engineering Previous Year Questions

ax³ + bx² + cx + d is a polynomial on real x over real coefficients a, b, c, d wherein a ≠ 0. Which of the following statements is true?

a) No choice of coefficients can make all roots identical.
b) a, b, c, d can be chosen to ensure that all roots are complex.
c) d can be chosen to ensure that x = 0 is a root for any given set a, b, c.
d) c alone cannot ensure that all roots are real.

Which of the following statements is true about the two sided Laplace transform?

a) It has no poles for any bounded signal that is non-zero only inside a finite time interval.
b) If a signal can be expressed as a weighted sum of shifted one sided exponentials, then its Laplace Transform will have no poles
c) It exists for every signal that may or may not have a Fourier transform.
d) The number of finite poles and finite zeroes must be equal.

Which one of the following functions is analytic in the region |z| ≤ 1?

a)

The rank of the matrix, M= , is ___________.

M is a 2 × 2 matrix with eigenvalues 4 and 9. The eigenvalues of M² are

a) 2 and 3
b) −2 and −3
c) 4 and 9
d) 16 and 81

The inverse Laplace transform of H(s) =

a) 3 te^-t+e^-t
b) 2 te^-t+e^-t
c) 4 te^-t+e^-t
d) 3e^-t

The partial differential equation

a) Poisson’s equation
b) Laplace equation
c) Wave equation
d) heat equation

Let z(t) - x(t) * y(t), where "*" denotes convolution. Let c be a positive real-valued constant, Choose the correct expression for z(ct).

a) c.x(ct) * y(ct)
b) x(ct) * y(ct)
c) c.x(t) * y(ct)
d) c.x(ct) * y(t)