GATE Core Subject Knowledge & Technical Concepts 3

Question 1

The Laplace transform of the unit step function u(t) is:

Accepted Answer

1/s

Answer

The Laplace transform of u(t) is 1/s for Re(s) > 0.

Question 2

A system is BIBO stable if and only if its impulse response h(t) satisfies:

Accepted Answer

∫|h(t)|dt < ∞

Answer

A system is BIBO stable if and only if its impulse response is absolutely integrable (L1 norm is finite).

Question 3

In a second-order control system, the damping ratio ζ = 0.5 corresponds to which response?

Accepted Answer

Underdamped

Answer

When 0 < ζ < 1 (here ζ = 0.5), the system is underdamped and exhibits oscillatory response.

Question 4

The Nyquist sampling theorem states that the sampling frequency must be:

Accepted Answer

At least twice the signal's highest frequency

Answer

The sampling frequency must be at least 2fmax (Nyquist rate) to allow perfect reconstruction of the signal.

Question 5

For a causal LTI system, which condition must the region of convergence (ROC) of its z-transform satisfy?

Accepted Answer

ROC extends to infinity (includes |z| = ∞)

Answer

For a causal (right-sided) sequence, the ROC is of the form |z| > r and must include |z| = ∞.

(GATE) Graduate Aptitude Test in Engineering Practice Test