Explore topic-wise MCQs in Signals & Systems Questions and Answers.

This section includes 12 Mcqs, each offering curated multiple-choice questions to sharpen your Signals & Systems Questions and Answers knowledge and support exam preparation. Choose a topic below to get started.

1.

Given x(t)=e-t u(t). Find the inverse Laplace transform of e-3s X(2s).

A. \(\frac{1}{2}\) e-(t-3)/2 u(t+3)
B. \(\frac{1}{2}\) e-(t-3)/2 u(t-3)
C. \(\frac{1}{2}\) e(t-3)/2 u(t-3)
D. \(\frac{1}{2}\) e(t-3)/2 u(t+3)
Answer» C. \(\frac{1}{2}\) e(t-3)/2 u(t-3)
Discussion
2.

Find the inverse Laplace transform for the function X(s) = \(\frac{1+e^{-2s}}{3s^2+2s}\).

A. e-(2/3)t u(t) – u(t) + e-(2/3)(t-2) u(t-2)-u(t-2)
B. e-(2/3)t u(t) + e-(2/3)(t-2) u(t-2)
C. e-(2/3)(t-2) u(t-2) – u(t-2)
D. e-(2/3)t u(t) – u(t)
Answer» B. e-(2/3)t u(t) + e-(2/3)(t-2) u(t-2)
Discussion
3.

Find the inverse Laplace transform for the function X(s) = \(\frac{2s-1}{s^2+4s+8}\).

A. e-2t cos⁡2t u(t) – e-2t sin⁡2t u(t)
B. 2e-2t cos⁡2t u(t) – \(\frac{5}{2}\) e-2t sin⁡2t u(t)
C. 2e-2t cos⁡2t u(t) – e-2t sin⁡2t u(t)
D. e-2t cos⁡2t u(t) – \(\frac{5}{2}\) e-2t sin⁡2t u(t)
Answer» C. 2e-2t cos⁡2t u(t) – e-2t sin⁡2t u(t)
Discussion
4.

Find the inverse Laplace transform for X(s) = \(ln ⁡(\frac{s+a}{s+b})\).

A. \(\frac{e^{-at} – e^{-bt}}{t}\)
B. \(\frac{e^{-bt} – e^{-at}}{t}\)
C. \(\frac{e^{-at} + e^{-bt}}{t}\)
D. \(\frac{e^{bt} + e^{-at}}{t}\)
Answer» C. \(\frac{e^{-at} + e^{-bt}}{t}\)
Discussion
5.

Find the inverse Laplace transform for X(s) = \(\frac{s}{2s^2-8}\).

A. cosh⁡2t
B. \(\frac{1}{2}\) cosh⁡2t
C. sinh⁡2t
D. \(\frac{1}{2}\) sinh⁡2t
Answer» C. sinh⁡2t
Discussion
6.

If F1 (s) = \(\frac{1}{s+2}\) and F2 (s) = \(\frac{1}{s+3}\), find the inverse Laplace transform of F(s) = F1 (s) F2 (s).

A. [e-2t + e-3t]u(t)
B. [e-2t – e-3t]u(t)
C. [e2t + e3t]u(t)
D. [e2t + e-3t]u(t)
Answer» C. [e2t + e3t]u(t)
Discussion
7.

Find the inverse Laplace transform of X(s) = \(\frac{s}{(s^2+a^2)^2}\).

A. \(\frac{1}{a}\) t sin⁡at
B. \(\frac{1}{2a}\) t sin⁡at
C. \(\frac{1}{a}\) t cos⁡at
D. \(\frac{1}{2a}\) t cos⁡at
Answer» C. \(\frac{1}{a}\) t cos⁡at
Discussion
8.

Find the inverse Laplace transform of X(s) = \(\frac{s}{s^2 a^2+b^2}\).

A. \(\frac{1}{a^2} \,cos⁡(\frac{a}{b})t\)
B. \(\frac{1}{a^2} \,cos⁡(\frac{b}{a})t\)
C. \(\frac{1}{a^2} \,sin⁡(\frac{b}{a})t\)
D. \(\frac{1}{a^2} \,sin⁡(\frac{a}{b})t\)
Answer» C. \(\frac{1}{a^2} \,sin⁡(\frac{b}{a})t\)
Discussion
9.

Find the inverse Laplace transform for \(\frac{s}{(s+2)^2+1}\).

A. [2e-2t cos⁡t + e-2t sin⁡t]u(t)
B. [e-2t cos⁡t + 2e-2t sin⁡t]u(t)
C. [2e-2t cos⁡t – e-2t sin⁡t]u(t)
D. [e-2t cos⁡t – 2e-2t sin⁡t]u(t)
Answer» E.
Discussion
10.

Find the inverse Laplace transform for \(\frac{s}{(s+2)^2}\).

A. te-t u(t)
B. e-t sin⁡t u(t)
C. e-2t (1-2t)u(t)
D. e2t (1-2t)u(t)
Answer» D. e2t (1-2t)u(t)
Discussion
11.

Find the inverse Laplace transform for \(\frac{1}{(s+1)^2+1}\).

A. te-t u(t)
B. e-t sin⁡t u(t)
C. e-t cos⁡t u(t)
D. e-t u(t)
Answer» C. e-t cos⁡t u(t)
Discussion
12.

Find the inverse Laplace transform for \(\frac{1}{(s+1)^2}\).

A. tet u(t)
B. te-t u(t)
C. tu(t)
D. et u(t)
Answer» C. tu(t)
Discussion