Explore topic-wise MCQs in Signals Systems.

This section includes 8 Mcqs, each offering curated multiple-choice questions to sharpen your Signals Systems 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 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
4.

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
5.

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
6.

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
7.

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
8.

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