Inverse Laplace Transform MCQ’s

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This set of Signals & Systems Multiple Choice Questions & Answers (MCQs) focuses on “Inverse Laplace Transform”.

1. 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)

2. 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)

3. 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)

4. 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)

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

6. 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

7. 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

8. 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)

9. 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)

10. 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}

11. 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)

12. 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)

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