# The Laplace Transform MCQ’s

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

1. Find the Laplace transform of e-at u(t) and its ROC.
a) \frac{1}{s-a}, Re{s}>-a
b) \frac{1}{s}, Re{s}>a
c) \frac{1}{s×a}, Re{s}>a
d) \frac{1}{s+a}, Re{s}>-a

2. Find the Laplace transform of δ(t).
a) 1
b) 0
c) ∞
d) 2

3. The necessary condition for convergence of the Laplace transform is the absolute integrability of f(t)e-σt.
a) True
b) False

4. Find the Laplace transform of u(t) and its ROC.
a) \frac{1}{s}, σ<0
b) \frac{1}{s}, σ>0
c) \frac{1}{s-1}, σ=0
d) \frac{1}{1-s}, σ≤0

5. Find the Laplace transform of cos⁡ωt u(t).
a) \frac{s}{s^2+ω^2}
b) \frac{s}{s^2-ω^2}
c) \frac{ω}{s^2+ω^2}
d) \frac{ω}{s^2-ω^2}

6. Find the Laplace transform of the signal x(t)=et sin⁡2t for t≤0.
a) \frac{2}{(s-1)^2+2^2}
b) -\frac{2}{(s-1)^2+2^2}
c) \frac{2}{(s+1)^2+2^2}
d) -\frac{2}{(s+1)^2+2^2}

7. Find the ROC of x(t) = e-2t u(t) + e-3t u(t).
a) σ>2
b) σ>3
c) σ>-3
d) σ>-2

8. Find the Laplace transform of e-at sin⁡ωt u(t).
a) \frac{s+a}{(s+a)^2-ω^2}
b) \frac{ω}{(s+a)^2-ω^2}
c) \frac{s+a}{(s+a)^2+ω^2}
d) \frac{ω}{(s+a)^2+ω^2}

9. Find the Laplace transform of the signal x(t)=te-2|t|.
a) -\frac{1}{(s-2)^2} + \frac{1}{(s+2)^2}
b) \frac{1}{(s-2)^2} + \frac{1}{(s+2)^2}
c) \frac{1}{(s-2)^2} – \frac{1}{(s+2)^2}
d) -\frac{1}{(s-2)^2} – \frac{1}{(s+2)^2}

10. Find the Laplace transform of [1 +sin 2t cos ⁡2t]u(t).
a) \frac{s^2+2s+16}{s(s^2-4^2)}
b) \frac{s^2+2s+16}{s(s^2+4^2)}
c) \frac{s^2+2s+16}{(s^2+4^2)}
d) \frac{s^2+2s+16}{s}

11. Find the Laplace transform of (cos⁡2t)3 u(t).
a) \frac{s(s^2+28)}{(s^2+36)(s^2+4)}
b) \frac{s(s^2+36)}{(s^2+28)(s^2+4)}
c) \frac{s(s^2+4)}{(s^2+36)(s^2+28)}
d) \frac{s}{(s^2+36)(s^2+4)}

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