Common Laplace Transforms – 1 MCQ’s

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This set of Signals & Systems Multiple Choice Questions & Answers (MCQs) focuses on “Common Laplace Transforms – 1″.

1. Given f (t) = t2e-2x cos (3t). The value of L {f(t)} is __________________
a) \frac{2(s+2)(s^2+4s-23)}{(s^2+4s+13)^3}
b) \frac{2(s-2)(s^2-4s-23)}{(s^2+4s+13)^3}
c) \frac{2(s+2)(s^2+4s+23)}{(s^2+4s+13)^3}
d) \frac{2(s-2)(s^2+4s-23)}{(s^2+4s-13)^3}

2. The inverse Laplace transform of F(s) = \frac{2}{s+c} e^{-bs} is _________________
a) 2 e-k (t-b)
b) 2 e-k (t-b) u (t-b)
c) e-k (t-b) u (t-b)
d) 2 u (t-b)

3. The Laplace transform of f(t) = (e-2t – 1)2 is ________________
a) \frac{2}{s+2} + \frac{1}{s}
b) \frac{1}{s+4}
c) \frac{1}{s+4} – \frac{2}{s+2} + \frac{1}{s}
d) –\frac{2}{s+2} + \frac{1}{s}

4. The inverse Laplace transform of F(s) = \frac{2}{s^2+3s+2} is ______________
a) -2e-2t + 2e-t
b) 2e-2t + 2e-t
c) -2e-2t – 2e-t
d) 2e-t + e-2t

5. The Laplace transform of the signal u (t+2) is _________
a) \frac{1}{s}
b) \frac{-1}{s}
c) \frac{e^{-2s}}{s}
d) \frac{-e^{-2s}}{s}

6. The Laplace transform of the signal e2tu(-t+2) is ___________
a) \frac{e^{2(s-2)-1}}{s-2}
b) \frac{e^{-2s}}{s+2}
c) \frac{1-e^{-2(s-2)}}{s-2}
d) \frac{e^{-2s}}{s-2}

7. The Laplace transform of signal u(t-2) is ___________
a) \frac{-e^{-2s}}{s}
b) \frac{e^{-2s}}{s}
c) \frac{e^{-2s}}{1+s}
d) Zero

8. The Laplace transform of the signal e-2tu(t+1) is ___________
a) \frac{1}{s+2}
b) \frac{e^{-s}}{s+2}
c) \frac{e^{-(s+2)}}{s+2}
d) \frac{-e^{-s}}{s+2}

9. The Laplace transform of the signal sin 5t is _____________
a) \frac{5}{s^2+5}
b) \frac{s}{s^2+5}
c) \frac{5}{s^2+25}
d) \frac{s}{s^2+25}

10. The Laplace transform of the signal \frac{d}{dx}(te-t u(t)) is ______________
a) \frac{1}{s(s+1)^2}
b) \frac{s}{(s+1)^2}
c) \frac{e^{-s}}{s+1}
d) \frac{e^{-s}}{(s+1)^2}

11. The Laplace transform of the signal t3 u(t) is _____________
a) \frac{3}{s^4}
b) \frac{-3}{s^4}
c) \frac{6}{s^4}
d) \frac{-6}{s^4}

12. The Laplace transform of the signal u(t) – u(t-2) is ______________
a) \frac{e^{-2s}-1}{s}
b) \frac{-e^{-2s}+1}{s}
c) \frac{2}{s}
d) \frac{-2}{s}

13. The Laplace transform of the signal t u(t) * cos 2πt u(t) is _____________
a) \frac{1}{s(s^2+4π^2)}
b) \frac{2π}{s^2 (s^2+4π^2)}
c) \frac{1}{s^2 (s^2+4π^2)}
d) \frac{s^3}{(s^2+4π^2)}

14. The Laplace transform of the signal u(t-1) * e-2t u(t-1) is ___________
a) \frac{e^{-2(s+1)}}{2s+1}
b) \frac{e^{-2(s+1)}}{s+1}
c) \frac{e^{-(s+2)}}{s+2}
d) \frac{e^{-2(s+1)}}{s+2}

15. The Laplace transform of the signal \int_0^t e^{-3t} cos⁡2t dt is _____________
a) \frac{-(s+3)}{s[(s+3)^2+4]}
b) \frac{(s+3)}{s[(s+3)^2+4]}
c) \frac{s(s+3)}{(s+3)^2+4}
d) \frac{-s(s+3)}{(s+3)^2+4}

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