Objective Questions on Laplace Transform

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Objective Questions on Laplace Transform

Objective Questions on Laplace Transform, The Laplace Transform – MCQ Test | 20 Questions MCQ Test, Laplace Transform question and answer, MCQs of Laplace Transform and Inverse Laplace, Laplace Transform – MCQs with answers, Laplace Transform MCQ Questions with Answer, Gate Objectives on Laplace Transform

Multiple Choice Questions

  1. Laplace transform of a unit impulse function is
  • S
  • 0
  • e-s
  • 1

Answer: 1

2. Laplace transforms of a damped sine wave e−αt sin (θt) · u(t) is

  • \frac{1}{(s+\alpha )^{2}+\phi ^{2}}
  • \frac{s}{(s+\alpha )^{2}+\phi ^{2}}
  • \frac{\phi ^{2}}{(s+\alpha )^{2}+\phi ^{2}}
  • \frac{\phi}{(s+\alpha )^{2}+\phi ^{2}}

Answer: \frac{\phi ^{2}}{(s+\alpha )^{2}+\phi ^{2}}

3. The final value of f(t) for a given F(s)=\frac{s}{(s+4)(s+2)}

  • Zero
  • 1/15
  • 1/8
  • 1/6

Answer: Zero

4. Laplace transforms of the function e−2t is

  • \frac{1}{2s}
  • (s + 2)
  • \frac{1}{s+2}
  • 2s

Answer: \frac{1}{s+2}

5. The Laplace transform of a function is \frac{1}{s}Ee^{-as}. The function is

  • E sin ωt
  • Eeat
  • Eu(t − a)
  • E cos ωt

Answer: Eu(t − a)

6. If f(t) = r(t − α), f (s) =

  • \frac{e^{-as}}{s^{2}}
  • \frac{\alpha }{s+\alpha }
  • \frac{1}{s+\alpha }
  • \frac{e^{-as}}{s}

Answer: \frac{e^{-as}}{s^{2}}

7. The integral of a step function is

  • A ramp function
  • An impulse function
  • Modified ramp function
  • A sinusoidal function

Answer: A ramp function

8. Laplace transform of the function f (t) = (1 − e−αt) sin αt, where α is a constant is

  • \frac{s}{s^{2}+\alpha ^{2}}-\frac{s+\alpha }{(s+\alpha )^{2}+\alpha ^{2}}
  • \frac{1}{s^{2}+\alpha ^{2}}-\frac{\alpha }{(s+\alpha )^{2}+\alpha ^{2}}
  • \frac{\alpha }{s^{2}+\alpha ^{2}}-\frac{\alpha }{(s+\alpha )^{2}+\alpha ^{2}}
  • None of the above

Answer: \frac{\alpha }{s^{2}+\alpha ^{2}}-\frac{\alpha }{(s+\alpha )^{2}+\alpha ^{2}}

9. Laplace inverse equation \frac{1}{(s+2)(s+3)} is

(a)e−t − e−2t

(b)e e−2t

(c)e e2t

(d)NOT

10. Laplace transform equation tn eat is

  • \frac{n!}{s^{n+1}}
  • \frac{n!}{s^{n-1}}
  • \frac{n!}{(s-a)^{n-1}}
  • \frac{n!}{(s-a)^{n+1}}

Answer: \frac{n!}{(s-a)^{n-1}}

11. Inverse Laplace transform for \frac{2s+3}{s^{2}+3s} is

  • 1 − e−3t
  • 1 + e−3t
  • 1 + e3t
  • 1 − 3t

Answer: 1 + e−3t

12. Inverse Laplace transform for \frac{3s^{2}+4}{s(s^{2}+4)} is

  • 1 + cos 2t
  • 1 + 3cos 2t
  • 1 + 2cos 2t
  • 1 + 3cos t

Answer: 1 + 2cos 2t

13. Inverse Laplace transform for \frac{6s}{(s+1)(s+2)(s+4)}  is

  • -2e−t + 6 e−2t + 4e−4t
  • -2e−t + 6 e−2t − 4e−4t
  • −2e−t + 6e2t + 4e−4t
  • −2e−t + 6e−2t + 4e4t

Answer: -2e−t + 6 e−2t − 4e−4t

14. The value of function f(s)=\frac{4(s+25)}{s(s+10)} at t = 0 is

  • 10
  • 4
  • 0

Answer: 4

15. Laplace transforms of tn u(t) is

  • \frac{n!}{s^{n}}
  • \frac{n!}{s^{n-1}}
  • \frac{(n-1)!}{s^{n-1}}
  • \frac{n!}{s^{n+1}}

Answer: \frac{n!}{s^{n+1}}

16. The final value of the function I(s)=\frac{s+6}{s(s+3)} is

  • 0
  • 1
  • 2
  • 3

Answer: 2

17. If I(s)=\frac{3s}{(s+1)(s+4)}, then i(t) is

  • e−t + 4e-4t
  • e−t + 4e4t
  • −e−t + 4e−4t
  • −e−t − 4e−4t

Answer: −e−t + 4e−4t

18. Laplace transform of t sin 2t is

  • \frac{4s}{(s^{2}+4)^{2}}
  • \frac{s}{(s^{2}+4)^{2}}
  • \frac{4s}{s^{2}+4}
  • \frac{4s}{(s^{2}+4)^{3}}

Answer: \frac{4s}{(s^{2}+4)^{2}}

19. If f1(t) = e −at and f2(t) = t, then convolution of f1(t) and f2(t) is

  • \frac{e^{at}}{a^{2}}\left [ ate^{at}+e^{at}+1 \right ]
  • \frac{e^{-at}}{a^{2}}\left [ ate^{-at}-e^{at}+1 \right ]
  • \frac{e^{-at}}{a^{2}}\left [ ate^{at}-e^{at}+1 \right ]
  • \frac{e^{-at}}{a^{2}}\left [ ate^{at}-e^{at}-1 \right ]

Answer: \frac{e^{-at}}{a^{2}}\left [ ate^{at}-e^{at}+1 \right ]

20. The Laplace transform of t cos 4t is

  • \frac{s^{2}-16}{(s^{2}+16)^{2}}
  • \frac{s^{2}+16}{(s^{2}+16)^{2}}
  • \frac{s^{2}}{(s^{2}+16)^{2}}
  • None of the above

Answer: \frac{s^{2}-16}{(s^{2}+16)^{2}}

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