DAE MATH-233

Applied Mathematics-II

Chapter 12 : The Laplace Transform

DAE Common Technologies | Second Year

Multiple Choice Questions

Chapter:12 (The Laplace Transform)

Question 1:

\(L\,\left\{ f(t) \right\}\) (the Laplace Transform of \({f(t)}\) ) is

\({\int_{0}^{\infty}}\,f(t)\,{e^{-st}}\,{.dt}\) \({\int_{0}^{\infty}}\,f(t)\,{e^{st}}\,{.dt}\) \({\int_{0}^{\infty}}\,f(t)\,{e^{t}}\,{.dt}\) \({\int_{0}^{\infty}}\,f(t)\,{e^{s}}\,{.dt}\)

Question 2:

Laplace transform of the function \(f(x)\,=\,1\) is

\(\frac{1}{s^3}\) \(\frac{1}{s^2}\) \(\frac{1}{s}\) \(-\frac{1}{s}\)

Question 3:

Laplace transform of the function \(f(x)\,=\,t\) is

\(\frac{1}{s}\) \(\frac{1}{s^2}\) \(\frac{1}{s^3}\) \(-\frac{1}{s}\)

Question 4:

Laplace transform of the function \(f(x)\,=\,2\) is

\(\frac{s}{2}\) \(\frac{2}{s^2}\) \(\frac{2}{s^3}\) \(\frac{2}{s}\)

Question 5:

Laplace transform of the function \(f(x)\,=\,{e^t}\) is

\(\frac{1}{s-1}\) \(\frac{1}{s}\) \(s\,-\,1\) \(s\)

Question 6:

Laplace transform of the function \(f(x)\,=\,{e^{a\,t}}\) is

\(\frac{1}{s\,+\,a}\) \(\frac{1}{s\,-\,a}\) \({s\,-\,a}\) \({s\,+\,a}\)

Question 7:

Laplace transform of the function \(f(x)\,=\,{e^{-a\,t}}\) is

\(\frac{1}{s\,+\,a}\) \(\frac{1}{s\,-\,a}\) \({s\,-\,a}\) \({s\,+\,a}\)

Question 8:

The Laplace Transform of \(f(t)\,=\,Sin\,\omega{t}\)

\(\frac{\omega}{{S^2}\,+\,{\omega}^2}\) \(\frac{1}{{S^2}\,+\,{\omega}^2}\) \(\frac{S}{{S^2}\,+\,{\omega}^2}\) \(\frac{1}{{S^2}\,-\,{\omega}^2}\)

Question 9:

The Laplace Transform of \(f(t)\,=\,{t^n}\)

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

Question 10:

The inverse Laplace transform \({L^{-1}}\,(\frac{1}{s})\) is equal to

1 2 3 4

Question 11:

The inverse Laplace transform \({L^{-1}}\,(\frac{1}{s^2})\) is equal to

\(1\) \(t\) \(t^2\) \(\frac{t}{2}\)

Question 12:

\(\frac{S}{{S^2}\,+\,{\omega}^2}\) is inverse Laplace transform of

\(Sin\,\omega{t}\) \(cos\,\omega{t}\) \(sin\,(\frac{t}{\omega})\) \(cos\,(\frac{t}{\omega})\)

Question 13:

\(\frac{\omega}{{S^2}\,+\,{\omega}^2}\) is inverse Laplace transform of

\(Sin\,\omega{t}\) \(cos\,\omega{t}\) \(sin\,(\frac{t}{\omega})\) \(cos\,(\frac{t}{\omega})\)

Question 14:

\({\frac{1}{{s^2}\,+\,1}}\) is inverse Laplace transform of

\(Sin\,{t}\) \(cos\,{t}\) \(sin\,(\frac{1}{t})\) \(cos\,(\frac{1}{t})\)

Question 15:

\({\frac{s}{{s^2}\,+\,1}}\) is inverse Laplace transform of

\(Sin\,{t}\) \(cos\,{t}\) \(sin\,(\frac{1}{t})\) \(cos\,(\frac{1}{t})\)

Question 16:

\({L^{-1}}\,(\frac{1}{s\,-\,1})\) is equal to

\(e^{-t}\) \(e^{2\,t}\) \(\frac{1}{t}\) \(e^{t}\)

Question 17:

\({L^{-1}}\,(\frac{1}{s\,+\,1})\) is equal to

\(e^{t}\) \(e^{2\,t}\) \(\frac{1}{t}\) \(e^{-t}\)

NOTE
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INSTRUCTOR
MUHAMMAD BIN JAMEEL
BSC ENGG. CIVIL

PBTE | DAE | MATH-233 APPLIED MATHEMATICS-I | MCQs | Chapter : 12 The Laplace Transform