MCQs of Laplace Transform and Inverse Laplace Transform (Mathematics - II - 3110015) | GTU MCQ

Mathematics - II (3110015) MCQs

MCQs of Laplace Transform and Inverse Laplace Transform

Showing 1 to 10 out of 56 Questions

1.

Laplace transform of f(t) is given by _________ .

(a)	$f (s) = \int_{0}^{\infty} e^{- s t} f (t) d t$
(b)	$f (t) = \int_{0}^{\infty} e^{- s t} f (t) d t$
(c)	$F (s) = \int_{0}^{\infty} e^{- s t} F (t) d t$
(d)	$F (s) = \int_{0}^{\infty} e^{- s t} f (t) d t$

2.

Laplace transformation of δ (t - a) is

(a)	$e^{δ s}$
(b)	$e^{a s}$
(c)	$e^{- a s}$
(d)	$e^{δ t}$

3.

Laplace transform of

f (t) = \{\begin{cases} \frac{t}{k} & , t < k \\ 1 & , t > k \end{cases}

is

(a)	$- \frac{e^{- k s}}{s^{2}} [s + \frac{1}{k}]$
(b)	$\frac{k e^{- k s}}{s^{2}} [k s + 1]$
(c)	$\frac{1}{k s^{2}} [1 - e^{- k s}]$
(d)	$\frac{e^{- k s}}{s^{2}} [s + \frac{1}{k}]$

4.

L [t^{\frac{4}{3}}] =

(a)	$\frac{(\frac{1}{3})!}{s^{\frac{7}{3}}}$
(b)	$\frac{Γ (\frac{4}{3})}{s^{\frac{7}{3}}}$
(c)	$\frac{4 Γ (\frac{1}{3})}{9 s^{\frac{7}{3}}}$
(d)	$\frac{Γ (\frac{4}{3})}{3 s^{\frac{7}{3}}}$

5.

L [2^{t}] =

(a)	$\frac{1}{\log (2)}$
(b)	$\frac{1}{s - \log (2)}$
(c)	$\frac{\log (2)}{s - 2}$
(d)	$\log (s - 2)$

6.

L [100^{t} + 2 t^{10}] =

(a)	$\frac{1}{s - 100} + \frac{2 \cdot 10!}{s^{11}}$
(b)	$\frac{1}{s + 100} + \frac{20!}{s^{11}}$
(c)	$\frac{1}{s - \log_{e} (100)} + \frac{20!}{s^{11}}$
(d)	$\frac{1}{s - 2 \log_{e} (10)} + \frac{2 \cdot 10!}{s^{11}}$

7.

Laplace transform of

f (t) = \sin^{2} 2 t \cos t

is

(a)	$\frac{1}{4} [\frac{2 s}{s^{2} + 1} - \frac{s}{s^{2} + 25} - \frac{s}{s^{2} + 9}]$
(b)	$\frac{1}{4} [\frac{s}{s^{2} + 1} - \frac{s}{s^{2} + 25} - \frac{9}{s^{2} + 9}]$
(c)	$\frac{1}{4} [\frac{s}{s^{2} + 1} - \frac{s}{s^{2} + 25} - \frac{s}{s^{2} + 9}]$
(d)	$\frac{1}{4} [\frac{s}{s^{2} + 1} - \frac{3}{s^{2} + 9} \frac{5}{s^{2} + 25}]$

8.

Laplace transform of periodic function

f (t) where f (T + t) = f (t), \forall T > 0 is

.

(a)	$\frac{1}{1 - e^{- t s}} \int_{0}^{\infty} e^{- s t} f (t) d t, s > 0$
(b)	$\frac{1}{1 - e^{- T s}} \int_{0}^{T} e^{- s t} f (t) d t, s > 0$
(c)	$\frac{1}{1 - e^{- a s}} \int_{0}^{T} e^{- s t} f (t) d t, s > 0$
(d)	$\frac{1}{1 - e^{- T s}} \int_{0}^{\infty} e^{- s t} f (t) d t, s > 0$

9.

If

f (t) = {(3 t + 2)}^{2}

then

L [f (t)] =

(a)	$\frac{3}{s^{2}} + \frac{2}{s}$
(b)	$\frac{9}{s^{3}} + \frac{6}{s^{2}} + \frac{2}{s}$
(c)	$\frac{18}{s^{3}} + \frac{12}{s^{2}} + \frac{4}{s}$
(d)	$\frac{18}{s^{3}} + \frac{18}{s^{2}} + \frac{4}{s}$

10.

L [e^{- 3 t} t^{\frac{3}{2}}] =

(a)	$\frac{2 \sqrt{π}}{4 {(s + 3)}^{\frac{5}{2}}}$
(b)	$\frac{3 \sqrt{π}}{4 {(s + 3)}^{\frac{5}{2}}}$
(c)	$\frac{3! \sqrt{π}}{4 {(s + 3)}^{\frac{5}{2}}}$
(d)	$\frac{2! \sqrt{π}}{4 {(s + 3)}^{\frac{5}{2}}}$

Showing 1 to 10 out of 56 Questions