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 51 to 56 out of 56 Questions

51.

Find

L [f^{'} (t)]

when

f (t) = t \sin t

.

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

52.

If

f (t) = \frac{1 - \cos 4 t}{t}

then find

L [f (t)]

.

(a)	$\frac{s \log (s)}{\sqrt{s^{2} + 16}}$
(b)	$\frac{1}{2} \log (\frac{s^{2} + 16}{s^{2}})$
(c)	$- \frac{s \log (s)}{\sqrt{s^{2} + 16}}$
(d)	$- \frac{\log (s)}{\sqrt{s^{2} + 16}}$

53.

Find

L [f (t)]

if

f (t) = \{\begin{cases} 1 - t & 0 \leq t \leq 2 \\ 0 & t \geq 2 \end{cases}

.

(a)	$e^{- 2 s} + [1 + \frac{1}{s^{2}}]$
(b)	$(1 - e^{- 2 s}) (\frac{1}{s} + \frac{1}{s^{2}})$
(c)	$e^{- 2 s} + \frac{1}{s^{2}}$
(d)	None of these

54.

Find

L [\int_{0}^{t} t e^{- 2 t} d t]

=________ .

(a)	$\frac{1}{{(s + 2)}^{2}}$
(b)	$\frac{1}{s (s + 2)}$
(c)	$\frac{1}{s {(s + 2)}^{2}}$
(d)	None of these

55.

L [\int_{0}^{t} e^{2 t} \sin t d t]

=________ .

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

56.

L [e^{- t} u (t - 2)]

=__________ .

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

Showing 51 to 56 out of 56 Questions