1
GATE ME 2015 Set 3
+1
-0.3
Laplace transform of the function $$f(t)$$ is given by $$f\left( s \right) = L\left\{ {f\left( t \right)} \right\} = \int\limits_0^\infty {f\left( t \right){e^{ - st}}\,dt.}$$

Laplace transform of the function shown below is given by.

A
$${{1 - {e^{ - 2s}}} \over s}$$
B
$${{1 - {e^{ - s}}} \over s}$$
C
$${{2 - 2{e^{ - s}}} \over s}$$
D
$${{1 - 2{e^{ - s}}} \over s}$$
2
GATE ME 2015 Set 2
+1
-0.3
Laplace transform of $$\cos \left( {\omega t} \right)$$ is
A
$${s \over {{s^2} + {\omega ^2}}}$$
B
$${\omega \over {{s^2} + {\omega ^2}}}$$
C
$${s \over {{s^2} - {\omega ^2}}}$$
D
$${\omega \over {{s^2} - {\omega ^2}}}$$
3
GATE ME 2015 Set 2
+1
-0.3
The Laplace transform of $${e^{i5t}}$$ where $$i = \sqrt { - 1} ,$$
A
$${{s - 5i} \over {{s^2} - 25}}$$
B
$${{s + 5i} \over {{s^2} + 25}}$$
C
$${{s + 5i} \over {{s^2} - 25}}$$
D
$${{s - 5i} \over {{s^2} + 25}}$$
4
GATE ME 2015 Set 1
+1
-0.3
The Laplace Transform of $$f\left( t \right) = {e^{2t}}\sin \left( {5t} \right)\,u\left( t \right)$$ is
A
$${5 \over {{s^2} - 4s + 29}}$$
B
$${5 \over {{s^2} + 5}}$$
C
$${{s - 2} \over {{s^2} - 4s + 29}}$$
D
$${5 \over {s + 5}}$$
GATE ME Subjects
EXAM MAP
Medical
NEET