1
GATE CE 2011
+1
-0.3
Given two continuous time signals $$x\left( t \right) = {e^{ - t}}$$ and $$y\left( t \right) = {e^{ - 2t}}$$ which exists for $$t>0$$ then the convolution $$z\left( t \right) = x\left( t \right) * y\left( t \right)$$ is ____________.
A
$${e^{ - t}} - {e^{ - 2t}}$$
B
$${e^{ - 2t}}$$
C
$${e^{ - t}}$$
D
$${e^{ - t}} + {e^{ - 3t}}$$
2
GATE CE 2009
+1
-0.3
Laplace transform of $$f\left( x \right) = \cos \,h\left( {ax} \right)$$ is
A
$${a \over {{s^2} - {a^2}}}$$
B
$${s \over {{s^2} - {a^2}}}$$
C
$${a \over {{s^2} + {a^2}}}$$
D
$${s \over {{s^2} + {a^2}}}$$
3
GATE CE 2005
+1
-0.3
The Laplace transform of a function $$f(t)$$ is $$F\left( s \right) = {{5{s^2} + 23s + 6} \over {s\left( {{s^2} + 2s + 2} \right)}}$$$As $$t \to \propto ,\,\,f\left( t \right)$$ approaches A $$3$$ B $$5$$ C $$17/2$$ D $$\propto$$ 4 GATE CE 2004 MCQ (Single Correct Answer) +1 -0.3 A delayed unit step function is defined as $$u\left( {t - a} \right) = \left\{ {\matrix{ {0,} & {t < a} \cr {1,} & {t \ge a} \cr } } \right.$$$

Its Laplace transform is ____________.

A
$$a\,\,{e^{ - as}}$$
B
$${e^{ - as}}/s$$
C
$${e^{ as}}/s$$
D
$${e^{ - as}}/a$$
GATE CE Subjects
Construction Material and Management
Geomatics Engineering Or Surveying
Engineering Mechanics
Transportation Engineering
Environmental Engineering
Geotechnical Engineering
Fluid Mechanics and Hydraulic Machines
General Aptitude
EXAM MAP
Medical
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