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
Strength of Materials Or Solid Mechanics
Reinforced Cement Concrete
Steel Structures
Irrigation
Environmental Engineering
Engineering Mathematics
Structural Analysis
Geotechnical Engineering
Fluid Mechanics and Hydraulic Machines
General Aptitude
EXAM MAP
Joint Entrance Examination