GATE CE

Transform Theory

Engineering Mathematics

(Past Years Questions)

Marks 1

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Given two continuous time signals $$x\left( t \right) = {e^{ - t}}$$ and $$y\left( t \right) = {e^{ - 2t}}$$ which exist...
GATE CE 2011
Laplace transform of $$f\left( x \right) = \cos \,h\left( {ax} \right)$$ is
GATE CE 2009
The Laplace transform of a function $$f(t)$$ is $$$F\left( s \right) = {{5{s^2} + 23s + 6} \over {s\left( {{s^2} + 2s +...
GATE CE 2005
A delayed unit step function is defined as $$$u\left( {t - a} \right) = \left\{ {\matrix{ {0,} & {t Its Laplace tran...
GATE CE 2004
If $$L$$ denotes the laplace transform of a function, $$L\left\{ {\sin \,\,at} \right\}$$ will be equal to
GATE CE 2003
The inverse Laplace transform of $$1/\left( {{s^2} + 2s} \right)$$ is
GATE CE 2001
The Laplace transform of the function $$\eqalign{ & f\left( t \right) = k,\,0 is ...
GATE CE 1999
The Laplace Transform of a unit step function $${u_a}\left( t \right),$$ defined as $$\matrix{ {{u_a}\left( t \right...
GATE CE 1998
$${\left( {s + 1} \right)^{ - 2}}$$ is laplace transform of
GATE CE 1998
The inverse Laplace transform of $${{\left( {s + 9} \right)} \over {\left( {{s^2} + 6s + 13} \right)}}$$ is
GATE CE 1995

Marks 2

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If $$F\left( s \right) = L\left\{ {f\left( t \right)} \right\} = {{2\left( {s + 1} \right)} \over {{s^2} + 4s + 7}}$$ th...
GATE CE 2011
Laplace transform of $$f\left( t \right) = \cos \left( {pt + q} \right)$$ is
GATE CE 2005
The Laplace transform of the following function is $$$f\left( t \right) = \left\{ {\matrix{ {\sin t} & {for\,\,0 \le...
GATE CE 2002
Using Laplace transforms, solve $${a \over {{s^2} - {a^2}}}\,\,\left( {{d^2}y/d{t^2}} \right) + 4y = 12t\,\,$$ given th...
GATE CE 2002
Let $$F\left( s \right) = L\left[ {f\left( t \right)} \right]$$ denote the Laplace transform of the function $$f(t)$$. W...
GATE CE 2000
Using Laplace transform, solve the initial value problem $$9{y^{11}} - 6{y^1} + y = 0$$ $$y\left( 0 \right) = 3$$ and $...
GATE CE 1996

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