GATE EE

Transform Theory

Engineering Mathematics

(Past Years Questions)

Marks 1

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The solution of the differential equation, for $$t > 0,\,\,y''\left( t \right) + 2y'\left( t \right) + y\left( t \right...
GATE EE 2016 Set 2
The Laplace transform of $$f\left( t \right) = 2\sqrt {t/\pi } $$$$\,\,\,\,\,$$ is$$\,\,\,\,\,$$ $${s^{ - 3/2}}.$$ The L...
GATE EE 2015 Set 2
Let $$X\left( s \right) = {{3s + 5} \over {{s^2} + 10s + 20}}$$ be the Laplace Transform of a signal $$x(t).$$ Then $$\...
GATE EE 2014 Set 1
If $$x\left[ N \right] = {\left( {1/3} \right)^{\left| n \right|}} - {\left( {1/2} \right)^n}\,u\left[ n \right],$$ then...
GATE EE 2012
The unilateral Laplace transform of $$f(t)$$ is $$\,{1 \over {{s^2} + s + 1}}.$$ The unilateral Laplace transform of $$...
GATE EE 2012
Given $$f\left( t \right) = {L^{ - 1}}\left[ {{{3s + 1} \over {{s^3} + 4{s^2} + \left( {k - 3} \right)}}} \right].$$ $$...
GATE EE 2010
Let $$Y(s)$$ be the Laplace transform of function $$y(t),$$ then the final value of the function is __________.
GATE EE 2002
The Laplace transform of $$\,\left( {{t^2} - 2t} \right)\,u\left( {t - 1} \right)$$ is ______________.
GATE EE 1998
The Laplace transform of $$f(t)$$ is $$F(s).$$ Given $$F\left( s \right) = {\omega \over {{s^2} + {\omega ^2}}},$$ the ...
GATE EE 1995

Marks 2

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Consider the differential equation $${{{d^2}y\left( t \right)} \over {d{t^2}}} + 2{{dy\left( t \right)} \over {dt}} + y...
GATE EE 2012
Given $$f(t)$$ and $$g(t)$$ as shown below $$g(t)$$ can be expressed as...
GATE EE 2011
Given $$f(t)$$ and $$g(t)$$ as shown below The laplace transform of $$g(t)$$ is ...
GATE EE 2011

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