GATE CE
Engineering Mathematics
Transform Theory
Previous Years Questions

## Marks 1

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 conv...
Laplace transform of $$f\left( x \right) = \cos \,h\left( {ax} \right)$$ is
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 $$t \to \... A delayed unit step function is defined as$$$u\left( {t - a} \right) = \left\{ {\matrix{ {0,} & {t < a} \cr {1,} & {t \ge a} \cr...
If $$L$$ denotes the laplace transform of a function, $$L\left\{ {\sin \,\,at} \right\}$$ will be equal to
The inverse Laplace transform of $$1/\left( {{s^2} + 2s} \right)$$ is
The Laplace transform of the function \eqalign{ & f\left( t \right) = k,\,0 < t < c \cr & \,\,\,\,\,\,\,\,\, = 0,\,c < t <... The Laplace Transform of a unit step function{u_a}\left( t \right),$$defined as$$\matrix{ {{u_a}\left( t \right) = 0} & {for\,\,\,t < ...
$${\left( {s + 1} \right)^{ - 2}}$$ is laplace transform of
The inverse Laplace transform of $${{\left( {s + 9} \right)} \over {\left( {{s^2} + 6s + 13} \right)}}$$ is

## Marks 2

If $$F\left( s \right) = L\left\{ {f\left( t \right)} \right\} = {{2\left( {s + 1} \right)} \over {{s^2} + 4s + 7}}$$ then the initial and final value...
Laplace transform of $$f\left( t \right) = \cos \left( {pt + q} \right)$$ is
The Laplace transform of the following function is $$f\left( t \right) = \left\{ {\matrix{ {\sin t} & {for\,\,0 \le t \le \pi } \cr 0 &a... Using Laplace transforms, solve$${a \over {{s^2} - {a^2}}}\,\,\left( {{d^2}y/d{t^2}} \right) + 4y = 12t\,\,$$given that$$y=0$$and$$dy/dt=9$$at ... Let$$F\left( s \right) = L\left[ {f\left( t \right)} \right]$$denote the Laplace transform of the function$$f(t)$$. Which of the following statemen... Using Laplace transform, solve the initial value problem$$9{y^{11}} - 6{y^1} + y = 0y\left( 0 \right) = 3$$and$${y^1}\left( 0 \right) = 1, ...
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