GATE EE
Engineering Mathematics
Transform Theory
Previous Years Questions

## Marks 1

The solution of the differential equation, for $$t > 0,\,\,y''\left( t \right) + 2y'\left( t \right) + y\left( t \right) = 0$$ with initial condit...
The Laplace transform of $$f\left( t \right) = 2\sqrt {t/\pi }$$$$\,\,\,\,\,$$ is$$\,\,\,\,\,$$ $${s^{ - 3/2}}.$$ The Laplace transform of $$g\left( ... Let$$X\left( s \right) = {{3s + 5} \over {{s^2} + 10s + 20}}$$be the Laplace Transform of a signal$$x(t).$$Then$$\,x\left( {{0^ + }} \right)$$i... If$$x\left[ N \right] = {\left( {1/3} \right)^{\left| n \right|}} - {\left( {1/2} \right)^n}\,u\left[ n \right],$$then the region of convergence$$(...
The unilateral Laplace transform of $$f(t)$$ is $$\,{1 \over {{s^2} + s + 1}}.$$ The unilateral Laplace transform of $$t$$ $$f(t)$$ is
Given $$f\left( t \right) = {L^{ - 1}}\left[ {{{3s + 1} \over {{s^3} + 4{s^2} + \left( {k - 3} \right)}}} \right].$$ $$\mathop {Lt}\limits_{t \to \p... Let$$Y(s)$$be the Laplace transform of function$$y(t),$$then the final value of the function is __________. The Laplace transform of$$\,\left( {{t^2} - 2t} \right)\,u\left( {t - 1} \right)$$is ______________. The Laplace transform of$$f(t)$$is$$F(s).$$Given$$F\left( s \right) = {\omega \over {{s^2} + {\omega ^2}}},$$the final value of$$f(t)$$is ___... ## Marks 2 Consider the differential equation$${{{d^2}y\left( t \right)} \over {d{t^2}}} + 2{{dy\left( t \right)} \over {dt}} + y\left( t \right) = \delta \lef...
Given $$f(t)$$ and $$g(t)$$ as shown below $$g(t)$$ can be expressed as...
Given $$f(t)$$ and $$g(t)$$ as shown below The laplace transform of $$g(t)$$ is ...
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