GATE ECE
Engineering Mathematics
Transform Theory
Previous Years Questions

## Marks 1

Consider the function $$g\left( t \right) = {e^{ - t}}\,\sin \left( {2\pi t} \right)u\left( t \right)$$ ,where $$u(t)$$ is the unit step function. The...
The unilateral Laplace transform of $$f(t)$$ is $${1 \over {{s^2} + s + 1}}$$. Which one of the following is the unilateral Laplace transform of $$g\l... If$$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 that $$F(s)$$ is the one-sided Laplace transform of $$f(t),$$ the Laplace transform of $$\int\limits_0^t {f\left( \tau \right)} d\tau$$ is
Consider the function $$f(t)$$ having laplace transform $$F\left( s \right) = {{{\omega _0}} \over {{s^2} + \omega _0^2}},\,\,{\mathop{\rm Re}\nolimi... In what range should$$Re(s)$$remain so that the laplace transform of the function$${e^{\left( {a + 2} \right)t + 5}}$$exists? The laplace transform of$$i(t)$$is given by$$I\left( s \right) = {2 \over {s\left( {1 + s} \right)}}$$As$$t \to \infty ,$$the value of$$i(t)$$... If$$\,\,L\left\{ {f\left( t \right)} \right\} = F\left( s \right)$$then$$\,\,\,L\left\{ {f\left( {t - T} \right)} \right\}$$is equal to If$$\,\,\,L\,\,\left\{ {f\left( t \right)} \right\} = {w \over {{s^2} + {w^2}}}$$then the value of$$\mathop {Lim}\limits_{t \to \infty } f\left( t...
The laplace transform of $${e^{\alpha t}}\,\cos \,\alpha \,t$$ is equal to ____________.
The inverse laplace transform of the function $${{s + 5} \over {\left( {s + 1} \right)\left( {s + 3} \right)}}$$ is _______________.
If $$L\left\{ {f\left( t \right)} \right\} = {{2\left( {s + 1} \right)} \over {{s^2} + 2s + 5}}$$ then $$f\left( {{0^ + }} \right)$$ and $$f\left( \p... ## Marks 2 The bilateral Laplace transform of a function$$f\left( t \right) = \left\{ {\matrix{ 1 & {if\,\,a \le t \le b} \cr 0 & {otherwise} ...
A system is described by the following differential equation, where $$u(t)$$ is the input to the system and $$y(t)$$ is the output of the system. $$... Consider the differential equation$${{{d^2}y\left( t \right)} \over {d{t^2}}} + 2{{dy\left( t \right)} \over {dt}} + y\left( t \right) = \delta \lef...
The Dirac delta Function $$\delta \left( t \right)$$ is defined as
If $$\,\,\,$$ L\left\{ {f\left( t \right)} \right\} = {{s + 2} \over {{s^2} + 1}},\,\,L\left\{ {g\left( t \right)} \right\} = {{{s^2} + 1} \over {\...
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