GATE EE
Signals and Systems
Continuous Time Signal Laplace Transform
Previous Years Questions

## Marks 1

The Laplace transform of f(t)=$$2\sqrt{t/\mathrm\pi}$$ is $$s^{-3/2}$$. The Laplace transform of g(t)=$$\sqrt{1/\mathrm{πt}}$$ is
Which one of the following statements is NOT TRUE for a continuous time causal and stable LTI system?
The unilateral Laplace transform of f(t) is $$\frac1{s^2\;+\;s\;+\;1}$$. The unilateral Laplace transform of tf(t) is
Let Y(s) be the Laplace transformation of the function y(t), then the final value of the function is
The Laplace transformation of f(t) is F(s). Given F(s)=$$\frac\omega{s^2+\omega^2}$$, the final value of f(t) is

## Marks 2

Let the Laplace transform of a function f(t) which exists for t > 0 be F1(s) and the Laplace transform of its delayed version f(1 - $$\tau$$) be F2...
A function y(t) satisfies the following differential equation:$$\frac{\operatorname dy\left(t\right)}{\operatorname dt}+\;y\left(t\right)\;=\;\delta\... The Laplace transform of a function f(t) is F(s) =$$\frac{5s^2+23s+6}{s\left(s^2+2s+2\right)}$$. As$$t\rightarrow\infty$$, f(t) approaches For the equation$$\ddot x\left(t\right)+3\dot x\left(t\right)+2x\left(t\right)=5$$, the solution x(t) approaches which of the following values as t$$...
A rectangular current pulse of duration T and magnitude 1 has the Laplace transform
The Laplace transform of $$\left(t^2\;-\;2t\right)u\left(t\;-\;1\right)$$ is
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