1
GATE ECE 2006
MCQ (Single Correct Answer)
+2
-0.6
Consider the function f(t) having Laplace transform $$F\left( s \right) = {{{\omega _0}} \over {{s^2} + {\omega _0}^2}}\,\,\,\,\,\,{\mathop{\rm Re}\nolimits} \left( s \right) > 0$$

The final value of f(t) would be:

A
0
B
1
C
$$- e\,\,\, - 1 \le f\left( \infty \right) \le 1$$
D
$$\infty$$
2
GATE ECE 2005
MCQ (Single Correct Answer)
+2
-0.6
In what range should Re(s) remain so that the Laplace transform of the function e(a+2)t+5 exists?
A
Re(s) > a+2
B
Re(s) > a+7
C
Re(s) < 2
D
Re(s) > a+5
3
GATE ECE 2002
MCQ (Single Correct Answer)
+2
-0.6
The Laplace transform of a continuous - time signal x(t) is $$X\left( s \right) = {{5 - s} \over {{s^2} - s - 2}}$$. If the Fourier transform of tyhis signal exists, then x(t) is
A
$${e^{2t}}u\left( t \right) - 2\,{e^{ - t}}u\left( t \right)$$
B
$$- {e^{2t}}u\left( { - t} \right) + 2\,{e^{ - t}}u\left( t \right)$$
C
$$- {e^{2t}}u\left( { - t} \right) - 2\,{e^{ - t}}u\left( t \right)$$
D
$${e^{2t}}u\left( { - t} \right) - 2\,{e^{ - t}}u\left( t \right)$$
4
GATE ECE 1996
MCQ (Single Correct Answer)
+2
-0.6
The inverse Laplace transform of the function $${{s + 5} \over {\left( {s + 1} \right)\left( {s + 3} \right)}}$$ is
A
$$\,2{e^{ - t}}\, - \,{e^{ \to - 3t}}$$
B
$$\,2{e^{ - t}}\, + \,{e^{ \to - 3t}}$$
C
$${e^{ - t}}\, - \,2\,{e^{ - 3t}}\,$$
D
$$\,\,{e^{ - t}}\, + \,2{e^{ - 3t}}$$
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