1
GATE ECE 2005
+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
2
GATE ECE 2002
+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
$${e^{2t}}u\left( { - t} \right) - 2\,{e^{ - t}}u\left( t \right)$$
3
GATE ECE 1996
+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
$$\,\,{e^{ - t}}\, + \,2{e^{ - 3t}}$$
4
GATE ECE 1993
+2
-0.6
If $$F\left( s \right) = L\left[ {f\left( t \right)} \right] = {K \over {\left( {s + 1} \right)\,\left( {{s^2} + 4} \right)}}$$ then $$\matrix{ {Lim\,f\,\left( t \right)} \cr {t \to \infty } \cr }$$ is given by
A
K/4
B
zero
C
infinite
D
undefined
EXAM MAP
Medical
NEET