1
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
$$\,\,{e^{ - t}}\, + \,2{e^{ - 3t}}$$
2
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
3
GATE ECE 1993
Fill in the Blanks
+2
-0
The Laplace transform of the periodioc function f(t) describe4d by the curve below, i.e., $$f\left( t \right) = \left\{ {\matrix{ {\sin \,t\,\,\,if\,\left( {2n - 1} \right)\pi \le t \le 2n\pi } \cr {0\,\,\,\,\,\,\,\,otherwise} \cr } } \right.$$
is _________. (fill in the blank), n is an integer.
4
GATE ECE 1988
+2
-0.6
The Laplace transform of a function f(t)u(t), where f(t) is periodic with period T, is A(s) times the Laplace transform of its first period. Then
A
A(s) = s
B
A(s) = 1/(1-exp(-Ts))
C
A(s) = 1/(1+exp(-Ts))
D
A(s) = exp (Ts)
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