1
GATE ECE 2000
+1
-0.3
Given that $$L\left[ {f\left( t \right)} \right]\, = \,$$ $${{s + 2} \over {{s^2} + 1}},$$ $$L\left[ {g\left( t \right)} \right] = {{{s^2} + 1} \over {\left( {s + 3} \right)\left( {s + 2} \right)}},$$$$$h\left( t \right) = \int\limits_0^t {f\left( \tau \right)\,g\left( {t - \tau } \right)\,d\tau ,}$$$ $$L\left[ {h\left( t \right)} \right]$$ is
A
$${{{s^2} + 1} \over {s + 3}}$$
B
$${1 \over {s + 3}}$$
C
$${{{s^2} + 1} \over {\left( {s + 3} \right)\left( {s + 2} \right)}} + {{s + 2} \over {{s^2} + 1}}$$
D
None of the above
2
GATE ECE 1999
+1
-0.3
$$If\,\,L\left[ {f\left( t \right)} \right]\, = \,F\left( s \right),$$ then $$L\left[ {f\left( {t - T} \right)} \right]$$ is equal to
A
$${e^{sT}}F\left( s \right)\,$$
B
$${e^{ - sT}}\,F\left( s \right)\,\,$$
C
$${{F\left( s \right)} \over {1 + {e^{sT}}}}\,$$
D
$${{F\left( s \right)} \over {1 - {e^{ - sT}}}}$$
3
GATE ECE 1998
+1
-0.3
If L$$\left[ {f\left( t \right)} \right]$$ = $$\omega /\left( {{s^2} + {\omega ^2}} \right),$$ then the value of $$\matrix{ {Lim\,f\,\left( t \right)} \cr {t \to \infty } \cr }$$
A
cannot be determined
B
is zero
C
is unity
D
is infinite
4
GATE ECE 1997
+1
-0.3
The Laplace Transform of eat .cos$$\left( {\alpha t} \right).u\left( t \right)$$ is equal to
A
$${{\left( {s - \alpha } \right)} \over {{{\left( {s - \alpha } \right)}^2} + {\alpha ^2}}}$$
B
$${{\left( {s + \alpha } \right)} \over {{{\left( {s + \alpha } \right)}^2} + {\alpha ^2}}}$$
C
$${1 \over {{{\left( {s - \alpha } \right)}^2}}}$$
D
none of the above
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