1
GATE ECE 2007
+1
-0.3
If the Laplace transform of a signal y(t) is $$Y\left( s \right) = {1 \over {s\left( {s - 1} \right)}},$$ then its final value is
A
-1
B
0
C
1
D
Unbounded
2
GATE ECE 2003
+1
-0.3
The Laplace transform of i(t) tends to
$$I\left( s \right)\,\, = \,{2 \over {s\left( {1 + s} \right)}}$$

As $$t \to \infty$$ , the value of i(t) tends to

A
0
B
1
C
2
D
3
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
4
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
$${{F\left( s \right)} \over {1 - {e^{ - sT}}}}$$
EXAM MAP
Medical
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