1
GATE ECE 1999
MCQ (Single Correct Answer)
+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
$${e^{s\,T}}F\left( s \right)$$
B
$${e^{ - s\,T}}F\left( s \right)$$
C
$${{F\left( s \right)} \over {1 - {e^{s\,T}}}}$$
D
$${{F\left( s \right)} \over {1 - {e^{ - s\,T}}}}$$
2
GATE ECE 1998
MCQ (Single Correct Answer)
+1
-0.3
If $$\,\,\,L\,\,\left\{ {f\left( t \right)} \right\} = {w \over {{s^2} + {w^2}}}$$ then the value of
$$\mathop {Lim}\limits_{t \to \infty } f\left( t \right) = $$ ____________.
A
can not be determined
B
zero
C
unity
D
infinite
3
GATE ECE 1997
MCQ (Single Correct Answer)
+1
-0.3
The laplace transform of $${e^{\alpha t}}\,\cos \,\alpha \,t$$ is equal to ____________.
A
$${{s - \alpha } \over {{{\left( {s - \alpha } \right)}^2} + {\alpha ^2}}}$$
B
$${{s + \alpha } \over {{{\left( {s + \alpha } \right)}^2} + {\alpha ^2}}}$$
C
$${1 \over {{{\left( {s - \alpha } \right)}^2}}}$$
D
None
4
GATE ECE 1996
MCQ (Single Correct Answer)
+1
-0.3
The inverse laplace transform of the function $${{s + 5} \over {\left( {s + 1} \right)\left( {s + 3} \right)}}$$ is _______________.
A
$$2\,{e^{ - t}} - {e^{ - 3t}}$$
B
$$2\,{e^{ - t}} + {e^{ - 3t}}$$
C
$${e^{ - t}} - 2\,{e^{ - 3t}}$$
D
$${e^{ - t}} + 2\,{e^{ - 3t}}$$
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