1
GATE ECE 2014 Set 1
Numerical
+1
-0
A continuous, linear time - invariant fiilter has an impulse response h(t) described by $$h\left( t \right) = \left\{ {\matrix{ {3\,for\,0 \le t \le 3} \cr {0\,otherwise} \cr } } \right.$$

Whjen a constant input of value 5 is applied to this filter, the steady state output is ____.

Your input ____
2
GATE ECE 2007
MCQ (Single Correct Answer)
+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
3
GATE ECE 2003
MCQ (Single Correct Answer)
+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
4
GATE ECE 2000
MCQ (Single Correct Answer)
+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
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