1
GATE ECE 2015 Set 2
+1
-0.3
The bilateral Laplace transform of a function $$f\left( t \right) = \left\{ {\matrix{ {1\,if\,a \le t \le b} \cr {0\,otherwise} \cr } } \right.$$ is
A
$${{a - b} \over s}\,$$
B
$${{{e^s}\left( {a - b} \right)} \over s}$$
C
$${{{e^{ - as}} - {e^{ - bs}}} \over s}$$
D
$${{{e^{s\left( {a - b} \right)}}} \over s}$$
2
GATE ECE 2014 Set 3
Numerical
+1
-0
The input $$- 3{e^{2t}}\,\,u\left( t \right)$$, where u(t) is the unit step function$$\, {{s - 2} \over {s + 3}}$$. If the initial value of the output is -2, then the value of the output at steady state is _____.
3
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 ____.

4
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
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