1
GATE EE 2012
MCQ (Single Correct Answer)
+2
-0.6
Consider the differential equation
$${{{d^2}y\left( t \right)} \over {d{t^2}}} + 2{{dy\left( t \right)} \over {dt}} + y\left( t \right) = \delta \left( t \right)$$
with $$y\left( t \right)\left| {_{t = 0} = - 2} \right.$$ and $${{dy} \over {dt}}\left| {_{t = 0}} \right. = 0.$$

The numerical value of $${{dy} \over {dt}}\left| {_{t = 0}.} \right.$$ is

A
$$-2$$
B
$$-1$$
C
$$0$$
D
$$-1$$
2
GATE EE 2011
MCQ (Single Correct Answer)
+2
-0.6
Given $$f(t)$$ and $$g(t)$$ as shown below

$$g(t)$$ can be expressed as

A
$$g(t)=f(2t-3)$$
B
$$g\left( t \right) = f\left( {{t \over 2} - 3} \right)$$
C
$$g\left( t \right) = f\left( {2t - {3 \over 2}} \right)$$
D
$$g\left( t \right) = f\left( {{t \over 2} - {3 \over 2}} \right)$$
3
GATE EE 2011
MCQ (Single Correct Answer)
+2
-0.6
Given $$f(t)$$ and $$g(t)$$ as shown below

The laplace transform of $$g(t)$$ is

A
$${1 \over s}\left[ {{e^{ - 3s}} - {e^{ - 5s}}} \right]$$
B
$${1 \over s}\left[ {{e^{ - 5s}} - {e^{ - 3s}}} \right]$$
C
$${{{e^{ - 3s}}} \over s}\left[ {1 - {e^{ - 2s}}} \right]$$
D
$${1 \over s}\left[ {{e^{ - 5s}} - {e^{ - 3s}}} \right]$$
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