1
GATE ECE 2015 Set 2
MCQ (Single Correct Answer)
+2
-0.6
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 1
MCQ (Single Correct Answer)
+2
-0.6
A system is described by the following differential equation, where $$u(t)$$ is the input to the system and $$y(t)$$ is the output of the system. $$\mathop y\limits^ \bullet \left( t \right) + 5y\left( t \right) = u\left( t \right)$$\$

When $$y(0)=1$$ and $$u(t)$$ is a unit step function, $$y(t)$$ is

A
$$0.2 + 0.8{e^{ - 5t}}$$
B
$$0.2 - 0.2{e^{ - 5t}}$$
C
$$0.8 + 0.2{e^{ - 5t}}$$
D
$$0.8 - 0.8{e^{ - 5t}}$$
3
GATE ECE 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
$$1$$
4
GATE ECE 2005
MCQ (Single Correct Answer)
+2
-0.6
The Dirac delta Function $$\delta \left( t \right)$$ is defined as
A
$$\delta \left( t \right) = \left\{ {\matrix{ 1 & {t = 0} \cr {0\,{\,^,}} & {otherwise} \cr } } \right.$$
B
$$\delta \left( t \right) = \left\{ {\matrix{ \infty & {t = 0} \cr {0\,\,,} & {otherwise} \cr } } \right.$$
C
$$\delta \left( t \right) = \left\{ {\matrix{ 1 & {t = 0} \cr {0\,\,,} & {otherwise} \cr } } \right.$$ and $$\int\limits_{ - \infty }^\infty {\delta \left( t \right)\,dt = 1}$$
D
$$\delta \left( t \right) = \left\{ {\matrix{ \infty & {t = 0} \cr {0\,\,,} & {otherwise} \cr } } \right.$$ and $$\int\limits_{ - \infty }^\infty {\delta \left( t \right)\,dt = 1}$$
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