1
GATE EE 2017 Set 1
Numerical
+2
-0
For a system having transfer function $$G\left( s \right) = {{ - s + 1} \over {s + 1}},$$ a unit step input is applied at time $$t=0.$$ The value of the response of the system at $$t=1.5$$ sec (round off to three decimal places) is __________.
2
GATE EE 2017 Set 1
+2
-0.6
Let a causal $$LTI$$ system be characterized by the following differential equation, with initial rest condition
$${{{d^2}y} \over {d{t^2}}} + 7{{dy} \over {dt}} + 10y\left( t \right) = 4x\left( t \right) + 5{{dx\left( t \right)} \over {dt}}\,\,$$

Where, $$x(t)$$ and $$y(t)$$ are the input and output respectively. The impulse response of the system is ($$u(t)$$ is the unit step function)

A
$$2{e^{ - 2t}}u\left( t \right) - 7{e^{ - 5t}}u\left( t \right)$$
B
$$- 2{e^{ - 2t}}u\left( t \right) + 7{e^{ - 5t}}u\left( t \right)$$
C
$$7{e^{ - 2t}}u\left( t \right) - 2{e^{ - 5t}}u\left( t \right)$$
D
$$- 7{e^{ - 2t}}u\left( t \right) + 2{e^{ - 5t}}u\left( t \right)$$
3
GATE EE 2002
+2
-0.6
The transfer function of the system described by $${{{d^2}y} \over {d{t^2}}} + {{dy} \over {dt}} = {{du} \over {dt}} + 2u$$ with $$u$$ as input and $$y$$ as output is
A
$${{\left( {s + 2} \right)} \over {\left( {{s^2} + s} \right)}}$$
B
$${{\left( {s + 1} \right)} \over {\left( {{s^2} + s} \right)}}$$
C
$${2 \over {\left( {{s^2} + s} \right)}}$$
D
$${{2s} \over {\left( {{s^2} + s} \right)}}$$
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