1
GATE EE 1996
+2
-0.6
The unit impulse response of a system is given as $$c\left( t \right) = - 4{e^{ - t}} + 6{e^{ - 2t}}.\,\,\,$$ The step response of the same system for $$\,t \ge 0$$ is equal to
A
$$- 3{e^{ - 2t}} - 4{e^{ - t}} + 1$$
B
$$- 3{e^{ - 2t}} + 4{e^{ - t}} - 1$$
C
$$- 3{e^{ - 2t}} - 4{e^{ - t}} - 1$$
D
$$3{e^{ - 2t}} + 4{e^{ - t}} - 1$$
2
GATE EE 1996
+2
-0.6
For the system shown in Figure, with a damping ratio $$\xi$$ of $$0.7$$ and an undamped natural frequency $${\omega _n}$$ of $$4$$ rad/sec, the values of $$' K '$$ and $$' a '$$ are
A
$$K = 4,a = 0.35$$
B
$$K = 8,a = 0.455$$
C
$$K = 16,a = 0.225$$
D
$$K = 64,a = 0.9$$
3
GATE EE 1996
+1
-0.3
The closed - loop transfer function of a control system is given by $${{C\left( s \right)} \over {R\left( s \right)}} = {1 \over {\left( {1 + s} \right)}}$$
For the input $$\,r\left( t \right)\,\, = \,\,\sin \,t,$$ the steady state value of $$c(t)$$ is equal to
A
$${1 \over {\sqrt 2 }}\cos t$$
B
$$1$$
C
$${1 \over {\sqrt 2 }}sint$$
D
$${1 \over {\sqrt 2 }}sin\left( {1 - {\pi \over 4}} \right)$$
4
GATE EE 1996
+1
-0.3
The Boolean expression for the output of the logic circuit shown in figure is
A
$$Y = \overline A \overline B + AB + \overline C$$
B
$$Y = \overline A \overline B + AB + C$$
C
$$Y = \overline A B + \overline A B + C$$
D
$$Y = \overline A B + \overline A \overline B + \overrightarrow C$$
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