1
GATE ECE 2015 Set 2
+2
-0.6
Input x(t) and output y(t) of an LTI system are related by the differential equation y"(t) - y'(t) - 6y(t) = x(t). If the system is neither causal nor stable, the imulse response h(t) of the system is
A
$${1 \over 5}{e^{3t}}u( - t) + {1 \over 5}{e^{ - 2t}}u( - t)$$
B
$${{ - 1} \over 5}{e^{3t}}u( - t) + {1 \over 5}{e^{ - 2t}}u( - t)$$
C
$${1 \over 5}{e^{3t}}u( - t) + {1 \over 5}{e^{ - 2t}}u(t)$$
D
$${{ - 1} \over 5}{e^{3t}}u( - t) - {1 \over 5}{e^{ - 2t}}u(t)$$
2
GATE ECE 2015 Set 2
+2
-0.6
The output of a standrad second-order system for a unit step input is given as $$y(t) = 1 - {2 \over {\sqrt 3 }}{e^{ - t}}\cos \left( {\sqrt 3 t - {\pi \over 6}} \right)$$.

The transfer function of the system is

A
$${2 \over {(s + 2)(s + \sqrt 3) }}$$
B
$${1 \over {{s^2} + 2s + 1}}$$
C
$${3 \over {{s^2} + 2s + 3}}$$
D
$${3 \over {{s^2} + 2s + 4}}$$
3
GATE ECE 2013
+2
-0.6
The impulse response of a continuous time system is given by $$h(t) = \delta (t - 1) + \delta (t - 3)$$. The value of the step response at t = 2 is
A
0
B
1
C
2
D
3
4
GATE ECE 2012
+2
-0.6
The input x(t) and output y(t) of a system are related as y(t) = $$\int\limits_{ - \infty }^t x (\tau )\cos (3\tau )d\tau$$.

The system is

A
time-invariant and stable.
B
stable and not time-invariant.
C
time-invariant and not stable.
D
not time-invariant and not stable.
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