1
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
2
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.
3
GATE ECE 2011
+2
-0.6
An input x(t) = exp( -2t) u(t) + $$\delta$$(t-6) is applied to an LTI system with impulse response h(t) = u(t). The output is
A
[ 1- exp( -2t)] u(t) + u(t+6)
B
[ 1- exp( -2t)] u(t) + u(t-6)
C
0.5 [1 - exp( -2t)] u(t) + u(t+6)
D
0.5 [1- exp( -2t)] u(t) + u(t-6)
4
GATE ECE 2010
+2
-0.6
A continuous time LTI system is described by $${{{d^2}y(t)} \over {d{t^2}}} + 4{{dy(t)} \over {dt}} + 3y(t)\, = 2{{dx(t)} \over {dt}} + 4x(t)$$.

Assuming zero initial conditions, the response y(t) of the above system for the input x(t) = $${e^{ - 2t}}$$ u(t) is given by

A
$$({e^t} - {e^{3t}})\,u(t)$$
B
$$({e^{ - t}} - {e^{ - 3t}})\,u(t)$$
C
$$({e^{ - t}} + {e^{ - 3t}})\,u(t)$$
D
$$({e^t} + {e^{3t}})\,u(t)$$
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