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.
GATE ECE Subjects
Network Theory
Control Systems
Electronic Devices and VLSI
Analog Circuits
Digital Circuits
Microprocessors
Signals and Systems
Communications
Electromagnetics
General Aptitude
Engineering Mathematics
EXAM MAP
Joint Entrance Examination