1
GATE ECE 1994
Subjective
+2
-0
Match each of the items A, B and C with an appropriate item from 1, 2, 3, 4 and 5.

List - 1
(A) $${a_1}{{{d^{2y}}} \over {d{x^2}}} + {a_2}y{{dy} \over {dx}} + {a_3}y = {a_4}$$
(B) $${a_1}{{{d^3}y} \over {d{x^3}}} + {a_2}y = {a_3}$$
(C) \eqalign{ & {a_1}{{{d_2}y} \over {d{x_2}}} + {a_2}x{{dy} \over {dx}} + {a_3}\,{x^2}y = 0 \cr & \cr}

List - 2
(1) Non linear differential equation.
(2) Linear differential equation with constant coefficients.
(3) Linear homogeneous differential equation.
(4) Non - Linear homogeneous differential equation.
(5) Non - linear first order differential equation.

2
GATE ECE 1991
+2
-0.6
The voltage across an impedance in a network is V(s) = Z(s) I(s), where V(s), Z(s) and $${\rm I}$$(s) are the Laplace Transforms of the corresponding time functions V(t), z(t) and i(t).

The voltage v(t) is

A
$$v\left( t \right) = z\left( t \right)\,.\,i\left( t \right)$$
B
$$v\left( t \right) = \int\limits_0^t {i\left( \tau \right)\,z\left( {t - \tau } \right)d\tau }$$
C
$$v\left( t \right) = \int\limits_0^t {i\left( \tau \right)z\left( {t + \tau } \right)d\tau }$$
D
$$v\left( t \right) = z\left( t \right) + i\left( t \right)$$
3
GATE ECE 1991
+2
-0.6
An excitation is applied to a system at $$t = T$$ and its response is zero for $$- \infty < t < T$$. Such a system is a
A
non-causal system
B
stable system
C
causal system
D
unstable system
4
GATE ECE 1990
+2
-0.6
The response of an initially relaxed linear constant parameter network to a unit impulse applied at $$t = 0$$ is $$4{e^{ - 2t}}u\left( t \right).$$ The response of this network to a unit step function will be:
A
$$2\left[ {1 - {e^{ - 2t}}} \right]u\left( t \right)$$
B
$$4\left[ {{e^{ - t}} - {e^{ - 2t}}} \right]u\left( t \right)$$
C
$$\sin 2t$$
D
$$\left( {1 - 4{e^{ - 4t}}} \right)u\left( t \right)$$
GATE ECE Subjects
Signals and Systems
Network Theory
Control Systems
Digital Circuits
General Aptitude
Electronic Devices and VLSI
Analog Circuits
Engineering Mathematics
Microprocessors
Communications
Electromagnetics
EXAM MAP
Medical
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