1
GATE ECE 2014 Set 1
MCQ (Single Correct Answer)
+2
-0.6
A system is described by the following differential equation, where $$u(t)$$ is the input to the system and $$y(t)$$ is the output of the system.
$$$\mathop y\limits^ \bullet \left( t \right) + 5y\left( t \right) = u\left( t \right)$$$
When $$y(0)=1$$ and $$u(t)$$ is a unit step function, $$y(t)$$ is
2
GATE ECE 2012
MCQ (Single Correct Answer)
+2
-0.6
Consider the differential equation
$${{{d^2}y\left( t \right)} \over {d{t^2}}} + 2{{dy\left( t \right)} \over {dt}} + y\left( t \right) = \delta \left( t \right)$$
with $$y\left( t \right)\left| {_{t = 0} = - 2} \right.$$ and $${{dy} \over {dt}}\left| {_{t = 0}} \right. = 0.$$
$${{{d^2}y\left( t \right)} \over {d{t^2}}} + 2{{dy\left( t \right)} \over {dt}} + y\left( t \right) = \delta \left( t \right)$$
with $$y\left( t \right)\left| {_{t = 0} = - 2} \right.$$ and $${{dy} \over {dt}}\left| {_{t = 0}} \right. = 0.$$
The numerical value of $${{dy} \over {dt}}\left| {_{t = 0}.} \right.$$ is
3
GATE ECE 2005
MCQ (Single Correct Answer)
+2
-0.6
The Dirac delta Function $$\delta \left( t \right)$$ is defined as
4
GATE ECE 2000
MCQ (Single Correct Answer)
+2
-0.6
If $$\,\,\,$$ $$L\left\{ {f\left( t \right)} \right\} = {{s + 2} \over {{s^2} + 1}},\,\,L\left\{ {g\left( t \right)} \right\} = {{{s^2} + 1} \over {\left( {s + 3} \right)\left( {s + 2} \right)}},$$
$$h\left( t \right) = \int\limits_0^t {f\left( T \right)} g\left( {t - T} \right)dT$$
then $$L\left\{ {h\left( t \right)} \right\}$$ is _______________.
$$h\left( t \right) = \int\limits_0^t {f\left( T \right)} g\left( {t - T} \right)dT$$
then $$L\left\{ {h\left( t \right)} \right\}$$ is _______________.
Questions Asked from Transform Theory (Marks 2)
Number in Brackets after Paper Indicates No. of Questions
GATE ECE Subjects
Signals and Systems
Representation of Continuous Time Signal Fourier Series Fourier Transform Continuous Time Signal Laplace Transform Discrete Time Signal Fourier Series Fourier Transform Discrete Fourier Transform and Fast Fourier Transform Discrete Time Signal Z Transform Continuous Time Linear Invariant System Discrete Time Linear Time Invariant Systems Transmission of Signal Through Continuous Time LTI Systems Sampling Transmission of Signal Through Discrete Time Lti Systems Miscellaneous
Network Theory
Control Systems
Digital Circuits
General Aptitude
Electronic Devices and VLSI
Analog Circuits
Engineering Mathematics
Microprocessors
Communications
Electromagnetics