ExamSIDE
Questions (Powered by ExamGOAL)
Engineering Mathematics
Linear Algebra
Marks 1Marks 2
Calculus
Marks 1Marks 2
Vector Calculus
Marks 1Marks 2
Complex Variable
Marks 1Marks 2
Probability and Statistics
Marks 1Marks 2
Differential Equations
Marks 1Marks 2
Numerical Methods
Marks 1Marks 2
Transform Theory
Marks 1Marks 2
Next
1
GATE ECE 2015 Set 2
MCQ (Single Correct Answer)
+2
-0.6
The bilateral Laplace transform of a function
$$f\left( t \right) = \left\{ {\matrix{ 1 & {if\,\,a \le t \le b} \cr 0 & {otherwise} \cr } } \right.$$ is
A
$${{a - b} \over s}$$
B
$${{{e^s}\left( {a - b} \right)} \over s}$$
C
$${{{e^{ - as}} - {e^{ - bs}}} \over s}$$
D
$${{{e^{s\left( {a - b} \right)}}} \over s}$$
2
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

A
$$0.2 + 0.8{e^{ - 5t}}$$
B
$$0.2 - 0.2{e^{ - 5t}}$$
C
$$0.8 + 0.2{e^{ - 5t}}$$
D
$$0.8 - 0.8{e^{ - 5t}}$$
3
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 $${{dy} \over {dt}}\left| {_{t = 0}} \right. = 0.$$

The numerical value of $${{dy} \over {dt}}\left| {_{t = 0}.} \right.$$ is

A
$$-2$$
B
$$-1$$
C
$$0$$
D
$$1$$
4
GATE ECE 2005
MCQ (Single Correct Answer)
+2
-0.6
The Dirac delta Function $$\delta \left( t \right)$$ is defined as
A
$$\delta \left( t \right) = \left\{ {\matrix{ 1 & {t = 0} \cr {0\,{\,^,}} & {otherwise} \cr } } \right.$$
B
$$\delta \left( t \right) = \left\{ {\matrix{ \infty & {t = 0} \cr {0\,\,,} & {otherwise} \cr } } \right.$$
C
$$\delta \left( t \right) = \left\{ {\matrix{ 1 & {t = 0} \cr {0\,\,,} & {otherwise} \cr } } \right.$$ and $$\int\limits_{ - \infty }^\infty {\delta \left( t \right)\,dt = 1} $$
D
$$\delta \left( t \right) = \left\{ {\matrix{ \infty & {t = 0} \cr {0\,\,,} & {otherwise} \cr } } \right.$$ and $$\int\limits_{ - \infty }^\infty {\delta \left( t \right)\,dt = 1} $$
Next
Questions Asked from Marks 2
GATE ECE 2015 Set 2 (1) GATE ECE 2014 Set 1 (1) GATE ECE 2012 (1) GATE ECE 2005 (1) GATE ECE 2000 (1)
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