GATE ECE 2014 Set 1 | Transform Theory Question 4 | Engineering Mathematics

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

$$0.2 + 0.8{e^{ - 5t}}$$

$$0.2 - 0.2{e^{ - 5t}}$$

$$0.8 + 0.2{e^{ - 5t}}$$

$$0.8 - 0.8{e^{ - 5t}}$$

GATE ECE 2012

MCQ (Single Correct Answer)

-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

$$-2$$

$$-1$$

$$0$$

$$1$$

GATE ECE 2005

MCQ (Single Correct Answer)

-0.6

The Dirac delta Function $$\delta \left( t \right)$$ is defined as

$$\delta \left( t \right) = \left\{ {\matrix{ 1 & {t = 0} \cr {0\,{\,^,}} & {otherwise} \cr } } \right.$$

$$\delta \left( t \right) = \left\{ {\matrix{ \infty & {t = 0} \cr {0\,\,,} & {otherwise} \cr } } \right.$$

$$\delta \left( t \right) = \left\{ {\matrix{ 1 & {t = 0} \cr {0\,\,,} & {otherwise} \cr } } \right.$$ and $$\int\limits_{ - \infty }^\infty {\delta \left( t \right)\,dt = 1} $$

$$\delta \left( t \right) = \left\{ {\matrix{ \infty & {t = 0} \cr {0\,\,,} & {otherwise} \cr } } \right.$$ and $$\int\limits_{ - \infty }^\infty {\delta \left( t \right)\,dt = 1} $$

GATE ECE 2000

MCQ (Single Correct Answer)

-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 _______________.

$${{{s^2} + 1} \over {s + 3}}$$

$${1 \over {s + 3}}$$

$${{{s^2} + 1} \over {\left( {s + 3} \right)\left( {s + 2} \right)}} + {{s + 2} \over {{s^2} + 1}}$$

None

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