GATE ECE 2012 | Transform Theory Question 5 | Engineering Mathematics

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