GATE ME 2015 Set 1 | Transform Theory Question 7 | Engineering Mathematics

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GATE ME 2015 Set 1

MCQ (Single Correct Answer)

-0.3

The Laplace Transform of $$f\left( t \right) = {e^{2t}}\sin \left( {5t} \right)\,u\left( t \right)$$ is

$${5 \over {{s^2} - 4s + 29}}$$

$${5 \over {{s^2} + 5}}$$

$${{s - 2} \over {{s^2} - 4s + 29}}$$

$${5 \over {s + 5}}$$

GATE ME 2014 Set 4

MCQ (Single Correct Answer)

-0.3

Laplace transform of $$\cos \,\left( {\omega t} \right)$$ is $${s \over {{s^2} + {\omega ^2}.}}$$. The Laplace transform of $${e^{ - 2t}}\,\cos \left( {4t} \right)$$ is

$${{s - 2} \over {{{\left( {s - 2} \right)}^2} + 16}}$$

$${{s + 2} \over {{{\left( {s - 2} \right)}^2} + 16}}$$

$${{s - 2} \over {{{\left( {s + 2} \right)}^2} + 16}}$$

$${{s + 2} \over {{{\left( {s + 2} \right)}^2} + 16}}$$

GATE ME 2013

MCQ (Single Correct Answer)

-0.3

The function $$f(t)$$ satisfies the differential equation $${{{d^2}f} \over {d{t^2}}} + f = 0$$ and the auxiliary conditions, $$f\left( 0 \right) = 0,\,{{df} \over {dt}}\left( 0 \right) = 4.$$ The laplace transform of $$f(t)$$ is given by

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

$${4 \over {s + 1}}$$

$${4 \over {{s^2} + 1}}$$

$${2 \over {{s^4} + 1}}$$

GATE ME 2012

MCQ (Single Correct Answer)

-0.3

The inverse Laplace transform of the function $$F\left( s \right) = {1 \over {s\left( {s + 1} \right)}}$$ is given by

$$f\left( t \right) = \sin \,t$$

$$f\left( t \right) = {e^{ - t}}\sin \,t$$

$$f\left( t \right) = {e^{ - t}}$$

$$f\left( t \right) = 1 - {e^{ - t}}$$