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## Marks 1

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Given two continuous time signals $$x\left( t \right) = {e^{ - t}}$$ and $$y\left( t \right) = {e^{ - 2t}}$$ which exist...
GATE CE 2011
Laplace transform of $$f\left( x \right) = \cos \,h\left( {ax} \right)$$ is
GATE CE 2009
The Laplace transform of a function $$f(t)$$ is $$F\left( s \right) = {{5{s^2} + 23s + 6} \over {s\left( {{s^2} + 2s +... GATE CE 2005 A delayed unit step function is defined as$$u\left( {t - a} \right) = \left\{ {\matrix{ {0,} &amp; {t &lt; a} \cr... GATE CE 2004 If $$L$$ denotes the laplace transform of a function, $$L\left\{ {\sin \,\,at} \right\}$$ will be equal to GATE CE 2003 The inverse Laplace transform of $$1/\left( {{s^2} + 2s} \right)$$ is GATE CE 2001 The Laplace transform of the function \eqalign{ &amp; f\left( t \right) = k,\,0 &lt; t &lt; c \cr &amp; \,\,\,\... GATE CE 1999{\left( {s + 1} \right)^{ - 2}}$$is laplace transform of GATE CE 1998 The Laplace Transform of a unit step function$${u_a}\left( t \right),$$defined as$$\matrix{ {{u_a}\left( t \right... GATE CE 1998 The inverse Laplace transform of $${{\left( {s + 9} \right)} \over {\left( {{s^2} + 6s + 13} \right)}}$$ is GATE CE 1995 ## Marks 2 More If $$F\left( s \right) = L\left\{ {f\left( t \right)} \right\} = {{2\left( {s + 1} \right)} \over {{s^2} + 4s + 7}}$$ th... GATE CE 2011 Laplace transform of $$f\left( t \right) = \cos \left( {pt + q} \right)$$ is GATE CE 2005 Using Laplace transforms, solve $${a \over {{s^2} - {a^2}}}\,\,\left( {{d^2}y/d{t^2}} \right) + 4y = 12t\,\,$$ given th... GATE CE 2002 The Laplace transform of the following function is $$f\left( t \right) = \left\{ {\matrix{ {\sin t} &amp; {for\,\,0... GATE CE 2002 Let$$F\left( s \right) = L\left[ {f\left( t \right)} \right]$$denote the Laplace transform of the function$$f(t)$$. W... GATE CE 2000 Using Laplace transform, solve the initial value problem$$9{y^{11}} - 6{y^1} + y = 0y\left( 0 \right) = 3$and$...
GATE CE 1996

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