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## Marks 1

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The unilateral Laplace transform of $$f(t)$$ is $$\,{1 \over {{s^2} + s + 1}}.$$ The unilateral Laplace transform of $$... GATE IN 2012 If$$x\left[ N \right] = {\left( {1/3} \right)^{\left| n \right|}} - {\left( {1/2} \right)^n}\,u\left[ n \right],$$then... GATE IN 2012$$u(t)$$represents the unit step function. The Laplace transform of$$u\left( {t - \tau } \right)$$is GATE IN 2010 Find$$L\left\{ {{e^{at}}\,\cos \,\omega t} \right\}$$when$$L\left\{ {\cos \,\,\omega t} \right\} = {s \over {{s^2} +...
GATE IN 1995
The laplace transform of a function $$f(t)$$ is defined by $$F\left( s \right) = L\left\{ {f\left( t \right)} \right\} ... GATE IN 1995 ## Marks 2 More Consider the differential equation$${{{d^2}y\left( t \right)} \over {d{t^2}}} + 2{{dy\left( t \right)} \over {dt}} + y...
GATE IN 2012
The integral \int\limits_{ - \alpha }^\alpha \delta \left( {t - {\pi \over 6}} \right)6\,\sin \,\left( t \right)dt\$...
GATE IN 2010

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Class 12