1
GATE EE 2012
+1
-0.3
The unilateral Laplace transform of $$f(t)$$ is
$$\,{1 \over {{s^2} + s + 1}}.$$ The unilateral Laplace transform of $$t$$ $$f(t)$$ is
A
$$- {s \over {{{\left( {{s^2} + s + 1} \right)}^2}}}$$
B
$$- {{2s + 1} \over {{{\left( {{s^2} + s + 1} \right)}^2}}}$$
C
$${s \over {{{\left( {{s^2} + s + 1} \right)}^2}}}$$
D
$${{2s + 1} \over {{{\left( {{s^2} + s + 1} \right)}^2}}}$$
2
GATE EE 2010
+1
-0.3
Given $$f\left( t \right) = {L^{ - 1}}\left[ {{{3s + 1} \over {{s^3} + 4{s^2} + \left( {k - 3} \right)}}} \right].$$
$$\mathop {Lt}\limits_{t \to \propto } \,\,f\left( t \right) = 1$$ then value of $$k$$ is
A
$$1$$
B
$$2$$
C
$$3$$
D
$$4$$
3
GATE EE 2002
+1
-0.3
Let $$Y(s)$$ be the Laplace transform of function $$y(t),$$ then the final value of the function is __________.
A
$$\mathop {Lim}\limits_{s \to 0} \,\,Y\left( s \right)$$
B
$$\mathop {Lim}\limits_{s \to \infty } \,\,Y\left( s \right)$$
C
$$\mathop {Lim}\limits_{s \to 0} \,s\,\,Y\left( s \right)$$
D
$$\mathop {Lim}\limits_{s \to \infty } \,s\,\,Y\left( s \right)$$
4
GATE EE 1998
+1
-0.3
The Laplace transform of $$\,\left( {{t^2} - 2t} \right)\,u\left( {t - 1} \right)$$ is ______________.
A
$${2 \over {{s^3}}}{e^{ - s}} - {2 \over {{s^2}}}{e^{ - s}}$$
B
$$\,\,{2 \over {{s^3}}}{e^{ - 2s}} - {2 \over {{s^2}}}{e^{ - s}}$$
C
$${2 \over {{s^3}}}{e^{ - s}} - {2 \over s}{e^{ - s}}$$
D
None
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