1
GATE EE 2016 Set 2
+1
-0.3
The solution of the differential equation, for
$$t > 0,\,\,y''\left( t \right) + 2y'\left( t \right) + y\left( t \right) = 0$$ with initial conditions $$y\left( 0 \right) = 0$$ and $$y'\left( 0 \right) = 1,$$ is $$\left[ {u\left( t \right)} \right.$$ denotes the unit step function$$\left. \, \right]$$,
A
$$t{e^{ - t}}\,u\left( t \right)$$
B
$$\left( {{e^{ - t}} - t{e^{ - t}}} \right)u\left( t \right)$$
C
$$\left( { - {e^{ - t}} + t{e^{ - t}}} \right)u\left( t \right)$$
D
$${e^{ - t}}u\left( t \right)$$
2
GATE EE 2015 Set 2
+1
-0.3
The Laplace transform of $$f\left( t \right) = 2\sqrt {t/\pi }$$$$\,\,\,\,\,$$ is$$\,\,\,\,\,$$ $${s^{ - 3/2}}.$$ The Laplace transform of $$g\left( t \right) = \sqrt {1/\pi t}$$ is
A
$$3{s^{ - 5/2}}/2$$
B
$${s^{ - 1/2}}$$
C
$${s^{1/2}}$$
D
$${s^{3/2}}$$
3
GATE EE 2014 Set 1
+1
-0.3
Let $$X\left( s \right) = {{3s + 5} \over {{s^2} + 10s + 20}}$$ be the Laplace Transform of a signal $$x(t).$$
Then $$\,x\left( {{0^ + }} \right)$$ is
A
$$0$$
B
$$3$$
C
$$5$$
D
$$21$$
4
GATE EE 2012
+1
-0.3
If $$x\left[ N \right] = {\left( {1/3} \right)^{\left| n \right|}} - {\left( {1/2} \right)^n}\,u\left[ n \right],$$ then the region of convergence $$(ROC)$$ of its $$Z$$-transform in the $$Z$$-plane will be
A
$${1 \over 3} < \left| z \right| < 3$$
B
$${1 \over 3} < \left| z \right| < {1 \over 2}$$
C
$${1 \over 2} < \left| z \right| < 3$$
D
$${1 \over 3} < \left| z \right|$$
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