1
GATE ECE 2015 Set 3
Numerical
+1
-0
Consider the function $$g\left( t \right) = {e^{ - t}}\,\sin \left( {2\pi t} \right)u\left( t \right)$$ ,where $$u(t)$$ is the unit step function. The area under $$g(t)$$ is _______________.
Your input ____
2
GATE ECE 2014 Set 4
MCQ (Single Correct Answer)
+1
-0.3
The unilateral Laplace transform of $$f(t)$$ is $${1 \over {{s^2} + s + 1}}$$. Which one of the following is the unilateral Laplace transform of $$g\left( t \right) = t.f\left( t \right)?$$
A
$${{ - s} \over {{{\left( {{s^2} + s + 1} \right)}^2}}}$$
B
$${{ - \left( {2s + 1} \right)} \over {{{\left( {{s^2} + s + 1} \right)}^2}}}$$
C
$${s \over {{{\left( {{s^2} + s + 1} \right)}^2}}}$$
D
$${{2s + 1} \over {{{\left( {{s^2} + s + 1} \right)}^2}}}$$
3
GATE ECE 2012
MCQ (Single Correct Answer)
+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
$${1 \over 3} < \left| z \right|$$
4
GATE ECE 2012
MCQ (Single Correct Answer)
+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
$${{2s + 1} \over {{{\left( {{s^2} + s + 1} \right)}^2}}}$$
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