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1
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
$${{2s + 1} \over {{{\left( {{s^2} + s + 1} \right)}^2}}}$$
2
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
$${{2s + 1} \over {{{\left( {{s^2} + s + 1} \right)}^2}}}$$
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 2009
MCQ (Single Correct Answer)
+1
-0.3
Given that $$F(s)$$ is the one-sided Laplace transform of $$f(t),$$ the Laplace transform of $$\int\limits_0^t {f\left( \tau \right)} d\tau $$ is
A
$$s\,\,F\left( s \right) - f\left( 0 \right)$$
B
$${1 \over s}F\left( s \right)$$
C
$$\int\limits_0^s {f\left( \tau \right)} d\tau $$
D
$${1 \over s}\left[ {F\left( s \right) - f\left( 0 \right)} \right]$$
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Questions Asked from Marks 1
GATE ECE 2015 Set 3 (1) GATE ECE 2014 Set 4 (1) GATE ECE 2012 (2) GATE ECE 2009 (1) GATE ECE 2006 (1) GATE ECE 2005 (1) GATE ECE 2003 (1) GATE ECE 1999 (1) GATE ECE 1998 (1) GATE ECE 1997 (1) GATE ECE 1996 (1) GATE ECE 1995 (1)
GATE ECE Subjects
Signals and Systems
Network Theory
Control Systems
Digital Circuits
General Aptitude
Electronic Devices and VLSI
Analog Circuits
Engineering Mathematics
Microprocessors
Communications
Electromagnetics