1
GATE IN 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
$${1 \over 3} < \left| z \right|$$
2
GATE IN 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
$${{2s + 1} \over {{{\left( {{s^2} + s + 1} \right)}^2}}}$$
3
GATE IN 2010
+1
-0.3
$$u(t)$$ represents the unit step function. The Laplace transform of $$u\left( {t - \tau } \right)$$ is
A
$${1 \over {s\tau }}$$
B
$${1 \over {s - \tau }}$$
C
$${{{e^{ - s\tau }}} \over s}$$
D
$${e^{ - s\tau }}$$
4
GATE IN 1995
Fill in the Blanks
+1
-0
The laplace transform of a function $$f(t)$$ is defined by
$$F\left( s \right) = L\left\{ {f\left( t \right)} \right\} = \int\limits_0^\infty {{e^{ - st}}f\left( t \right)dt.}$$.
Find the inverse laplace transform of $$F(s-a)$$
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