GATE ECE 2014 Set 4 | Transform Theory Question 3 | Engineering Mathematics

GATE ECE 2014 Set 4

MCQ (Single Correct Answer)

-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 $$g\left( t \right) = t.f\left( t \right)?$$

$${{ - s} \over {{{\left( {{s^2} + s + 1} \right)}^2}}}$$

$${{ - \left( {2s + 1} \right)} \over {{{\left( {{s^2} + s + 1} \right)}^2}}}$$

$${s \over {{{\left( {{s^2} + s + 1} \right)}^2}}}$$

$${{2s + 1} \over {{{\left( {{s^2} + s + 1} \right)}^2}}}$$

GATE ECE 2012

MCQ (Single Correct Answer)

-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

$$ - {s \over {{{\left( {{s^2} + s + 1} \right)}^2}}}$$

$$ - {{2s + 1} \over {{{\left( {{s^2} + s + 1} \right)}^2}}}$$

$${s \over {{{\left( {{s^2} + s + 1} \right)}^2}}}$$

$${{2s + 1} \over {{{\left( {{s^2} + s + 1} \right)}^2}}}$$

GATE ECE 2012

MCQ (Single Correct Answer)

-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

$${1 \over 3} < \left| z \right| < 3$$

$${1 \over 3} < \left| z \right| < {1 \over 2}$$

$${1 \over 2} < \left| z \right| < 3$$

$${1 \over 3} < \left| z \right|$$

GATE ECE 2009

MCQ (Single Correct Answer)

-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

$$s\,\,F\left( s \right) - f\left( 0 \right)$$

$${1 \over s}F\left( s \right)$$

$$\int\limits_0^s {f\left( \tau \right)} d\tau $$

$${1 \over s}\left[ {F\left( s \right) - f\left( 0 \right)} \right]$$