GATE ECE 2012 | GATE ECE Year Wise Previous Years Questions

GATE ECE 2012

MCQ (Single Correct Answer)

-0.6

A fair coin is tossed till a head appears for the first time. The probability that the number of required tosses is odd, is

$$1/3$$

$$1/2$$

$$2/3$$

$$3/4$$

GATE ECE 2012

MCQ (Single Correct Answer)

-0.3

With initial condition $$x\left( 1 \right)\,\,\, = \,\,\,\,0.5,\,\,\,$$ the solution of the differential equation, $$\,\,\,t{{dx} \over {dt}} + x = t\,\,\,$$ is

$$x = t - {1 \over 2}$$

$$x = {t^2} - {1 \over 2}$$

$$xt = {{{t^2}} \over 2}$$

$$x = {t \over 2}$$

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 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

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

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

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

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

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