GATE ECE 2015 Set 1 | GATE ECE Year Wise Previous Years Questions

GATE ECE 2015 Set 1

MCQ (Single Correct Answer)

-0.6

The Solution of the differential equation $$\,{{{d^2}y} \over {d{t^2}}} + 2{{dy} \over {dt}} + y = 0\,\,$$ with $$\,y\left( 0 \right) = {y^1}\left( 0 \right) = 1\,\,$$ is

$$\left( {2 - t} \right){e^t}$$

$$\left( {1 + 2t} \right){e^{ - t}}$$

$$\left( {2 + t} \right){e^{ - t}}$$

$$\left( {1 - 2t} \right){e^t}$$

GATE ECE 2015 Set 1

MCQ (Single Correct Answer)

-0.6

Let $$z=x+iy$$ be a complex variable. Consider that contour integration is performed along the unit circle in anticlockwise direction . Which one of the following statement is NOT TRUE?

The residue of $${z \over {{z^2} - 1}}$$ at $$z=1$$ is $${1 \over 2}$$

$$\oint\limits_C {{z^2}\,\,dz = 0} $$

$${1 \over {2\pi i}}\oint\limits_c {{1 \over z}} dz = 1$$

$$\overline z $$ (complex conjugate of $$z$$ ) is an analytical function.

GATE ECE 2015 Set 1

MCQ (Single Correct Answer)

-0.3

In an 8085 microprocessor, the shift registers which store the result of an addition and the overflew bit are, respectively.

B & F

A & F

H & F

A & C

GATE ECE 2015 Set 1

MCQ (Single Correct Answer)

-0.6

The damping ratio of a series $$RLC$$ circuit can be expressed as

$${{{R^2}C} \over {2L}}$$

$${{2L} \over {{R^2}C}}$$

$${R \over 2}\sqrt {{C \over L}} $$

$${2 \over R}\sqrt {{L \over C}} $$

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