GATE ECE 2016 Set 1 | GATE ECE Year Wise Previous Years Questions

GATE ECE 2016 Set 1

Numerical

-0

Two random variables $$X$$ and $$Y$$ are distributed according to $$${f_{X,Y}}\left( {x,y} \right) = \left\{ {\matrix{ {\left( {x + y} \right),} & {0 \le x \le 1,} & {0 \le y \le 1} \cr {0,} & {otherwise} & \, \cr } } \right.$$$

The probability $$P\left( {X + Y \le 1} \right)$$ is ________.

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GATE ECE 2016 Set 1

Numerical

-0

In the following integral, the contour $$C$$ encloses the points $${2\pi j}$$ and $$-{2\pi j}$$. The value of the integral $$ - {1 \over {2\pi }}\oint\limits_c {{{\sin z} \over {{{\left( {z - 2\pi j} \right)}^3}}}} dz$$ is ___________.

Your input ____

GATE ECE 2016 Set 1

MCQ (Single Correct Answer)

-0.6

In an 8085 system, a PUSH operation requires more clock cycles than a POP operation. Which one of the following options is the correct reason for this?

For POP, the data transceivers remain in the same direction as for instruction fetch (memory to processor), whereas for PUSH their direction has to be reversed.

Memory write operations are slower than memory read operations in an 8085 based system.

The stack pointer needs to be pre-decremented before writing registers in a PUSH, whereas a POP operation uses the address already in the stack pointer.

Order of registers has to be interchanged for a PUSH operation, whereas POP uses their natural order.

GATE ECE 2016 Set 1

MCQ (Single Correct Answer)

-0.6

A network consisting of a finite number of linear resistor (R), inductor (L), and capacitor (C) elements, connected all in series or all in parallel, is excited with a source of the form
$$\sum\limits_{k = 1}^3 {{a_k}\,\,\cos \,\left( {k{\omega _0}t} \right),\,\,\,} $$ where $${a_k} \ne 0,\,\,{\omega _0} \ne 0$$.

The source has nonzero impedance. Which one of the following is a possible form of the output measured across a resistor in the network?

$$\sum\limits_{k = 1}^3 {{b_k}{\mkern 1mu} {\mkern 1mu} \cos \left( {k{\omega _0}t + {\phi _k}} \right),{\mkern 1mu} {\mkern 1mu} {\mkern 1mu} } $$ where $${b_k} \ne {a_k},\,\,\forall k$$

$$\sum\limits_{k = 1}^3 {{b_k}\,\,\cos \left( {k{\omega _0}t + {\phi _k}} \right)\,\,\,} $$ , where $${b_k} \ne 0,\,\,\forall k$$

$$\sum\limits_{k = 1}^3 {{a_k}\,\,\cos \left( {k{\omega _0}t + {\phi _k}} \right)\,\,\,} $$

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