GATE ECE year:2019 PYQs & Answers — Page 4

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Questions 31–40 of 65. Imported answers require independent review unless marked reviewed.

Topic practice 65 questionsPage 4 of 7

Consider the signal

, where

is in seconds. Its fundamental time period, in seconds, is _____.

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The baseband signal

shown in the figure is phase-modulated to generate the PM signal

. The time

on the x-axis in the figure is in milliseconds. If the carrier frequency is

kHz and

, then the ratio of the minimum instantaneous frequency (in kHz) to the maximum instantaneous frequency (in kHz) is _____ (rounded off to 2 decimal places).

Diagram for Electronics and Communication Engineering question 22

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Radiation resistance of a small dipole current element of length

at a frequency of 3 GHz is 3 ohms. If the length is changed by 1%, then the percentage change in the radiation resistance, rounded off to two decimal places, is _____ %.

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In the circuit shown,

is a square wave of period

with maximum and minimum values of 8 V and -10 V, respectively. Assume that the diode is ideal and

. The average value of

is ____ volts (rounded off to 1 decimal place).

Diagram for Electronics and Communication Engineering question 24

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In the circuit shown, the clock frequency, i.e., the frequency of the Clk signal, is 12 kHz. The frequency of the signal at

is ____ kHz.

Diagram for Electronics and Communication Engineering question 25

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Consider a differentiable function

on the set of real numbers such that

and

. Given these conditions, which one of the following inequalities is necessarily true for all

Your answerChoose one option.

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Consider the line integral

, the integral being taken in a counterclockwise direction over the closed curve

that forms the boundary of the region

shown in the figure below. The region

is the area enclosed by the union of a

rectangle and a semi-circle of radius 1. The line integral evaluates to

Diagram for Electronics and Communication Engineering question 27

Your answerChoose one option.

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Consider a six-point decimation-in-time Fast Fourier Transform (FFT) algorithm, for which the signal-flow graph corresponding to

is shown in the figure. Let

. In the figure, what should be the values of the coefficients

in terms of

so that

is obtained correctly?

Diagram for Electronics and Communication Engineering question 28

Your answerChoose one option.

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It is desired to find a three-tap causal filter which gives zero signal as an output to an input of the form

, where

and

are arbitrary real numbers. The desired three-tap filter is given by

and

for

. What are the values of the filter taps

and

if the output is

for all

, when

is as given above?

Diagram for Electronics and Communication Engineering question 29

Your answerChoose one option.

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In the circuit shown, if

volts,

and

, then the steady-state current

, in milliamperes (mA), is

Diagram for Electronics and Communication Engineering question 30

Your answerChoose one option.

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GATE ECE year:2019 PYQs

Question 21

Question 22

Question 23

Question 24

Question 25

Question 26

Question 27

Question 28

Question 29

Question 30