GATE ECE year:2021 PYQs & Answers — Page 4

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

The autocorrelation function

of a wide-sense stationary random process

is shown in the figure. The average power of

is ______.

Diagram for Electronics and Communication Engineering question 21

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Consider a carrier signal which is amplitude modulated by a single-tone sinusoidal message signal with a modulation index of 50%. If the carrier and one of the sidebands are suppressed in the modulated signal, the percentage of power saved (rounded off to one decimal place) is ______.

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A speech signal, band limited to 4 kHz, is sampled at 1.25 times the Nyquist rate. The speech samples, assumed to be statistically independent and uniformly distributed in the range −5 V to +5 V, are subsequently quantized in an 8-bit uniform quantizer and transmitted over a voice-grade AWGN telephone channel. If the ratio of transmitted signal power to channel noise power is 26 dB, the minimum channel bandwidth required to ensure reliable transmission of the signal with arbitrarily small probability of transmission error (rounded off to two decimal places) is ______ kHz.

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A 4 kHz sinusoidal message signal having amplitude 4 V is fed to a delta modulator (DM) operating at a sampling rate of 32 kHz. The minimum step size required to avoid slope overload noise in the DM (rounded off to two decimal places) is ______ V.

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The refractive indices of the core and cladding of an optical fiber are 1.50 and 1.48, respectively. The critical propagation angle, which is defined as the maximum angle that the light beam makes with the axis of the optical fiber to achieve the total internal reflection, (rounded off to two decimal places) is ______ degree.

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Consider the integral

where

is a counter-clockwise oriented circle defined as

. The value of the integral is

Your answerChoose one option.

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A box contains the following three coins. I. A fair coin with head on one face and tail on the other face. II. A coin with heads on both the faces. III. A coin with tails on both the faces.

A coin is picked randomly from the box and tossed. Out of the two remaining coins in the box, one coin is then picked randomly and tossed. If the first toss results in a head, the probability of getting a head in the second toss is

Your answerChoose one option.

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The switch in the circuit in the figure is in position P for a long time and then moved to position Q at time

Diagram for Electronics and Communication Engineering question 28

The value of

Your answerChoose one option.

0 V/s

3 V/s

−3 V/s

−5 V/s

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Consider the two-port network shown in the figure.

Diagram for Electronics and Communication Engineering question 29

The admittance parameters, in siemens, are

Your answerChoose one option.

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For an n-channel silicon MOSFET with 10 nm gate oxide thickness, the substrate sensitivity

is found to be 50 mV/V at a substrate voltage

V, where

is the threshold voltage of the MOSFET. Assume that,

, where

is the separation between the Fermi energy level

and the intrinsic level

in the bulk. Parameters given are

Electron charge

C Vacuum permittivity

F/m Relative permittivity of silicon

Relative permittivity of oxide

The doping concentration of the substrate is

Your answerChoose one option.

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GATE ECE year:2021 PYQs

Question 21

Question 22

Question 23

Question 24

Question 25

Question 26

Question 27

Question 28

Question 29

Question 30