GATE ECE year:2017 PYQs & Answers — Page 11

Questions 101–110 of 130. Imported answers require independent review unless marked reviewed.

Let

be a wide sense stationary random process with the power spectral density

as shown in Figure (a), where

is in Hertz (Hz).

Diagram for Electronics and Communication Engineering question 51

The random process

is input to an ideal lowpass filter with the frequency response

as shown in Figure (b).

Diagram for Electronics and Communication Engineering question 51 (figure 2)

The output of the lowpass filter is

Let

be the expectation operator and consider the following statements:

II.

III.

Select the correct option:

Your answerChoose one option.

only I is true

only II and III are true

only I and II are true

only I and III are true

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A modulating signal given by

V is fed to a phase modulator with phase deviation constant

rad/V. If the carrier frequency is 20 kHz, the instantaneous frequency (in kHz) at

ms is __________

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A continuous time signal

, where

is in seconds, is the input to a linear time invariant (LTI) filter with the impulse response

Let

be the output of this filter. The maximum value of

is ________.

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Consider a binary memoryless channel characterized by the transition probability diagram shown in the figure.

Diagram for Electronics and Communication Engineering question 52

The channel is

Your answerChoose one option.

lossless

noiseless

useless

deterministic

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An optical fiber is kept along the

direction. The refractive indices for the electric fields along

and

directions in the fiber are

and

, respectively (

due to the imperfection in the fiber cross-section). The free space wavelength of a light wave propagating in the fiber is 1.5

m. If the lightwave is circularly polarized at the input of the fiber, the minimum propagation distance after which it becomes linearly polarized, in centimetres, is ________.

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An electron (

) is moving in free space with velocity

m/s towards a stationary electron (

) far away. The closest distance that this moving electron gets to the stationary electron before the repulsive force diverts its path is __________

m. [Given, mass of electron

kg, charge of electron

C, and permittivity

F/m]

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The expression for an electric field in free space is

, where

represent the spatial coordinates,

represents time, and

are constants. This electric field

Your answerChoose one option.

does not represent a plane wave.

represents a circularly polarized plane wave propagating normal to the z-axis.

represents an elliptically polarized plane wave propagating along the x-y plane.

represents a linearly polarized plane wave.

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Standard air-filled rectangular waveguides of dimensions

cm and

cm are designed for radar applications. It is desired that these waveguides operate only in the dominant

mode with the operating frequency at least 25% above the cutoff frequency of the

mode but not higher than 95% of the next higher cutoff frequency. The range of the allowable operating frequency

Your answerChoose one option.

8.19 GHz

13.1 GHz

8.19 GHz

12.45 GHz

6.55 GHz

13.1 GHz

1.64 GHz

10.24 GHz

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A half wavelength dipole is kept in the

plane and oriented along 45° from the

-axis. Determine the direction of null in the radiation pattern for

. Here the angle

(

) is measured from the z-axis, and the angle

(

) is measured from the x-axis in the

plane.

Your answerChoose one option.

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The permittivity of water at optical frequencies is

. It is found that an isotropic light source at a distance

under water forms an illuminated circular area of radius 5 m, as shown in the figure. The critical angle is

Diagram for Electronics and Communication Engineering question 55

The value of

(in meter) is __________

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GATE ECE year:2017 PYQs

Question 51

Question 51

Question 52

Question 52

Question 53

Question 53

Question 54

Question 54

Question 55

Question 55