GATE ECE branch:ec PYQs & Answers — Page 33

Questions 321–330 of 715. Imported answers require independent review unless marked reviewed.

The transition diagram of a discrete memoryless channel with three input symbols and three output symbols is shown in the figure. The transition probabilities are as marked.

The parameter

lies in the interval

. The value of

for which the capacity of this channel is maximized, is ________ (rounded off to two decimal places).

Diagram for Electronics and Communication Engineering question 61

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Consider communication over a memoryless binary symmetric channel using a (7, 4) Hamming code. Each transmitted bit is received correctly with probability

, and flipped with probability

. For each codeword transmission, the receiver performs minimum Hamming distance decoding, and correctly decodes the message bits if and only if the channel introduces at most one bit error.

For

, the probability that a transmitted codeword is decoded correctly is ________ (rounded off to two decimal places).

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Consider a channel over which either symbol

or symbol

is transmitted. Let the output of the channel

be the input to a maximum likelihood (ML) detector at the receiver. The conditional probability density functions for

given

and

are:

where

is the standard unit step function. The probability of symbol error for this system is ________ (rounded off to two decimal places).

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Consider a real valued source whose samples are independent and identically distributed random variables with the probability density function,

, as shown in the figure.

Consider a 1 bit quantizer that maps positive samples to value

and others to value

. If

and

are the respective choices for

and

that minimize the mean square quantization error, then

________ (rounded off to two decimal places).

Diagram for Electronics and Communication Engineering question 64

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In an electrostatic field, the electric displacement density vector,

, is given by

where

are the unit vectors along

-axis,

-axis, and

-axis, respectively. Consider a cubical region

centered at the origin with each side of length 1 m, and vertices at

. The electric charge enclosed within

is ________ C (rounded off to two decimal places).

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The current population of a city is 11,02,500. If it has been increasing at the rate of 5% per annum, what was its population 2 years ago?

Your answerChoose one option.

9,92,500

9,95,006

10,00,000

12,51,506

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and

are positive integers and

, then,

Your answerChoose one option.

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The least number of squares that must be added so that the line P-Q becomes the line of symmetry is ________.

Diagram for Electronics and Communication Engineering question 3

Your answerChoose one option.

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Nostalgia is to anticipation as ________ is to ________. Which one of the following options maintains a similar logical relation in the above sentence?

Your answerChoose one option.

Present, past

Future, past

Past, future

Future, present

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Consider the following sentences: (i) I woke up from sleep. (ii) I woken up from sleep. (iii) I was woken up from sleep. (iv) I was wokened up from sleep. Which of the above sentences are grammatically CORRECT?

Your answerChoose one option.

(i) and (ii)

(i) and (iii)

(ii) and (iii)

(i) and (iv)

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GATE ECE branch:ec PYQs

Question 61

Question 62

Question 63

Question 64

Question 65

Question 1

Question 2

Question 3

Question 4

Question 5