GATE ECE exam:gate 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

You can attempt this question now. Sign in to view the answer key, explanations and discussion.Log in to check answer

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).

You can attempt this question now. Sign in to view the answer key, explanations and discussion.Log in to check answer

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).

You can attempt this question now. Sign in to view the answer key, explanations and discussion.Log in to check answer

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

You can attempt this question now. Sign in to view the answer key, explanations and discussion.Log in to check answer

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).

You can attempt this question now. Sign in to view the answer key, explanations and discussion.Log in to check answer

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

You can attempt this question now. Sign in to view the answer key, explanations and discussion.Log in to check answer

and

are positive integers and

, then,

Your answerChoose one option.

You can attempt this question now. Sign in to view the answer key, explanations and discussion.Log in to check answer

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.

You can attempt this question now. Sign in to view the answer key, explanations and discussion.Log in to check answer

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

You can attempt this question now. Sign in to view the answer key, explanations and discussion.Log in to check answer

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)

You can attempt this question now. Sign in to view the answer key, explanations and discussion.Log in to check answer

GATE ECE exam:gate PYQs

Question 61

Question 62

Question 63

Question 64

Question 65

Question 1

Question 2

Question 3

Question 4

Question 5