GATE ECE year:2025 PYQs & Answers — Page 6

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year:2025

Questions 51–60 of 65. Imported answers require independent review unless marked reviewed.

Topic practice 65 questionsPage 6 of 7

Consider a non-negative function

which is continuous and bounded over the interval

. Let

and

denote, respectively, the maximum and the minimum values of

over the interval.

Among the combinations of

and

given below, choose the one(s) for which the inequality

is guaranteed to hold.

Your answerSelect all correct options. You can choose more than one.

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Which of the following statements involving contour integrals (evaluated counter-clockwise) on the unit circle

in the complex plane is/are TRUE?

Your answerSelect all correct options. You can choose more than one.

, when

is an even integer

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Consider a system where

, and

are three internal state signals and

is the input signal. The differential equations governing the system are given by

Which of the following statements is/are TRUE?

Your answerSelect all correct options. You can choose more than one.

The signals

, and

are bounded for all bounded inputs

There exists a bounded input such that at least one of the signals

, and

is unbounded

There exists a bounded input such that the signals

, and

are unbounded

The signals

, and

are unbounded for all bounded inputs

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The random variable

takes values in

with probabilities

and

, where

. Let

denote the entropy of

(in bits), parameterized by

. Which of the following statements is/are TRUE?

Your answerSelect all correct options. You can choose more than one.

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Let

be a periodic signal with fundamental period

. Consider the signal

, where

. The Fourier series expansions of

and

are given by

Which of the following statements is/are TRUE?

Your answerSelect all correct options. You can choose more than one.

for all

is periodic with a fundamental period

for all

is periodic with a fundamental period

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Consider a system represented by the block diagram shown below. Which of the following signal flow graphs represent(s) this system? Choose the correct option(s).

Diagram for Electronics and Communication Engineering question 56

Your answerSelect all correct options. You can choose more than one.

Diagram for Electronics and Communication Engineering question 56 (figure 2)

Diagram for Electronics and Communication Engineering question 56 (figure 3)

Diagram for Electronics and Communication Engineering question 56 (figure 4)

Diagram for Electronics and Communication Engineering question 56 (figure 5)

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All the diodes in the circuit given below are ideal. Which of the following plots is/are correct when

(in Volts) is swept from

Diagram for Electronics and Communication Engineering question 57

Your answerSelect all correct options. You can choose more than one.

Diagram for Electronics and Communication Engineering question 57 (figure 2)

Diagram for Electronics and Communication Engineering question 57 (figure 3)

Diagram for Electronics and Communication Engineering question 57 (figure 4)

Diagram for Electronics and Communication Engineering question 57 (figure 5)

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Two fair dice (with faces labeled 1, 2, 3, 4, 5, and 6) are rolled. Let the random variable

denote the sum of the outcomes obtained.

The expectation of

is ______ (rounded off to two decimal places).

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Consider the vectors

For real-valued scalar variable

, the value of

is __________ (rounded off to two decimal places).

denotes the Euclidean norm, i.e., for

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and

are Bernoulli random variables taking values in

. The joint probability mass function of the random variables is given by:

The mutual information

is __________ (rounded off to two decimal places).

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GATE ECE year:2025 PYQs

Question 51

Question 52

Question 53

Question 54

Question 55

Question 56

Question 57

Question 58

Question 59

Question 60