GATE ECE 2025 Paper 1 — page 18

Questions 52–54 of 65. Imported answers require review unless explicitly marked reviewed.

Paper practice 65 questionsPage 18 of 22

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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2025 · Paper 1