GATE ECE format:msq PYQs & Answers — Page 2

Questions 11–20 of 50. Imported answers require independent review unless marked reviewed.

Consider the function

, defined as

Which of the following statements is/are correct?

(Here,

is the set of real numbers.)

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

has no global maximizer

has no global minimizer

is a local minimizer of

is a local maximizer of

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Consider the unity-negative-feedback system shown in Figure (i) below, where gain

. The root locus of this system is shown in Figure (ii) below.

Diagram for Electronics and Communication Engineering question 26

Diagram for Electronics and Communication Engineering question 26 (figure 2)

For what value(s) of

will the system in Figure (i) have a pole at

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

For no positive value of

For all positive values of

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Let

be a discrete-time signal whose z-transform is

. Which of the following statements is/are TRUE?

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

The discrete-time Fourier transform (DTFT) of

always exists

The region of convergence (RoC) of

contains neither poles nor zeros

The discrete-time Fourier transform (DTFT) exists if the region of convergence (RoC) contains the unit circle

, where

is the unit impulse and

is a scalar, then the region of convergence (RoC) is the entire z-plane

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Consider a message signal

which is bandlimited to

, where

is in Hz. Consider the following two modulation schemes for the message signal:

• Double sideband-suppressed carrier (DSB-SC):

• Amplitude modulation (AM):

Here,

and

are the amplitude and frequency (in Hz) of the carrier, respectively. In the case of AM,

denotes the modulation index.

Consider the following statements: (i) An envelope detector can be used for demodulation in the DSB-SC scheme if

for all

. (ii) An envelope detector can be used for demodulation in the AM scheme only if

for all

Which of the following options is/are correct?

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

(i) is TRUE

(i) is FALSE

(ii) is TRUE

(ii) is FALSE

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Which of the following statements is/are TRUE with respect to an ideal opamp?

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

It has an infinite input resistance

It has an infinite output resistance

It has an infinite open-loop differential gain

It has an infinite open-loop common-mode gain

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Which of the following statements is/are TRUE with respect to ideal MOSFET-based DC-coupled single-stage amplifiers having finite load resistors?

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

The common-gate amplifier has an infinite input resistance

The common-source amplifier has an infinite input resistance

The input and output voltages of the common-source amplifier are in phase

The input and output voltages of the common-drain amplifier are in phase

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Which of the following can be used as an n-type dopant for silicon? Select the correct option(s).

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

Arsenic

Boron

Gallium

Phosphorus

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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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GATE ECE format:msq PYQs

Question 25

Question 26

Question 27

Question 28

Question 29

Question 30

Question 31

Question 51

Question 52

Question 53