GATE EE format:msq PYQs & Answers

Attempt a question, record the concept and assumptions, then check the available answer. Rework mistakes after revising the relevant concepts. Topic tags can overlap; review the question context.

Questions 1–10 of 22. Imported answers require independent review unless marked reviewed.

Topic practice 22 questionsPage 1 of 3

Two

matrices

and

have a common eigenvalue 2, and the same corresponding nonzero eigenvector.

Which of the following options is/are correct?

(Note:

is the

identity matrix.)

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

Determinant

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A 220V/12V single-phase transformer is designed for use in India and rated 100 VA at 50 Hz. Later, this unit is shipped to the USA where it is used as a 110V/6V transformer at 60 Hz.

Which of the following statements is/are correct?

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

No-load current drawn would be smaller for operation in the USA compared to that in India

For the same load current, the losses would be higher in the USA compared to that in India

The peak magnetic flux density in the core would be higher while operating in the USA compared to that in India

The eddy current losses in the core would be approximately 44% higher while operating in the USA compared to that in India

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For the balanced 3-phase transmission line shown, consider the following cases:

Case-1:

and

Case-2:

and

Diagram for Electrical Engineering question 54

Which of the following statements is/are correct about real power loss and reactive power loss in the line?

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

Real power loss in Case-1 is more than that in Case-2

Real power loss in Case-2 is more than that in Case-1

Reactive power loss in Case-1 is more than that in Case-2

Reactive power loss in Case-2 is more than that in Case-1

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Consider an

orthogonal matrix

with real entries and each column having unit Euclidean norm.

Which of the following statements is/are correct?

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

The value of the determinant of

is either +1 or −1

The eigenvalues of

have modulus 1

, for all

, where

denotes the Euclidean norm of

, and

, for all distinct

, for all

, where

denotes the Euclidean norm of

, and

, for all

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Consider the system of linear equations:

, where

is an

matrix, and

and

are n-dimensional column vectors.

Suppose this system of equations has a unique solution. Which of the following statements is/are correct?

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

exists

The system of equations

also has a unique solution for

, for

, where

denotes the augmented matrix.

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Instrument(s) required to synchronize an alternator to the grid is/are

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

Voltmeter

Wattmeter

Synchroscope

Stroboscope

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The open loop transfer function of the system shown in the figure, is

. For

, which of the following real axis point(s) is/are on the root locus?

Diagram for Electrical Engineering question 29

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

−1

−4

−6

−10

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Let

be the unit radial vector in the spherical co-ordinate system. For which of the following value(s) of n, the divergence of the radial vector field

is independent of R?

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

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Consider two coupled circuits, having self-inductances

and

, that carry non-zero currents

and

, respectively. The mutual inductance between the circuits is M with unity coupling coefficient. The stored magnetic energy of the coupled circuits is minimum at which of the following value(s) of

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

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Let

be a discrete random variable that is uniformly distributed over the set

. Which of the following random variables is/are uniformly distributed?

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

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GATE EE format:msq PYQs

How to practice format:msq

Question 30

Question 31

Question 54

Question 55

Question 56

Question 28

Question 29

Question 51

Question 52

Question 29