GATE MA area:engineering-mathematics PYQs & Answers — Page 18

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Questions 171–180 of 403. Imported answers require independent review unless marked reviewed.

Topic practice 403 questionsPage 18 of 41

Let

be a

real matrix such that

is the degree of the minimal polynomial of

, then

equals __________.

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Let

be the disk

with boundary

. If

is the solution of the Dirichlet problem

then the value of

is ____________.

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Let

be the solution of the non-homogeneous wave equation

Then the value of

is ____________ (rounded off to 2 decimal places).

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Suppose that the characteristic equation of

where

with

. Which of the following statements is TRUE?

Your answerChoose one option.

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Consider

P: Let

with

. If

, then the system of linear equations

has

as the only solution.

Q: Let

be a non-zero matrix such that

. Then

is a singular matrix.

Which of the following statements is TRUE?

Your answerChoose one option.

Both P and Q are TRUE

Both P and Q are FALSE

P is TRUE and Q is FALSE

P is FALSE and Q is TRUE

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Consider the real function of two real variables given by

Let

be the harmonic conjugate of

such that

. Let

and

, then the value of

Your answerChoose one option.

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The value of the integral

where

is the circle of radius 2 centred at the origin taken in the anti-clockwise direction is

Your answerChoose one option.

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Let

be a real normed linear space. Let

. If

contains two distinct points

and

and the line segment joining them, then, which of the following statements is TRUE?

Your answerChoose one option.

and

are linearly independent

and

are linearly dependent

and

are linearly independent

and

are linearly dependent

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Let

be an orthonormal basis for a Hilbert space

. Define

and

. Then

Your answerChoose one option.

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Consider

with the usual metric. Let

and

. Let

and

. Then, which of the following statements is TRUE?

Your answerChoose one option.

and

are connected

Neither

nor

is connected

is connected and

is not connected

is not connected and

is connected

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GATE MA area:engineering-mathematics PYQs

Question 60

Question 61

Question 64

Question 11

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Question 13

Question 14

Question 15

Question 16

Question 17