GATE MA topic:statistics PYQs & Answers — Page 28

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Questions 271–280 of 650. Imported answers require independent review unless marked reviewed.

Topic practice 650 questionsPage 28 of 65

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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The real sequence generated by the iterate scheme

Your answerChoose one option.

converges to

, for all

converges to

, whenever

converges to

, whenever

diverges for any

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The initial value problem

where

is a real constant, has

Your answerChoose one option.

a unique solution

exactly two solutions

infinitely many solutions

no solution

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If eigenfunctions corresponding to distinct eigenvalues

of the Sturm-Liouville problem

are orthogonal with respect to the weight function

, then

Your answerChoose one option.

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GATE MA topic:statistics PYQs

Question 11

Question 12

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Question 15

Question 16

Question 17

Question 18

Question 19

Question 20