GATE MA topic:statistics PYQs & Answers — Page 63

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Questions 621–630 of 650. Imported answers require independent review unless marked reviewed.

Topic practice 650 questionsPage 63 of 65

Let

and

with

be the roots of the indicial equation of

. Then

equals ________.

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Let

be the group of all permutations of the set

. Then the total number of elements of

that commute with

equals ________.

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Let

be the ring of polynomials over

. Then the total number of maximal ideals in the quotient ring

equals ________.

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Let

be an orthonormal basis of a Hilbert space

. Let

be given by

. For each

, define

. Then

Your answerChoose one option.

but for each

for each

but the sequence

is unbounded

there exist

such that

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Consider the subspace

of the Hilbert space

of all square summable real sequences. For

, define

. Consider the following statements: (P):

is pointwise bounded on

. (Q):

is uniformly bounded on

. Which of the above statements hold TRUE?

Your answerChoose one option.

Both P and Q

Only P

Only Q

Neither P nor Q

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Let

be the polynomial of degree at most 2 that interpolates the data

and

. If

is a polynomial of degree at most 3 such that

interpolates the data

and

, then

equals ________.

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Let

be the Jacobi iteration matrix of the linear system

. Consider the following statements: (P): One of the eigenvalues of

lies in the interval

. (Q): The Jacobi iteration converges for the above system. Which of the above statements hold TRUE?

Your answerChoose one option.

Both P and Q

Only P

Only Q

Neither P nor Q

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Let

be the solution of

satisfying the condition

on the circle

. Then

equals ________.

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Let

be the bounded solution of the following boundary value problem in polar coordinates:

Then

equals

Your answerChoose one option.

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Let

and

denote the usual topology and the discrete topology on

, respectively. Consider the following three topologies:

Then

Your answerChoose one option.

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GATE MA topic:statistics PYQs

Question 36

Question 37

Question 38

Question 39

Question 40

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Question 42

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Question 45