GATE MA kind:question PYQs & Answers — Page 19

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Questions 181–190 of 650. Imported answers require independent review unless marked reviewed.

Topic practice 650 questionsPage 19 of 65

Let

be two non-zero, non-identity

-linear transformations. Assume

. Which of the following is/are TRUE?

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

is necessarily invertible

and

are similar if

and

are similar if

has only 0 and 1 as eigenvalues

is necessarily diagonalizable

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Let

be the two fixed points of the function

, where

. For

, let the sequence

be generated by the fixed point iteration

Which one of the following is/are correct?

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

converges to

for any

converges to

for any

converges to

for any

converges to

for any

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Which of the following is/are eigenvalue(s) of the Sturm–Liouville problem

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

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Let

be a function such that

Which of the following is/are correct?

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

is continuous at

, but not differentiable at

is differentiable at

All the directional derivatives of

exist and they are equal to zero

Both the partial derivatives of

exist and they are equal to zero

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For an integer

, let

, where

. Let

. Consider the metric space

, where

Which of the following statement(s) is/are true?

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

is an equi-continuous family of continuous functions

is closed in

is bounded in

is compact in

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Let

be an

-linear transformation such that 1 and 2 are the only eigenvalues of

. Suppose the dimensions of

and

are 1 and 2, respectively. Which of the following is/are possible (upper triangular) Jordan canonical form(s) of

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

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Let

denote the space of all real-valued Lebesgue square-integrable functions on

, with the usual norm

. Let

be the subspace of

consisting of all the polynomials of degree at most 1. Let

be such that

, and

. Then

(round off to TWO decimal places)

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The maximum value of

subject to the constraints

is equal to

(round off to TWO decimal places)

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Let

be the field extension of

obtained by adding all the roots of the polynomial equation

. The number of distinct fields

such that

is equal to

(answer in integer)

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Let

be the subset of

consisting of all

such that

for all

. The number of elements in

is equal to

(answer in integer)

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