GATE MA topic:mathematical-sciences PYQs & Answers — Page 43

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Questions 421–430 of 650. Imported answers require independent review unless marked reviewed.

Topic practice 650 questionsPage 43 of 65

For

, define the sequence

Then the sequence

converges to __________ (correct up to two decimal places)

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Let

be equipped with the norm

and let

be the linear functional on

given by

Then

is equal to __________

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is the set of basic variables of a balanced transportation problem seeking to minimize cost of transportation from origins to destinations, where the cost matrix is, [table: columns

, Availability; rows

: 6, 2, -1, 0, 10;

: 4, 2, 2, 3,

;

: 3, 1, 2, 1,

; Demand: 10,

, 15]. and

, then

is equal to

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Let

be the ring of integers modulo 225. If

is the number of prime ideals and

is the number of nontrial units in

, then

is equal to

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Let

be the solution of

, where

is a twice continuously differentiable function. If

, and

, then the value of

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Let

be an orthonormal basis for a separable Hilbert space

with the inner product

. Define

for

. Then

Your answerChoose one option.

the closure of the span

equals

for all

is an orthogonal subset of

there does not exist nonzero

such that

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Suppose

is a finite dimensional non-zero vector space over

and

is a linear transformation such that

. Then which of the following statements is FALSE?

Your answerChoose one option.

The dimension of

is even

0 is the only eigenvalue of

Both 0 and 1 are eigenvalues of

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Let

. Consider the following statements: I: If

for all

and

, then

. II: If

is symmetric and

, then

. Then

Your answerChoose one option.

both I and II are true

I is true but II is false

I is false but II is true

both I and II are false

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For

, let

and

be the bounded linear operators defined by

, where

and

. Then

Your answerChoose one option.

does not converge to

converges to zero as

for all

converges to zero as

for each non-zero

, there exists a continuous linear functional

such that

does not converge to

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Let

denote the power set of

, equipped with the metric

, where

and

denote the characteristic functions of the subsets

and

, respectively, of

. The set

in the metric space

Your answerChoose one option.

bounded but not totally bounded

totally bounded but not compact

compact

not bounded

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GATE MA topic:mathematical-sciences PYQs

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