GATE MA branch:ma PYQs & Answers — Page 31

Questions 301–310 of 650. Imported answers require independent review unless marked reviewed.

Topic practice 650 questionsPage 31 of 65

Let

be the metric space with

. Let

. Then, the set

Your answerChoose one option.

closed but not compact

not closed but compact

compact

neither closed nor compact

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Let

be defined by

, where

almost everywhere. If

is the kernel of

, then the distance between the function

and

Your answerChoose one option.

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Let

and

be Banach spaces. Suppose that

is linear and

is linear, bounded and injective. In addition, if

is bounded, then which of the following statements is TRUE?

Your answerChoose one option.

is surjective

is bounded but not continuous

is bounded

is not bounded

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The first derivative of a function

is approximated by an interpolating polynomial of degree 2, using the data

and

. It is found that

. Then, the value of

Your answerChoose one option.

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The work done by the force

, where

and

are unit vectors in

and

directions, respectively, along the upper half of the circle

from

in the

-plane is

Your answerChoose one option.

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Let

be the solution of the wave equation

with the initial conditions

and the boundary conditions

. Then, the value of

Your answerChoose one option.

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Let

be a linear transformation defined by

For

, let

. Which of the following statements is TRUE?

Your answerChoose one option.

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Let

be a feasible solution for the dual problem of the linear programming problem

Which of the following statements is TRUE?

Your answerChoose one option.

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Let

denote the subset of

consisting of elements algebraic over

. Then, which of the following statements are TRUE?

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

No element of

is algebraic over

is an algebraically closed field

For any bijective ring homomorphism

, we have

There is no bijection between

and

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Let

be a Möbius transformation such that

and

, where

. Let

denote the straight line passing through the origin with slope

, and let

denote the circle of unit radius centred at the origin. Then, which of the following statements are TRUE?

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

maps

to a straight line

maps

to a circle

maps

to a straight line

maps

to a circle

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GATE MA branch:ma PYQs

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