GATE MA discipline:mathematics-and-statistics PYQs & Answers — Page 42

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Questions 411–420 of 650. Imported answers require independent review unless marked reviewed.

Topic practice 650 questionsPage 42 of 65

Let

denote the space of all real-valued continuous functions on

equipped with the supremum norm

. Let

be the linear operator defined by

Then

Your answerChoose one option.

is not invertible

is surjective

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Suppose that

is a

matrix with real entries and

. Then

Your answerChoose one option.

every eigenvalue of

is real if

is necessarily a polynomial in

of degree 4 if

is invertible

is not invertible if

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Let

denote the space of all real-valued continuous functions on

equipped with the supremum norm

. Let

be such that

For

, let

. If

, then

Your answerChoose one option.

the closure of

is compact

is closed and bounded

is bounded but not totally bounded

is compact

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Let

be a function such that the solution of the initial value problem

is given by

for all bounded continuous functions

. Then the value of

is ________

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The number of cyclic subgroups of the quaternion group

is __________

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The number of elements of order 3 in the symmetric group

is __________

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Let

be the field with 4096 elements. The number of proper subfields of

is __________

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is an optimal solution of the linear programming problem,

and

is an optimal solution of its dual problem, then

is equal to ________ (correct up to one decimal place)

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Let

be such that the quadrature rule

is exact for all polynomials of degree less than or equal to 2. Then

is equal to ________ (rounded off to two decimal places)

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Let

and let

be the interpolating polynomial of

at nodes 1, 2 and 3. Then

is equal to ________

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GATE MA discipline:mathematics-and-statistics PYQs

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