GATE MA topic:mathematical-sciences PYQs & Answers — Page 45

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topic:mathematical-sciences

Questions 441–450 of 650. Imported answers require independent review unless marked reviewed.

Topic practice 650 questionsPage 45 of 65

Suppose

is a finite dimensional vector space over

. If

and

are subspaces of

, then which of the following statements is TRUE?

Your answerChoose one option.

then

and

, then

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Let

. The system

has NO basic feasible solution if

Your answerChoose one option.

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Let

and let

. For

, define

. Then

Your answerChoose one option.

defines a norm on

for all

converges to

pointwise on

, then

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Suppose that

and

are linearly independent solutions of the differential equation

, and

. Then the smallest positive integer

such that

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Suppose that

and

. If

, then the value of

is equal to

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and

, then

is equal to (correct up to one decimal place)

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Let

, where

is a primitive cube root of unity. Then the degree of extension of

over

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Let

. If

is an optimal solution of the linear programming problem

minimize

subject to

then the maximum value of

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Suppose that

is a linear transformation over

satisfying

Then the coefficient of

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Let

and let

be the surface of the tetrahedron bounded by the planes

is the unit outward normal to the tetrahedron, then the value of

is (rounded off to two decimal places)

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GATE MA topic:mathematical-sciences PYQs

Question 41

Question 42

Question 43

Question 44

Question 45

Question 46

Question 47

Question 48

Question 49

Question 50