GATE MA format:nat PYQs & Answers — Page 13

Questions 121–130 of 222. Imported answers require independent review unless marked reviewed.

Topic practice 222 questionsPage 13 of 23

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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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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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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GATE MA format:nat PYQs

Question 18

Question 19

Question 20

Question 21

Question 22

Question 23

Question 24

Question 25

Question 44

Question 45