GATE MA format:nat PYQs & Answers — Page 10

Questions 91–100 of 222. Imported answers require independent review unless marked reviewed.

Topic practice 222 questionsPage 10 of 23

The optimal value for the linear programming problem

is _____.

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A certain product is manufactured by plants

and

whose capacities are 15, 25 and 10 units, respectively. The product is shipped to markets

and

, whose requirements are 10, 10, 10 and 20, respectively. The transportation costs per unit are given in the table below.\n\n| |

| Supply |\n|---|---:|---:|---:|---:|---:|\n|

| 1 | 3 | 1 | 3 | 15 |\n|

| 2 | 2 | 4 | 1 | 25 |\n|

| 2 | 1 | 1 | 2 | 10 |\n| Demand | 10 | 10 | 10 | 20 | |\n\nThen the cost corresponding to the starting basic solution by the Northwest-corner method is _____.

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Let

be a

real matrix such that

. If the determinant of

, then the trace of

equals _____.

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Let

be differentiable. Let

and

be the direction derivatives of

in the directions of the unit vectors

and

, respectively. If

and

, then

_____.

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Let

denote the boundary of the square region

with vertices

and

oriented in the counter-clockwise direction. Then

__________.

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The number of 5-Sylow subgroups in the symmetric group

of degree 5 is _____.

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Let

be the ideal generated by

in the polynomial ring

, where

denotes the ring of integers modulo 3. Then the number of units in the quotient ring

is ______.

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Let

be a linear transformation such that

, and

. Then the rank of

is _____.

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Let

be the solution of the following initial value problem

Then

__________.

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Let

for

. The order of convergence of the Newton-Raphson method

with

, for finding the root

of the equation

is _____.

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GATE MA format:nat PYQs

Question 63

Question 64

Question 65

Question 15

Question 16

Question 17

Question 18

Question 19

Question 20

Question 21