GATE MA topic:mathematical-sciences PYQs & Answers — Page 52

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topic:mathematical-sciences

Questions 511–520 of 650. Imported answers require independent review unless marked reviewed.

Topic practice 650 questionsPage 52 of 65

Let

be the vector space of all

matrices with complex entries over the real field. If

then the dimension of

is equal to ______. (

denotes the conjugate transpose of

)

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The number of elements of order 15 in the additive group

is ______. (

denotes the group of integers modulo

, under the operation of addition modulo

, for any positive integer

)

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Consider the following cost matrix of assigning four jobs to four persons:

Persons / Jobs	J₁	J₂	J₃	J₄
P₁	5	8	6	10
P₂	2	5	4	8
P₃	6	7	6	9
P₄	6	9	8	10

Then the minimum cost of the assignment problem subject to the constraint that job J₄ is assigned to person P₂, is ______.

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Let

with

satisfy the Legendre differential equation

Then the value of

is equal to ______ (round off to 2 places of decimal).

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Let

be the ring of integers modulo 125 under the operations of addition modulo 125 and multiplication modulo 125. If

is the number of maximal ideals of

and

is the number of non-units of

, then

is equal to ______.

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The maximum value of the error term of the composite Trapezoidal rule when it is used to evaluate the definite integral

with 12 sub-intervals of equal length, is equal to ______ (round off to 3 places of decimal).

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By the Simplex method, the optimal table of the linear programming problem:

where

are real constants, is

		3	0	0
Basic variable					Solution
	1	0	2	-1	6
	0	1	-1	1	2
	0	0	2	1	-

Then the value of

is ______.

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Consider the inner product space

of all polynomials of degree at most 2 over the field of real numbers with the inner product

for

. Let

be an orthogonal set in

, where

and

are real constants. Then the value of

is equal to _____.

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Consider the system of linear differential equations

with the initial conditions

. Then

is equal to _____.

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Consider the differential equation

The sum of the roots of the indicial equation of the Frobenius series solution for the above differential equation in a neighbourhood of

is equal to _____.

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GATE MA topic:mathematical-sciences PYQs

Question 46

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Question 55