GATE MA format:nat PYQs & Answers — Page 12

Questions 111–120 of 222. Imported answers require independent review unless marked reviewed.

Topic practice 222 questionsPage 12 of 23

(

) is the power series solution of the differential equation

, then

__________.

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solves the following initial boundary value problem

then

__________.

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Let

be the vector space of all polynomials of degree at most 2 over the real field

. Let

be the linear operator given by

Then the sum of the eigenvalues of

is __________.

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The quadrature formula

is exact for all polynomials of degree

. Then

__________.

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For each

, consider the decimal representation

. Define

is rational and

is irrational, where

is the number of zeroes immediately after the decimal point up to the first nonzero digit in the decimal representation of

. Then the Lebesgue integral

__________.

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Let

be an optimal solution of the following Linear Programming Problem

subject to

is an optimal solution of the dual of

, then

__________ (round off to two decimal places).

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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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GATE MA format:nat PYQs

Question 50

Question 51

Question 52

Question 53

Question 54

Question 55

Question 14

Question 15

Question 16

Question 17