GATE MA format:nat PYQs & Answers — Page 18

Questions 171–180 of 222. Imported answers require independent review unless marked reviewed.

Topic practice 222 questionsPage 18 of 23

The number of regular singular points of the differential equation

in the interval

is equal to ________.

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Let

be a field with

elements and let

be a subfield of

with 49 elements. Then the dimension of

as a vector space over

is ________.

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Let

be the real vector space of all continuous real valued functions on

, and let

be the linear operator on

given by

Then the dimension of the range space of

equals ________.

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Let

be such that the quadrature rule

is exact for all polynomials of degree less than or equal to 3. Then

________.

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Let

and

have joint probability density function given by

denotes the marginal probability density function of

, then

________.

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Let the cumulative distribution function of the random variable

be given by

Then

________.

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Let

be a sequence of independent Bernoulli random variables with

and let

. Then

converges, in probability, to ________.

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Let

be the vector space of all

real matrices over the field

. Define the linear transformation

, where

denotes the transpose of the matrix

. Then the trace of

equals _________.

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Consider

with the usual inner product. If

is the distance from

to the subspace

, then

_________.

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Consider the matrix

with

, where

is the

identity matrix and

is the transpose of

. If

and

are two distinct eigenvalues of

, then

_________.

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GATE MA format:nat PYQs

Question 19

Question 20

Question 21

Question 22

Question 23

Question 24

Question 25

Question 40

Question 41

Question 42