GATE MA purpose:exam-prep PYQs & Answers — Page 56

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Questions 551–560 of 650. Imported answers require independent review unless marked reviewed.

Topic practice 650 questionsPage 56 of 65

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 circle given by

, where

varies from 0 to

. Then

Your answerChoose one option.

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The image of the half plane

under the map

is given by

Your answerChoose one option.

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Let

denote the closed disc with center at the origin and radius 2. Then

Your answerChoose one option.

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Consider the polynomial

in the ring

of polynomials in the variable

with coefficients in the field

of rational numbers. Then

Your answerChoose one option.

the set of zeros of

forms a group under multiplication

is reducible in the ring

the splitting field of

has degree 3 over

the splitting field of

has degree 4 over

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Which one of the following statements is true?

Your answerChoose one option.

Every group of order 12 has a non-trivial proper normal subgroup

Some group of order 12 does not have a non-trivial proper normal subgroup

Every group of order 12 has a subgroup of order 6

Every group of order 12 has an element of order 12

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