GATE MA exam:gate PYQs & Answers — Page 55

Questions 541–550 of 650. Imported answers require independent review unless marked reviewed.

Topic practice 650 questionsPage 55 of 65

An urn contains four balls, each ball having equal probability of being white or black. Three black balls are added to the urn. The probability that five balls in the urn are black is

Your answerChoose one option.

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For a linear programming problem, which one of the following statements is FALSE?

Your answerChoose one option.

If a constraint is an equality, then the corresponding dual variable is unrestricted in sign

Both primal and its dual can be infeasible

If primal is unbounded, then its dual is infeasible

Even if both primal and dual are feasible, the optimal values of the primal and the dual can differ

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Let

, where

are real numbers and

. The geometric multiplicity of the largest eigenvalue of

equals ________.

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Consider the subspaces

. Then the dimension of

equals ________.

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Let

be the real vector space of all polynomials of degree less than or equal to 2 with real coefficients. Let

be the linear transformation given by

where

is the derivative of

. Then the number of nonzero entries in the Jordan canonical form of a matrix of

equals ________.

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Let

be the set of all rational numbers in the interval

be the Cantor (ternary) set, and let

. Then the Lebesgue measure of the set

equals ________.

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Let

for

. Then the directional derivative of

in the direction

at the point

is ________.

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If the Laplace transform of

is given by

, then

________.

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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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GATE MA exam:gate PYQs

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