GATE MA topic:mathematical-sciences PYQs & Answers — Page 61

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Questions 601–610 of 650. Imported answers require independent review unless marked reviewed.

Topic practice 650 questionsPage 61 of 65

If the quadrature rule

, where

, is exact for all polynomials of degree

, then

equals ______.

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, where

is a differentiable function, then

satisfies

Your answerChoose one option.

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The partial differential equation

Your answerChoose one option.

hyperbolic along the line

elliptic along the line

parabolic along the line

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Let

and

be topological spaces and let

be a continuous surjective function. Which one of the following statements is TRUE?

Your answerChoose one option.

is separable, then

is separable

is first countable, then

is first countable

is Hausdorff, then

is Hausdorff

is regular, then

is regular

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Consider the topology

. Then, the topological space

Your answerChoose one option.

compact but NOT connected

connected but NOT compact

both compact and connected

neither compact nor connected

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Let

be the distribution function of a random variable

. Consider the functions:

Which of the above functions are distribution functions?

Your answerChoose one option.

Neither

nor

Only

Both

and

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Let

(

) be independent and identically distributed random variables with finite variance

and let

. Then the covariance between

and

Your answerChoose one option.

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Let

(

) be a random sample from a

population, where

. The smallest

such that the length of the shortest 95% confidence interval for

will not exceed 10 is ______.

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Consider the linear programming problem (LP): Maximize

Subject to

is unrestricted in sign. Then the LP has

Your answerChoose one option.

no optimal solution

only one basic feasible solution and that is optimal

more than one basic feasible solution and a unique optimal solution

infinitely many optimal solutions

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For a linear programming problem (LP) and its dual, which one of the following is NOT TRUE?

Your answerChoose one option.

The dual of the dual is primal

If the primal LPP has an unbounded objective function, then the dual LPP is infeasible

If the primal LPP is infeasible, then the dual LPP must have unbounded objective function

If the primal LPP has a finite optimal solution, then the dual LPP also has a finite optimal solution

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GATE MA topic:mathematical-sciences PYQs

Question 16

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