GATE MA topic:statistics PYQs & Answers — Page 32

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topic:statistics

Questions 311–320 of 650. Imported answers require independent review unless marked reviewed.

Topic practice 650 questionsPage 32 of 65

Let

. Define

, almost everywhere, for

. Then, which of the following statements are TRUE?

Your answerSelect all correct options. You can choose more than one.

is a linear isometry

is a bijection

is bounded from below

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Let

be an orthonormal set in

such that

, where

is a constant and

is the Legendre polynomial of degree

, for each

. Then, which of the following statements are TRUE?

Your answerSelect all correct options. You can choose more than one.

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Let

, where

is the smallest topology on

in which all the singleton sets are closed. Then, which of the following statements are TRUE?

Your answerSelect all correct options. You can choose more than one.

is compact in

is not first countable

is second countable

is first countable

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Consider

, where

is the topology generated by sets of the form

, for

and

. Then, which of the following statements are TRUE?

Your answerSelect all correct options. You can choose more than one.

is connected

Each

is a closed subset of

is Hausdorff

is metrizable

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Let

and

. Consider the linear programming primal problem

Let

and

be feasible solutions of the primal and its dual, respectively. Which of the following statements are TRUE?

Your answerSelect all correct options. You can choose more than one.

, then

is optimal for the primal

, then

is optimal for the dual

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Consider

as a vector space with the usual operations of vector addition and scalar multiplication. Let

be denoted by

. Define subspaces

and

Let

denote the dimension of the subspace

Which of the following statements are TRUE?

Your answerSelect all correct options. You can choose more than one.

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Three companies

and

submit bids for three jobs

and

. The costs involved per unit are given in the table below:


10	12	8
9	15	10
15	10	9

Then, the cost of the optimal assignment is ________.

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The initial value problem

is solved by using the following second order Runge-Kutta method:

where

is the uniform step length between the points

and

. The value of the product

is ________ (round off to TWO decimal places).

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The surface area of the paraboloid

between the planes

and

is ________ (round off to ONE decimal place).

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The rate of change of

in the direction from

is ________.

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GATE MA topic:statistics PYQs

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Question 60