GATE MA topic:statistics PYQs & Answers — Page 5

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Questions 41–50 of 650. Imported answers require independent review unless marked reviewed.

Topic practice 650 questionsPage 5 of 65

Which one of the following statements is TRUE?

Your answerChoose one option.

The set of all

real matrices under usual matrix addition and multiplication is a Unique Factorization Domain.

The set of all real valued functions under usual function addition and multiplication is a Unique Factorization Domain.

The set of all polynomials with coefficients in

under usual polynomial addition and multiplication is a Unique Factorization Domain.

The set of Riemann integrable functions in

under usual function addition and multiplication is a Unique Factorization Domain.

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Let

with the supremum norm. Let

be given by

. Which one of the following is TRUE?

Your answerChoose one option.

is bounded but not one-to-one.

is one-to-one but not bounded.

is bounded and the inverse (from the range of

) exists but not bounded.

is bounded and the inverse (from the range of

) is bounded.

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Let

satisfy the wave equation

, with

and

. By using D’Alembert’s formula, the maximum value of

for

Your answerChoose one option.

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Consider the Laplace equation

, with the boundary conditions

. Then the value of

is equal to

Your answerChoose one option.

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Let

and

be subsets of a normed linear space

, and

. Which one of the following is NOT TRUE?

Your answerChoose one option.

If either of

is open, then

is open.

and

are convex, then

is convex.

and

are closed, then

is closed.

and

are connected, then

is connected.

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For a transportation problem, let

denote the unit cost of the cell

. Assume that

and

. Let

and

, represent the simplex multipliers associated with any basis corresponding to the unit cost

. Assume that

and

. The relative cost coefficient

is the difference between the current solution and the new improved solution. If

and

, then which one of the following is TRUE?

Your answerChoose one option.

and

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Let

and

be topological spaces and

be a continuous and bijective mapping. Which one of the following statements is TRUE?

Your answerChoose one option.

is a homeomorphism if

and

are compact.

is a homeomorphism if

is Hausdorff and

is compact.

is a homeomorphism if

is compact and

is Hausdorff.

is a homeomorphism if

and

are Hausdorff.

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Let

and

nonzero real matrices. Assume that there exists a

real nonsingular matrix

such that

and

are both upper triangular. Which of the following statements is/are TRUE?

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

The matrix

is invertible.

The matrix

is nilpotent.

The matrix

is invertible, where

is the

identity matrix.

is a nonzero matrix, then

is diagonalizable.

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Let

with usual topology. Which of the following statements is/are TRUE?

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

is not compact.

is compact.

is connected.

is not connected.

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Let

and

be two Möbius transformations defined on the unit disc

. Consider the following statements:

;

. Which of the following statements is/are CORRECT?

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

is true.

is true and

is false.

Neither

is true nor

is true.

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GATE MA topic:statistics PYQs

Question 41

Question 42

Question 43

Question 44

Question 45

Question 46

Question 47

Question 48

Question 49

Question 50