GATE MA topic:mathematics PYQs & Answers — Page 29

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Questions 281–290 of 650. Imported answers require independent review unless marked reviewed.

Topic practice 650 questionsPage 29 of 65

The steady state solution for the heat equation

with the initial condition

and the boundary conditions

and

, at

Your answerChoose one option.

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Consider

, where

is the subspace topology induced by the Euclidean topology on

, and let

be any topology on

. Consider the following statements:

P: If

is a proper subset of

, then

is not compact. Q: If

is a proper subset of

, then

is not Hausdorff.

Then

Your answerChoose one option.

P is TRUE and Q is FALSE

Both P and Q are TRUE

Both P and Q are FALSE

P is FALSE and Q is TRUE

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Let

be the quotient map, arising from the characteristic function on

, where

is the subspace topology induced by the Euclidean topology on

. Which of the following statements is TRUE?

Your answerChoose one option.

is an open map but not a closed map

is a closed map but not an open map

is a closed map as well as an open map

is neither an open map nor a closed map

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Set

for each

. Define

. Endow

with the product topology, where the topology on each

is the Euclidean topology. Consider the set

with the subspace topology induced from

. Which of the following statements is TRUE?

Your answerChoose one option.

is open in

is locally compact

is dense in

is disconnected

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Consider the linear system of equations

with

Which of the following statements are TRUE?

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

The Jacobi iterative matrix is

The Jacobi iterative method converges for any initial vector

The Gauss-Seidel iterative method converges for any initial vector

The spectral radius of the Jacobi iterative matrix is less than 1

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The number of non-isomorphic abelian groups of order

is ________.

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The number of subgroups of a cyclic group of order

is ________.

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The radius of convergence of the series

is ________ (round off to TWO decimal places).

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The number of zeros of the polynomial

in the unit disc

is ________.

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is a polynomial of degree 5 and

where

are distinct points in the interval

, then the value of

is ________.

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GATE MA topic:mathematics PYQs

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Question 29

Question 30