GATE MA exam:gate PYQs & Answers — Page 11

Questions 101–110 of 650. Imported answers require independent review unless marked reviewed.

Consider the linear system

, where

, and

for

, is a matrix with entries in

. For

, let

and

. Consider the following two statements:

S1: The approximation of

after one iteration of the Jacobi scheme with initial vector

S2: There exists an initial vector

for which Jacobi iterative scheme diverges.

Then, which one of the following is correct?

Your answerChoose one option.

S1 is TRUE and S2 is FALSE

S2 is TRUE and S1 is FALSE

both S1 and S2 are TRUE

neither S1 nor S2 is TRUE

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Let

be the solution of the differential equation

, satisfying

and

. Then, the value of

is equal to

Your answerChoose one option.

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Let

and

be the two linearly independent solutions of the differential equation

, satisfying the initial conditions

and

. Define

. Then, the value of

Your answerChoose one option.

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Let

be the curve of intersection of the surfaces

and

. If

is a point on

at a minimum distance from the

-plane, then the distance of

from the origin is

Your answerChoose one option.

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Let

be the solution of the initial-value problem

. Then, the value of

Your answerChoose one option.

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Let

be the Möbius transformation that maps the points

and

conformally onto the points

and

, respectively, in the extended complex plane. If

maps the circle centred at

with radius

onto a straight line given by the equation

, then the value of

is equal to

Your answerChoose one option.

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Let

and

, where

denotes the imaginary part of

. Let

be the set of all bijective analytic functions

such that

. Then, the value of

Your answerChoose one option.

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Let

be a non-empty open connected subset of

and

be a non-constant function. Let the functions

and

be defined by

Consider the following two statements:

S1: If

is continuous in

and

is analytic in

, then

is analytic in

S2: If

and

are analytic in

, then

is analytic in

Then, which one of the following is correct?

Your answerChoose one option.

S1 is TRUE and S2 is FALSE

S2 is TRUE and S1 is FALSE

both S1 and S2 are TRUE

neither S1 nor S2 is TRUE

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In the following, all subsets of Euclidean spaces are considered with the respective subspace topologies. Define an equivalence relation

on the sphere

, for

. Let

denote the equivalence class of

, and let

denote the set of all such equivalence classes. Let

be given by

. If

is provided with the quotient topology induced by the map

, then which one of the following is TRUE?

Your answerChoose one option.

is homeomorphic to

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Consider the following two spaces:

, the space of all real-valued continuous functions defined on

equipped with the norm

, the space of all real-valued continuous functions defined on

equipped with the norm

Let

be the linear span over

of all the Legendre polynomials. Then, which one of the following is correct?

Your answerChoose one option.

is dense in

but not in

is dense in

but not in

is dense in both

and

is dense neither in

nor in

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GATE MA exam:gate PYQs

Question 36

Question 37

Question 38

Question 39

Question 40

Question 41

Question 42

Question 43

Question 44

Question 45