GATE MA format:mcq PYQs & Answers — Page 6

Questions 51–60 of 366. Imported answers require independent review unless marked reviewed.

Topic practice 366 questionsPage 6 of 37

The partial differential equation

Your answerChoose one option.

elliptic in the region

hyperbolic in the region

elliptic in the region

hyperbolic in the region

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Let

be the solution of the following initial-boundary value problem

Then, for each

, the value of

Your answerChoose one option.

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Consider the function

given by

Then, for the function

, the inverse function theorem is

Your answerChoose one option.

applicable at all points of

not applicable at exactly one point of

not applicable at exactly two points of

not applicable at exactly three points of

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Let the functions

and

be given by

Consider the following statements:

S1: For every compact subset

is compact.

S2: For every compact subset

is compact.

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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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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GATE MA format:mcq PYQs

Question 19

Question 20

Question 21

Question 22

Question 36

Question 37

Question 38

Question 39

Question 40

Question 41