GATE MA format:mcq PYQs & Answers — Page 20

Questions 191–200 of 366. Imported answers require independent review unless marked reviewed.

Topic practice 366 questionsPage 20 of 37

Consider the following statements:

is a metric on

Then

Your answerChoose one option.

both P and Q are TRUE

P is TRUE and Q is FALSE

P is FALSE and Q is TRUE

both P and Q are FALSE

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Let

be a twice continuously differentiable scalar field such that

. Let

be the surface

and

be unit outward normal to

. Then the value of

Your answerChoose one option.

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Consider the following statements: P: Every compact metrizable topological space is separable. Q: Every Hausdorff topology on a finite set is metrizable. Then

Your answerChoose one option.

both P and Q are TRUE

P is TRUE and Q is FALSE

P is FALSE and Q is TRUE

both P and Q are FALSE

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Consider the following topologies on the set

of all real numbers:

. Then the closure of the set

Your answerChoose one option.

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Let

denote the ring of integers. Consider the subring

of the field

of complex numbers. Consider the following statements: P:

is an irreducible element. Q:

is a prime element. Then

Your answerChoose one option.

both P and Q are TRUE

P is TRUE and Q is FALSE

P is FALSE and Q is TRUE

both P and Q are FALSE

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Consider the second-order partial differential equation (PDE)

Consider the following statements: P: The PDE is parabolic on the ellipse

. Q: The PDE is hyperbolic inside the ellipse

. Then

Your answerChoose one option.

both P and Q are TRUE

P is TRUE and Q is FALSE

P is FALSE and Q is TRUE

both P and Q are FALSE

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is the solution for the Cauchy problem

then

is equal to

Your answerChoose one option.

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Let

be the solution of the initial value problem

obtained by the method of Laplace transform. Then

Your answerChoose one option.

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The critical point of the differential equation

is a

Your answerChoose one option.

node and is asymptotically stable

spiral point and is asymptotically stable

node and is unstable

saddle point and is unstable

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The initial value problem

where

, is solved by the following Euler method

with step-size

. Then

, provided

Your answerChoose one option.

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GATE MA format:mcq PYQs

Question 11

Question 12

Question 13

Question 14

Question 26

Question 27

Question 28

Question 29

Question 30

Question 31