GATE MA topic:mathematical-sciences PYQs & Answers — Page 35

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Questions 341–350 of 650. Imported answers require independent review unless marked reviewed.

Topic practice 650 questionsPage 35 of 65

The family of surfaces given by

, where

is a differentiable function, satisfies

Your answerChoose one option.

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The function

satisfies the initial value problem

Then

Your answerChoose one option.

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Consider the fixed-point iteration

with

and the initial approximation

Then, the order of convergence of the fixed-point iteration method is

Your answerChoose one option.

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Let

be an orthonormal basis of a complex Hilbert space

. Consider the following statements:

P: There exists a bounded linear functional

such that

for

Q: There exists a bounded linear functional

such that

for

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 given by

. Consider the following statements:

for all

has a fixed point.

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 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

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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

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Let

be differentiable. Let

and

be the direction derivatives of

in the directions of the unit vectors

and

, respectively. If

and

, then

_____.

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GATE MA topic:mathematical-sciences PYQs

Question 6

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Question 15