GATE MA year:2023 PYQs & Answers — Page 6

Questions 51–60 of 65. Imported answers require independent review unless marked reviewed.

Topic practice 65 questionsPage 6 of 7

Let

be a twice continuously differentiable function on

such that

and

for all

. Let

for some

. The Newton-Raphson method to compute

is given by

for an initial guess

for some

, then which of the following statements is/are correct?

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

For every

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Let

be defined by

Then

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

the directional derivative of

in the direction of

the directional derivative of

in the direction of

the directional derivative of

in the direction of

is NOT differentiable at

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Let

and

For each

, define

for all

Let

Which of the following statements is/are correct?

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

is totally bounded in

is bounded in

is closed in

is open in

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Let

be an abelian group and

be a surjective group homomorphism. Let

for some

. Consider the following statements:

: For every

, there exists an

such that

: Let

be the identity of

and

be the subgroup generated by

. Then

and

Which of the following statements is/are correct?

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

is TRUE

is FALSE

is TRUE

is FALSE

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Let

be the curve of intersection of the cylinder

and the plane

. Suppose

is oriented in the counterclockwise direction and the

-axis, when viewed from above. If

then the value of

equals __________.

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Let

. For a sequence

, define

Consider the subspace

. Let

denote the orthogonal complement of

in the Hilbert space

. Consider

If the orthogonal projection of

onto

is given by

for some

, then

equals __________.

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Consider the transportation problem between five sources and four destinations as given in the cost table below. The supply and demand at each of the source and destination are also provided:

Sources	P	Q	R	S	Supply
1	13	8	12	9	20
2	10	7	5	20	10
3	3	19	5	12	50
4	4	9	7	15	30
5	14	0	1	7	40
Demand	60	10	20	60

Let

and

be the total cost of the initial basic feasible solution obtained from the North-West corner method and the Least-Cost method, respectively. Then

equals __________.

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Let

, where

is the permutation group on 8 elements. Suppose

is the product of

and

, where

is a 4-cycle and

is a 3-cycle in

. If

and

are disjoint cycles, then the number of elements in

which are conjugate to

is __________.

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Let

be a

real matrix with

, where

and

is the

identity matrix. If

, then the trace of

is __________.

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Let

be a

real matrix such that

is the degree of the minimal polynomial of

, then

equals __________.

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GATE MA year:2023 PYQs

Question 51

Question 52

Question 53

Question 54

Question 55

Question 56

Question 57

Question 58

Question 59

Question 60