GATE MA year:2019 PYQs & Answers — Page 4

Questions 31–40 of 65. Imported answers require independent review unless marked reviewed.

Topic practice 65 questionsPage 4 of 7

Let

be a primitive complex cube root of unity and

. Then the degree of the field extension

over

(the field of rational numbers) is _____.

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Let

Then the greatest integer less than or equal to

is _____.

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Consider the system:

is a basic feasible solution of the above system (where

and

are real constants), then

is equal to _____.

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Let

be a function defined by

. Then the number of zeros of

is _____.

(

is the set of all complex numbers)

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Let

be a normed linear space with the norm

Let

be the bounded linear functional defined by

Then

is equal to _____ (round off to 3 places of decimal).

(

is the set of all complex numbers.)

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For the linear programming problem (LPP):

(

is the set of all real numbers)

consider the following statements:

I. The LPP always has a finite optimal value for any

II. The dual of the LPP may be infeasible for some

III. If for some

, the point

is feasible to the dual of the LPP, then

, for any feasible solution

of the LPP.

IV. If for some

and

are the basic variables in the optimal table of the LPP with

, then the optimal value of dual of the LPP is 10.

Then which of the above statements are TRUE?

Your answerChoose one option.

I and III only

I, III and IV only

II and IV only

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Let

be defined by

Consider the following statements:

I. The partial derivatives

exist at

but are unbounded in any neighbourhood of

II.

is continuous but not differentiable at

III.

is not continuous at

IV.

is differentiable at

(

is the set of all real numbers and

)

Which of the above statements is/are TRUE?

Your answerChoose one option.

I and II only

I and IV only

IV only

III only

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Let

be an infinite matrix over

(the set of all complex numbers) such that

(i) for each

(the set of all natural numbers), the

row

is in

and

(ii) for every

is summable for all

, and

, where

Let the set of all rows of

be denoted by

. Consider the following statements:

is a bounded set in

is a dense set in

Which of the above statements is/are TRUE?

Your answerChoose one option.

Both P and Q

P only

Q only

Neither P nor Q

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Consider the following heat conduction problem for a finite rod

with the boundary conditions

and the initial condition

. If

, then which one of the following is CORRECT?

Your answerChoose one option.

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Let

be non-zero and analytic at all points in

. If

for

, then the residue of

is _____.

(

is the set of all complex numbers,

is the set of all integers and

denotes the set of all complex numbers excluding integers)

Your answerChoose one option.

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GATE MA year:2019 PYQs

Question 21

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Question 28

Question 29

Question 30