GATE MA area:engineering-mathematics PYQs & Answers — Page 5

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Questions 41–50 of 403. Imported answers require independent review unless marked reviewed.

Topic practice 403 questionsPage 5 of 41

The number of zeros of the complex polynomial

in the annulus

is equal to ________. (answer in integer)

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Let

denote the space of all real valued Lebesgue square integrable functions on

. Let

be defined as follows:

Then the value of

is equal to ________. (answer in integer)

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Let

be the open unit disc and

be its boundary. If

is the solution of the following Dirichlet problem

then the value of

is ________. (answer in integer)

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Let

be equipped with the topology

. Then the number of subsets of

which are neither open nor closed is ________. (answer in integer)

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Let

and let

denote the smallest integer greater than or equal to

. Then the value of the integral

is ________. (answer in integer)

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Let

be diagonalizable and

, where

. Then, which one of the following is TRUE?

Your answerChoose one option.

is compact and connected

is neither compact nor connected

is compact but not connected

is connected but not compact

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Consider the following subsets of the Euclidean space

, and

Then, which one of the following is TRUE?

Your answerChoose one option.

is connected, but

and

are not connected

and

are connected, but

is not connected

and

are connected, but

is not connected

and

are connected, but

is not connected

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Consider the system of ordinary differential equations

where

is a

skew-symmetric matrix with entries in

. Then, for this system, the origin is a stable critical point for

Your answerChoose one option.

any such matrix

only such matrices

whose rank is 2

only such matrices

whose rank is 4

only such matrices

whose rank is 6

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Let

with the norm

, where

is the space of all real-valued continuous functions on

. Let

with the norm

. Let

and

be the closed unit balls in

and

centred at the origin, respectively. Consider

and

given by

Consider the following statements:

S1:

is attained at a point of

S2:

is attained at a point of

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 defined in

, where

is a continuously differentiable non-zero homogeneous function of degree 4. Then,

holds for

Your answerChoose one option.

all points

on the line given by

all points

in the region of

except on the line given by

all points

on the line given by

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GATE MA area:engineering-mathematics PYQs

Question 59

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