GATE MA topic:complex-analysis PYQs & Answers — Page 2

Home
GATE
Mathematics
Topics
topic:complex-analysis

Questions 11–20 of 54. Imported answers require independent review unless marked reviewed.

Topic practice 54 questionsPage 2 of 6

Let

be a non-empty open connected subset of

and

be a non-constant function. Let the functions

and

be defined by

Consider the following two statements:

S1: If

is continuous in

and

is analytic in

, then

is analytic in

S2: If

and

are analytic in

, then

is analytic in

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

You can attempt this question now. Sign in to view the answer key, explanations and discussion.Log in to check answer

Let

be distinct non-zero real numbers, and let

be a polynomial of degree less than 5. If the function

satisfies Morera’s theorem in

, then the value of

is equal to _____ (in integer)

You can attempt this question now. Sign in to view the answer key, explanations and discussion.Log in to check answer

Consider the following condition on a function

for all

such that

. (P)

Which one of the following is correct?

Your answerChoose one option.

There is a non-constant analytic polynomial

satisfying (P)

Every entire function

satisfying (P) is a constant function

Every entire function

satisfying (P) has no zeroes in

There is an entire function

satisfying (P) with infinitely many zeroes in

You can attempt this question now. Sign in to view the answer key, explanations and discussion.Log in to check answer

Let

be the ellipse

traversed counter-clockwise. The value of the contour integral

is equal to

Your answerChoose one option.

You can attempt this question now. Sign in to view the answer key, explanations and discussion.Log in to check answer

Let

and

. Then

is equal to

Your answerChoose one option.

You can attempt this question now. Sign in to view the answer key, explanations and discussion.Log in to check answer

Let

. For which one of the following functions

does there exist a sequence of polynomials in

that uniformly converges to

Your answerChoose one option.

You can attempt this question now. Sign in to view the answer key, explanations and discussion.Log in to check answer

Let

. Then

is equal to

Your answerChoose one option.

You can attempt this question now. Sign in to view the answer key, explanations and discussion.Log in to check answer

Let

and

be defined by

Consider the following statements:

has three zeros (counting multiplicity) in

has one zero in

. Then

Your answerChoose one option.

is TRUE but

is FALSE

is FALSE but

is TRUE

both

and

are TRUE

both

and

are FALSE

You can attempt this question now. Sign in to view the answer key, explanations and discussion.Log in to check answer

Let

for all

in some neighbourhood of

. Then the value of

is equal to __________.

You can attempt this question now. Sign in to view the answer key, explanations and discussion.Log in to check answer

Let

and

be an analytic function given by the power series

, where

and

for

. Consider the following statements:

: If

, then

is one-one in some neighbourhood of

: If

, then

is a closed subset of

Which of the following statements is/are correct?

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

is TRUE

is FALSE

You can attempt this question now. Sign in to view the answer key, explanations and discussion.Log in to check answer

GATE MA topic:complex-analysis PYQs

Question 43

Question 63

Question 11

Question 12

Question 36

Question 37

Question 13

Question 15

Question 27

Question 42