Mechanical Engineering
GATE ME topic:complex-analysis PYQs
Build your understanding with focused practice from past exam papers.
How to practice topic:complex-analysis
Attempt a question, record the concept and assumptions, then check the available answer. Rework mistakes after revising the relevant concepts. Topic tags can overlap; review the question context.
Questions 1–10 of 16. Imported answers require independent review unless marked reviewed.
Question 36
Open questionMEMCQ2 marksNeeds review
If
, where
, then which one of the following statements is correct?Your answerChoose one option.
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Open questionMENAT2 marksNeeds review
If
is the unit circle in the complex plane with its center at the origin, then the value of
in the equation given below is __________ (rounded off to 1 decimal place).
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You can attempt this question now. Sign in to view the answer key, explanations and discussion.Log in to check answerQuestion 13
Open questionMEMCQ1 markNeeds review
Let
be an analytic function, where
. If the real part of
is
, and the imaginary part of
is zero for
, then
isYour answerChoose one option.
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You can attempt this question now. Sign in to view the answer key, explanations and discussion.Log in to check answerQuestion 33
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The value of k that makes the complex-valued function
analytic, where
, is ________.(Answer in integer)
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You can attempt this question now. Sign in to view the answer key, explanations and discussion.Log in to check answerQuestion 36
Open questionMEMCQ2 marksNeeds review
The value of the integral
evaluated over a counter-clockwise circular contour in the complex plane enclosing only the pole
, where
is the imaginary unit, isYour answerChoose one option.
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Open questionMENAT2 marksNeeds review
Given
,
.
is a circle of radius 2 with the centre at the origin. If the contour
is traversed anticlockwise, then the value of the integral
is _______ (round off to one decimal place).Log in to check the answer
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Value of
, where
, is equal toYour answerChoose one option.
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You can attempt this question now. Sign in to view the answer key, explanations and discussion.Log in to check answerQuestion 27
Open questionMEMCQ2 marksNeeds review
Let
represent the unit circle centered at origin in the complex plane, and complex variable,
. The value of the contour integral
(where integration is taken counter clockwise) isYour answerChoose one option.
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You can attempt this question now. Sign in to view the answer key, explanations and discussion.Log in to check answerQuestion 4
Open questionMEMCQ1 markNeeds review
Which of the following function
, of the complex variable
, is NOT analytic at all the points of the complex plane?Your answerChoose one option.
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You can attempt this question now. Sign in to view the answer key, explanations and discussion.Log in to check answerQuestion 27
Open questionMEMCQ2 marksNeeds review
The function
of complex variable
, where
, is given as
. For this function to be analytic,
should beYour answerChoose one option.
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