Electronics and Communication Engineering
GATE ECE Calculus PYQs
Build your understanding with focused practice from past exam papers.
How to practice Calculus
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 21. Imported answers require independent review unless marked reviewed.
Question 61
Open questionECNAT2 marksNeeds review
Consider the square region
in the X-Y plane as shown with the dark shading in the Figure. The value of
is ___. (rounded off to two decimal places) 
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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 12
Open questionECMCQ1 markNeeds review
Consider the following series:
(i)
(ii)
(iii)
Choose the correct option.
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 25
Open questionECMSQ1 markNeeds review
Consider the function
, defined as
Which of the following statements is/are correct?
(Here,
is the set of real numbers.)Your answerSelect all correct options. You can choose more than one.
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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 51
Open questionECMSQ2 marksNeeds review
Consider a non-negative function
which is continuous and bounded over the interval
. Let
and
denote, respectively, the maximum and the minimum values of
over the interval.Among the combinations of
and
given below, choose the one(s) for which the inequality
is guaranteed to hold.
Your answerSelect all correct options. You can choose more than one.
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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 questionECMCQ2 marksNeeds review
Consider the Earth to be a perfect sphere of radius R. Then the surface area of the region, enclosed by the 60°N latitude circle, that contains the north pole in its interior is ______.
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 55
Open questionECNAT2 marksNeeds review
The value of the integral
over the region R, given in the figure
, is ______ (rounded off to the nearest 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 questionECMCQ2 marksNeeds review
The function
attains its minimum over the interval
at
________. (Here
is the natural logarithm of
.)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 45
Open questionECMSQ2 marksNeeds review
Consider the following series:
For which of the following combinations of
,
values does this series converge?Your answerSelect all correct options. You can choose more than one.
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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 53
Open questionECNAT2 marksNeeds review
The value of the integral
where
is the shaded triangular region shown in the diagram, is _____ (rounded off to the nearest 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 3
Open questionECMCQ1 markNeeds review
The partial derivative of the function
with respect to
at the point
isYour answerChoose one option.
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