Mechanical Engineering
GATE ME 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 39. Imported answers require independent review unless marked reviewed.
Question 11
Open questionMEMCQ1 markNeeds review
Domain
is bounded by curve
, ordinate
, and
axis. The value of
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 12
Open questionMEMCQ1 markNeeds review
Let
be a scalar function. 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 13
Open questionMEMCQ1 markNeeds review
The divergence of the curl of a vector field 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 36
Open questionMEMCQ2 marksNeeds review
In the closed interval [0, 3], the minimum value of the function
given below 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 46
Open questionMENAT2 marksNeeds review
The directional derivative of the function
given below at the point
in the direction of
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 12
Open questionMEMCQ1 markNeeds review
The value of the surface integral
where
is the external surface of the sphere
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 15
Open questionMEMCQ1 markNeeds review
Let
be a twice differentiable function from
. If
where
is sufficiently small (here
is the Euclidean norm or distance function), then
where
is a point on the line segment joining
and
. If
is a strict local minimum of
, then which one of the following statements is TRUE?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 42
Open questionMENAT2 marksNeeds review
If the value of the double integral
is
, then
is ______ (answer in integer).Log in to check the answer
You can attempt this question now. Sign in to view the answer key, explanations and discussion.Log in to check answerQuestion 12
Open questionMEMCQ1 markNeeds review
The figure shows the plot of a function over the interval
. Which one of the options given CORRECTLY identifies the function? 
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 31
Open questionMENAT1 markNeeds review
A vector field
is defined over a conical region having height h = 2, base radius r = 3 and axis along z, as shown in the figure. The base of the cone lies in the x-y plane and is centered at the origin.
If n denotes the unit outward normal to the curved surface S of the cone, the value of the integral
equals ________ . (Answer in integer)
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