Mechanical Engineering
GATE ME Calculus PYQs
Build your understanding with focused practice from past exam papers.
Questions 21–30 of 39. Imported answers require independent review unless marked reviewed.
Question 5
Open questionGAMCQ1 markNeeds review
Define
as the greatest integer less than or equal to
, for each
. If
, then area under
for
is _____.Your answerChoose one option.
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Open questionMEMCQ1 markNeeds review
The value of
isYour answerChoose one option.
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Open questionMEMCQ1 markNeeds review
Let
. Then,
may also be expressed asYour 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 26
Open questionMEMCQ2 marksNeeds review
The directional derivative of
at point
in the direction of vector
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 27
Open questionMEMCQ2 marksNeeds review
A vector field is defined as
where,
are unit vectors along the axes of a right-handed rectangular/Cartesian coordinate system. The surface integral
(where
is an elemental surface area vector) evaluated over the inner and outer surfaces of a spherical shell formed by two concentric spheres with origin as the center, and internal and external radii of 1 and 2, respectively, 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 2
Open questionMEMCQ1 markNeeds review
A parabola
with
is shown in the figure. The volume of the solid of rotation obtained by rotating the shaded area by 360° around the x-axis is
Your answerChoose one option.
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Open questionMEMCQ1 markNeeds review
The directional derivative of the function
along a line directed from
to
, evaluated at the point
isYour answerChoose one option.
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Open questionMEMCQ2 marksNeeds review
Given a vector
and
as the unit normal vector to the surface of the hemisphere
, the value of integral
evaluated on the curved surface of the hemisphere
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 51
Open questionMENAT2 marksNeeds review
The value of the following definite integral is____ (round off to three 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 1
Open questionMEMCQ1 markNeeds review
The Fourier cosine series for an even function
is given by
The value of the coefficient
for the function
in
isYour answerChoose one option.
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