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Previous year question hub

Calculus - Engineering Mathematics - Mechanical Engineering Previous Year Questions

Practice Calculus - Engineering Mathematics - Mechanical Engineering previous year questions organised from real papers, with year-wise coverage and clear topic navigation.

27Papers
17Years
92Questions
1Topics

Calculus question pattern

Every graph below is calculated only from this selection.

Questions by year

Year-wise coverage for Calculus. Each bar uses a separate theme-derived color.

Difficulty distribution

How the classified questions are distributed by difficulty.

Easy 76 82.6%
Medium 16 17.4%

Question type distribution

MCQ, numerical, multiple-select and other formats found in these papers.

MCQ 80 87%
Numerical Answer Type (NAT) 11 12%
MSQ 1 1.1%

Subject weightage

Top subjects by unique question coverage.

Mechanical Engineering
92 Qs

Most asked topics

Top topics across the included previous year papers.

Engineering Mathematics
92 Qs

Subtopic coverage

Top subtopics inside this exact selection.

Calculus
92 Qs

Paper coverage

Question coverage for the most populated papers. Every active PYP paper remains listed below.

Mechanical Engineering (ME) 2026
1 Qs
Mechanical Engineering (ME) 2025
3 Qs
Mechanical Engineering (ME) 2024
3 Qs
Mechanical Engineering (ME) 2023
4 Qs
Mechanical Engineering (ME) 2021 [Session 1]
3 Qs
Mechanical Engineering (ME) 2020 [Session 1]
3 Qs
Mechanical Engineering (ME) 2020 [Session 2]
2 Qs
Mechanical Engineering (ME) 2019 [Session 1]
2 Qs
Mechanical Engineering (ME) 2019 [Session 2]
1 Qs
Mechanical Engineering (ME) 2018 [Session 1]
3 Qs
Mechanical Engineering (ME) 2018 [Session 2]
1 Qs
Mechanical Engineering (ME) 2016 [Session 3]
5 Qs
Mechanical Engineering (ME) 2016 [Session 2]
2 Qs
Mechanical Engineering (ME) 2016 [Session 1]
1 Qs
Mechanical Engineering (ME) 2015 [Session 2]
2 Qs
Mechanical Engineering (ME) 2014 [Session 1]
2 Qs
Mechanical Engineering (ME) 2014 [Session 3]
2 Qs
Mechanical Engineering (ME) 2014 [Session 4]
2 Qs
Mechanical Engineering (ME) 2013 [Session 1]
6 Qs
Mechanical Engineering (ME) 2013 [Session 2]
5 Qs
Mechanical Engineering (ME) 2013 [Session 3]
5 Qs
Mechanical Engineering (ME) 2013 [Session 4]
4 Qs
Mechanical Engineering (ME) 2011
7 Qs
Mechanical Engineering (ME) 2010
5 Qs
Mechanical Engineering (ME) 2009
5 Qs
Mechanical Engineering (ME) 2008
8 Qs
Mechanical Engineering (ME) 2007
5 Qs

Included previous year papers

Newest papers appear first. Sort by year, question coverage or name.

PaperYear / sessionQuestions in this viewOpen
Mechanical Engineering (ME) 202620261View paper
Mechanical Engineering (ME) 202520253View paper
Mechanical Engineering (ME) 202420243View paper
Mechanical Engineering (ME) 202320234View paper
Mechanical Engineering (ME) 2021 [Session 1]20213View paper
Mechanical Engineering (ME) 2020 [Session 1]20203View paper
Mechanical Engineering (ME) 2020 [Session 2]20202View paper
Mechanical Engineering (ME) 2019 [Session 1]20192View paper
Mechanical Engineering (ME) 2019 [Session 2]20191View paper
Mechanical Engineering (ME) 2018 [Session 1]20183View paper
Mechanical Engineering (ME) 2018 [Session 2]20181View paper
Mechanical Engineering (ME) 2016 [Session 1]20161View paper
Mechanical Engineering (ME) 2016 [Session 2]20162View paper
Mechanical Engineering (ME) 2016 [Session 3]20165View paper
Mechanical Engineering (ME) 2015 [Session 2]20152View paper
Mechanical Engineering (ME) 2014 [Session 1]20142View paper
Mechanical Engineering (ME) 2014 [Session 3]20142View paper
Mechanical Engineering (ME) 2014 [Session 4]20142View paper
Mechanical Engineering (ME) 2013 [Session 1]20136View paper
Mechanical Engineering (ME) 2013 [Session 2]20135View paper
Mechanical Engineering (ME) 2013 [Session 3]20135View paper
Mechanical Engineering (ME) 2013 [Session 4]20134View paper
Mechanical Engineering (ME) 201120117View paper
Mechanical Engineering (ME) 201020105View paper
Mechanical Engineering (ME) 200920095View paper
Mechanical Engineering (ME) 200820088View paper
Mechanical Engineering (ME) 200720075View paper

All Calculus previous year questions

Practice every matching question in batches of 20, with every available option.

1
2007 · Mechanical Engineering · Engineering Mathematics · Calculus
Mechanical Engineering (ME) 2007
The minimum value of function \( y = x^2 \) in the interval \( [1,5] \) is
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2
2007 · Mechanical Engineering · Engineering Mathematics · Calculus
Mechanical Engineering (ME) 2007
If \( y = x + \sqrt{x + \sqrt{x + \cdots}} \), then \( y(2) = \)
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3
2007 · Mechanical Engineering · Engineering Mathematics · Calculus
Mechanical Engineering (ME) 2007
The area of a triangle formed by the tips of vectors \( \bar{a} \), \( \bar{b} \) and \( \bar{c} \) is
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4
2007 · Mechanical Engineering · Engineering Mathematics · Calculus
Mechanical Engineering (ME) 2007
If \( F(s) \) is the Laplace transform of function \( f(t) \), then Laplace transform of \( \int_{0}^{t} f(\tau) d\tau \) is
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5
2007 · Mechanical Engineering · Engineering Mathematics · Calculus
Mechanical Engineering (ME) 2007
\( \lim_{x \to 0} \frac{e^x - \left(1 + x + \frac{x^2}{2}\right)}{x^3} = \)
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6
2008 · Mechanical Engineering · Engineering Mathematics · Calculus
Mechanical Engineering (ME) 2008
In the Taylor series expansion of \(e^x\) about \(x = 2\), the coefficient of \((x-2)^4\) is
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7
2008 · Mechanical Engineering · Engineering Mathematics · Calculus
Mechanical Engineering (ME) 2008
The value of \(\lim_{x \to 8} \frac{x^{1/3} - 2}{x - 8}\) is
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8
2008 · Mechanical Engineering · Engineering Mathematics · Calculus
Mechanical Engineering (ME) 2008
The divergence of the vector field \((x-y)\hat{i} + (y-x)\hat{j} + (x+y+z)\hat{k}\) is
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9
2008 · Mechanical Engineering · Engineering Mathematics · Calculus
Mechanical Engineering (ME) 2008
Consider the shaded triangular region P shown in the figure. What is \(\iint_P xy \, dx \, dy\) ?
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10
2008 · Mechanical Engineering · Engineering Mathematics · Calculus
Mechanical Engineering (ME) 2008
The directional derivative of the scalar function \(f(x, y, z) = x^2 + 2y^2 + z\) at the point P = (1, 1, 2) in the direction of the vector \(\vec{a} = 3\hat{i} - 4\hat{j}\) is
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11
2008 · Mechanical Engineering · Engineering Mathematics · Calculus
Mechanical Engineering (ME) 2008

Which of the following integrals is unbounded?

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12
2008 · Mechanical Engineering · Engineering Mathematics · Calculus
Mechanical Engineering (ME) 2008
The length of the curve \(y = \frac{2}{3} x^{3/2}\) between \(x = 0\) and \(x = 1\) is
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13
2008 · Mechanical Engineering · Engineering Mathematics · Calculus
Mechanical Engineering (ME) 2008
Let \(f = y^x\). What is \(\frac{\partial^2 f}{\partial x \partial y}\) at \(x = 2, y = 1\)?
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14
2009 · Mechanical Engineering · Engineering Mathematics · Calculus
Mechanical Engineering (ME) 2009
The divergence of the vector field \( 3xz \hat{i} + 2xy \hat{j} - yz^2 \hat{k} \) at a point (1,1,1) is equal to
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15
2009 · Mechanical Engineering · Engineering Mathematics · Calculus
Mechanical Engineering (ME) 2009
The inverse Laplace transform of \( \frac{1}{(s^2 + s)} \) is
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16
2009 · Mechanical Engineering · Engineering Mathematics · Calculus
Mechanical Engineering (ME) 2009
A path AB in the form of one quarter of a circle of unit radius is shown in the figure. Integration of \((x + y)^2\) on path AB traversed in a counter-clockwise sense is
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17
2009 · Mechanical Engineering · Engineering Mathematics · Calculus
Mechanical Engineering (ME) 2009
The distance between the origin and the point nearest to it on the surface \(z^2 = 1 + xy\) is
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18
2009 · Mechanical Engineering · Engineering Mathematics · Calculus
Mechanical Engineering (ME) 2009
The area enclosed between the curves \(y^2 = 4x\) and \(x^2 = 4y\) is
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19
2010 · Mechanical Engineering · Engineering Mathematics · Calculus
Mechanical Engineering (ME) 2010
The parabolic arc \( y = \sqrt{x} \), \( 1 \le x \le 2 \) is revolved around the x-axis. The volume of the solid of revolution is
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20
2010 · Mechanical Engineering · Engineering Mathematics · Calculus
Mechanical Engineering (ME) 2010
The value of the integral \( \int_{-\pi}^{\pi} \frac{dx}{1 + x^2} \) is
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Showing 20 of 87 questions