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Previous year question hub

Calculus - Engineering Mathematics - Production & Industrial Engineering Previous Year Questions

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

21Papers
19Years
143Questions
1Topics

Calculus question pattern

Every graph below is calculated only from this selection.

Questions by year

Compare question counts across years.

Difficulty distribution

How the classified questions are distributed by difficulty.

Easy 115 80.4%
Medium 28 19.6%

Question type distribution

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

MCQ 118 82.5%
Numerical Answer Type (NAT) 23 16.1%
MSQ 2 1.4%

Subject weightage

Top subjects by unique question coverage.

Production & Industrial Engineering
143 Qs

Most asked topics

Top topics across the included previous year papers.

Engineering Mathematics
143 Qs

Subtopic coverage

Top subtopics inside this exact selection.

Calculus
143 Qs

Paper coverage

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

Production and Industrial Engineering (PI) 2026
3 Qs
Production & Industrial Engineering (PI) 2025
4 Qs
Production & Industrial Engineering (PI) 2024
5 Qs
Production & Industrial Engineering (PI) 2023
4 Qs
Production & Industrial Engineering (PI) 2022
4 Qs
Production & Industrial Engineering (PI) 2021
4 Qs
Production & Industrial Engineering (PI) 2020
5 Qs
Production & Industrial Engineering (PI) 2019
7 Qs
Production & Industrial Engineering (PI) 2018
6 Qs
Production & Industrial Engineering (PI) 2017
4 Qs
Production & Industrial Engineering (PI) 2016
5 Qs
Production & Industrial Engineering (PI) 2014
5 Qs
Production & Industrial Engineering (PI) 2013 [Session 1]
7 Qs
Production & Industrial Engineering (PI) 2013 [Session 2]
7 Qs
Production & Industrial Engineering (PI) 2013 [Session 4]
7 Qs
Production & Industrial Engineering (PI) 2012
9 Qs
Production & Industrial Engineering (PI) 2011
8 Qs
Production & Industrial Engineering (PI) 2010
7 Qs
Production & Industrial Engineering (PI) 2009
7 Qs
Production & Industrial Engineering (PI) 2008
18 Qs
Production & Industrial Engineering (PI) 2007
17 Qs

Included previous year papers

Newest papers appear first. Search these papers or sort by year and name.

Paper nameYearPDFAttempt
Production and Industrial Engineering (PI) 20262026
3 questions in this view		2026
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ExamElite solutions
Official documents
Official question paperOriginal authority-issued PDF Official Download Official answer keyOriginal authority-issued PDF Official Download
Production & Industrial Engineering (PI) 20252025
4 questions in this view		2025
ExamElite PDFs
ExamElite solutions
Official documents
Official question paperOriginal authority-issued PDF Official Download Official answer keyOriginal authority-issued PDF Official Download
Production & Industrial Engineering (PI) 20242024
5 questions in this view		2024
ExamElite PDFs
ExamElite solutions
Official documents
Official question paperOriginal authority-issued PDF Official Download Official answer keyOriginal authority-issued PDF Official Download
Production & Industrial Engineering (PI) 20232023
4 questions in this view		2023
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ExamElite solutions
Official documents
Official question paperOriginal authority-issued PDF Official Download Official answer keyOriginal authority-issued PDF Official Download
Production & Industrial Engineering (PI) 20222022
4 questions in this view		2022
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ExamElite solutions
Official documents
Official question paperOriginal authority-issued PDF Official Download Official answer keyOriginal authority-issued PDF Official Download
Production & Industrial Engineering (PI) 20212021
4 questions in this view		2021
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ExamElite solutions
Official documents
Official question paperOriginal authority-issued PDF Official Download Official answer keyOriginal authority-issued PDF Official Download
Production & Industrial Engineering (PI) 20202020
5 questions in this view		2020
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ExamElite solutions
Official documents
Official question paperOriginal authority-issued PDF Official Download
Production & Industrial Engineering (PI) 20192019
7 questions in this view		2019
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ExamElite solutions
Official documents
Official question paperOriginal authority-issued PDF Official Download
Production & Industrial Engineering (PI) 20182018
6 questions in this view		2018
ExamElite PDFs
ExamElite solutions
Official documents
Official question paperOriginal authority-issued PDF Official Download
Production & Industrial Engineering (PI) 20172017
4 questions in this view		2017
ExamElite PDFs
ExamElite solutions
Official documents
Official question paperOriginal authority-issued PDF Official Download
Production & Industrial Engineering (PI) 20162016
5 questions in this view		2016
ExamElite PDFs
ExamElite solutions
Official documents
Official question paperOriginal authority-issued PDF Official Download
Production & Industrial Engineering (PI) 20142014
5 questions in this view		2014
ExamElite PDFs
ExamElite solutions
Official documents
Official question paperOriginal authority-issued PDF Official Download
Production & Industrial Engineering (PI) 2013 [Session 1]2013
7 questions in this view		2013
ExamElite PDFs
ExamElite solutions
Official documents
Official question paperOriginal authority-issued PDF Official Download
Production & Industrial Engineering (PI) 2013 [Session 2]2013
7 questions in this view		2013
ExamElite PDFs
ExamElite solutions
Official documents
Official question paperOriginal authority-issued PDF Official Download
Production & Industrial Engineering (PI) 2013 [Session 4]2013
7 questions in this view		2013
ExamElite PDFs
ExamElite solutions
Official documents
Official question paperOriginal authority-issued PDF Official Download
Production & Industrial Engineering (PI) 20122012
9 questions in this view		2012
ExamElite PDFs
ExamElite solutions
Official documents
Official question paperOriginal authority-issued PDF Official Download
Production & Industrial Engineering (PI) 20112011
8 questions in this view		2011
ExamElite PDFs
ExamElite solutions
Official documents
Official question paperOriginal authority-issued PDF Official Download
Production & Industrial Engineering (PI) 20102010
7 questions in this view		2010
ExamElite PDFs
ExamElite solutions
Official documents
Official question paperOriginal authority-issued PDF Official Download
Production & Industrial Engineering (PI) 20092009
7 questions in this view		2009
ExamElite PDFs
ExamElite solutions
Official documents
Official question paperOriginal authority-issued PDF Official Download
Production & Industrial Engineering (PI) 20082008
18 questions in this view		2008
ExamElite PDFs
ExamElite solutions
Official documents
Official question paperOriginal authority-issued PDF Official Download
Production & Industrial Engineering (PI) 20072007
17 questions in this view		2007
ExamElite PDFs
ExamElite solutions
Official documents
Official question paperOriginal authority-issued PDF Official Download

All Calculus previous year questions

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

1
2007 · Production & Industrial Engineering · Engineering Mathematics · Calculus
Production & Industrial Engineering (PI) 2007
If a complex variable \( z = \frac{\sqrt{3}}{2} + i \frac{1}{2} \), then \( z^4 \) is
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2
2007 · Production & Industrial Engineering · Engineering Mathematics · Calculus
Production & Industrial Engineering (PI) 2007
The angle (in degrees) between two planer vectors \( \vec{a} = \frac{\sqrt{3}}{2} \hat{i} + \frac{1}{2} \hat{j} \) and \( \vec{b} = -\frac{\sqrt{3}}{2} \hat{i} + \frac{1}{2} \hat{j} \) is
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3
2007 · Production & Industrial Engineering · Engineering Mathematics · Calculus
Production & Industrial Engineering (PI) 2007
What is the value of \[ \lim_{x \to \frac{\pi}{4}} \frac{\cos x - \sin x}{x - \frac{\pi}{4}} \]
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4
2007 · Production & Industrial Engineering · Engineering Mathematics · Calculus
Production & Industrial Engineering (PI) 2007
\( f(x) = |x| \) is a function defined for real numbers \( x \). The directional derivative of \( f \) at \( x = 0 \) in the direction \( d = -1 \) is
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5
2007 · Production & Industrial Engineering · Engineering Mathematics · Calculus
Production & Industrial Engineering (PI) 2007
The angle (in degrees) between two planar vectors \( \vec{a} = \frac{\sqrt{3}}{2} \hat{i} + \frac{1}{2} \hat{j} \) and \( \vec{b} = -\frac{\sqrt{3}}{2} \hat{i} + \frac{1}{2} \hat{j} \) is
Open complete paper
6
2007 · Production & Industrial Engineering · Engineering Mathematics · Calculus
Production & Industrial Engineering (PI) 2007
\( f(x) = |x| \) is a function defined for real numbers x. The directional derivative of f at x = 0 in the direction d = -1 is
Open complete paper
7
2007 · Production & Industrial Engineering · Engineering Mathematics · Calculus
Production & Industrial Engineering (PI) 2007
The function \( e^x \) over the interval [0,1] is to be evaluated using the Taylor series \( 1 + x + \frac{x^2}{2!} + \frac{x^3}{3!} + ... \) to an accuracy of δ > 0. The number of terms in the series that is considered for this accuracy is n. Then
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8
2007 · Production & Industrial Engineering · Engineering Mathematics · Calculus
Production & Industrial Engineering (PI) 2007
For the function \( f(x, y) = x^2 - y^2 \) defined on \( R^2 \), the point [0,0] is
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9
2007 · Production & Industrial Engineering · Engineering Mathematics · Calculus
Production & Industrial Engineering (PI) 2007
The function \( e^x \) over the interval [0,1] is to be evaluated using the Taylor series \( 1 + x + \frac{x^2}{2!} + \frac{x^3}{3!} + ... \) to an accuracy of \( \delta > 0 \). The number of terms in the series that is considered for this accuracy is \( n \). Then
Open complete paper
10
2007 · Production & Industrial Engineering · Engineering Mathematics · Calculus
Production & Industrial Engineering (PI) 2007
When an ideal gas (\( C_p = 3.5 \)) is heated at constant pressure from 25°C to 425°C, the change in entropy is
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11
2007 · Production & Industrial Engineering · Engineering Mathematics · Calculus
Production & Industrial Engineering (PI) 2007
A radial disc cam rotating at a constant speed of 60 rpm provides a parabolic displacement of 0.2 m to its flat faced rectilinear follower during 90° of its rotation. The acceleration (m/s²) experienced by the follower is
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12
2007 · Production & Industrial Engineering · Engineering Mathematics · Calculus
Production & Industrial Engineering (PI) 2007
When an ideal gas (C_p = 3.5) is heated at constant pressure from 25°C to 425°C, the change in entropy is
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13
2007 · Production & Industrial Engineering · Engineering Mathematics · Calculus
Production & Industrial Engineering (PI) 2007
In a CAD package, a point P (6, 3, 2) is projected along a vector v = (-2, 1, -1). The projection of this point on X-Y plane will be
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14
2007 · Production & Industrial Engineering · Engineering Mathematics · Calculus
Production & Industrial Engineering (PI) 2007
The problem of finding the rectangle of maximum area with perimeter equal to 20 can be posed as the constrained optimization problem
\[ \begin{aligned} \text{Max} \quad & xy \\ \text{s.t.} \quad & 2x + 2y = 20 \\ & x, y \ge 0 \end{aligned} \]
The solution to this problem is \(x = y = 5\). What is the value of the Lagrange multiplier corresponding to the perimeter constraint?
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15
2008 · Production & Industrial Engineering · Engineering Mathematics · Calculus
Production & Industrial Engineering (PI) 2008
The value of the integral \(\int_{-\pi/2}^{\pi/2} x \cos(x) dx\) is
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16
2008 · Production & Industrial Engineering · Engineering Mathematics · Calculus
Production & Industrial Engineering (PI) 2008
The value of the expression \(\frac{-5+i10}{3+4i}\) is
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17
2008 · Production & Industrial Engineering · Engineering Mathematics · Calculus
Production & Industrial Engineering (PI) 2008
The value of the expression \(\lim_{x \to 0} \left[ \frac{\sin(x)}{e^x x} \right]\) is
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18
2008 · Production & Industrial Engineering · Engineering Mathematics · Calculus
Production & Industrial Engineering (PI) 2008
If \(\vec{r}\) is the position vector of any point on a closed surface \(S\) that encloses the volume \(V\), then \(\iint_S (\vec{r} \cdot d\vec{S})\) is equal to
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19
2008 · Production & Industrial Engineering · Engineering Mathematics · Calculus
Production & Industrial Engineering (PI) 2008
The value of the expression \(\frac{-5+i10}{3+i4}\) is
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20
2008 · Production & Industrial Engineering · Engineering Mathematics · Calculus
Production & Industrial Engineering (PI) 2008
The value of the expression \(\lim_{x \to 0} \left[\frac{\sin(x)}{e^x x}\right]\) is
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Showing 20 of 129 questions