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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

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

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. Sort by year, question coverage or name.

PaperYear / sessionQuestions in this viewOpen
Production and Industrial Engineering (PI) 202620263View paper
Production & Industrial Engineering (PI) 202520254View paper
Production & Industrial Engineering (PI) 202420245View paper
Production & Industrial Engineering (PI) 202320234View paper
Production & Industrial Engineering (PI) 202220224View paper
Production & Industrial Engineering (PI) 202120214View paper
Production & Industrial Engineering (PI) 202020205View paper
Production & Industrial Engineering (PI) 201920197View paper
Production & Industrial Engineering (PI) 201820186View paper
Production & Industrial Engineering (PI) 201720174View paper
Production & Industrial Engineering (PI) 201620165View paper
Production & Industrial Engineering (PI) 201420145View paper
Production & Industrial Engineering (PI) 2013 [Session 1]20137View paper
Production & Industrial Engineering (PI) 2013 [Session 2]20137View paper
Production & Industrial Engineering (PI) 2013 [Session 4]20137View paper
Production & Industrial Engineering (PI) 201220129View paper
Production & Industrial Engineering (PI) 201120118View paper
Production & Industrial Engineering (PI) 201020107View paper
Production & Industrial Engineering (PI) 200920097View paper
Production & Industrial Engineering (PI) 2008200818View paper
Production & Industrial Engineering (PI) 2007200717View paper

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
Open complete paper
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
Open complete paper
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
Open complete paper
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