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Previous year question hub

Vector Calculus - Engineering Sciences Previous Year Questions

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

19Papers
19Years
26Questions
1Topics

Vector 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.

Medium 18 69.2%
Easy 8 30.8%

Question type distribution

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

MCQ 17 65.4%
Numerical Answer Type (NAT) 9 34.6%

Subject weightage

Top subjects by unique question coverage.

Engineering Sciences
26 Qs

Most asked topics

Top topics across the included previous year papers.

Vector Calculus
26 Qs

Subtopic coverage

Top subtopics inside this exact selection.

Vector Derivatives and Line Integrals
26 Qs

Paper coverage

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

Engineering Sciences (XE) 2026
1 Qs
Engineering Sciences (XE) 2025
1 Qs
Engineering Sciences (XE) 2024
1 Qs
Engineering Sciences (XE) 2023
2 Qs
Engineering Sciences (XE) 2022
1 Qs
Engineering Sciences (XE) 2021
3 Qs
Engineering Sciences (XE) 2020
1 Qs
Engineering Sciences (XE) 2019
1 Qs
Engineering Sciences (XE) 2018
1 Qs
Engineering Sciences (XE) 2017
1 Qs
Engineering Sciences (XE) 2016
1 Qs
Engineering Sciences (XE) 2015
1 Qs
Engineering Sciences (XE) 2014
1 Qs
Engineering Sciences (XE) 2013
1 Qs
Engineering Sciences (XE) 2012
2 Qs
Engineering Sciences (XE) 2011
2 Qs
Engineering Sciences (XE) 2009
2 Qs
Engineering Sciences (XE) 2008
2 Qs
Engineering Sciences (XE) 2007
1 Qs

Browse by subtopics

Open a focused page built from the same verified paper data.

Vector Derivatives and Line Integrals

Explore previous-paper coverage, trends and focused practice for Vector Derivatives and Line Integrals.

26 questions19 papers19 years

Included previous year papers

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

Paper nameYearPDFAttempt
Engineering Sciences (XE) 20262026
1 questions in this view		2026
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Official question paperOriginal authority-issued PDF Official Download Official answer keyOriginal authority-issued PDF Official Download
Engineering Sciences (XE) 20252025
1 questions in this view		2025
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Official documents
Official question paperOriginal authority-issued PDF Official Download Official answer keyOriginal authority-issued PDF Official Download
Engineering Sciences (XE) 20242024
1 questions in this view		2024
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Official documents
Official question paperOriginal authority-issued PDF Official Download Official answer keyOriginal authority-issued PDF Official Download
Engineering Sciences (XE) 20232023
2 questions in this view		2023
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Official question paperOriginal authority-issued PDF Official Download Official answer keyOriginal authority-issued PDF Official Download
Engineering Sciences (XE) 20222022
1 questions in this view		2022
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Official question paperOriginal authority-issued PDF Official Download Official answer keyOriginal authority-issued PDF Official Download
Engineering Sciences (XE) 20212021
3 questions in this view		2021
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Official documents
Official question paperOriginal authority-issued PDF Official Download Official answer keyOriginal authority-issued PDF Official Download
Engineering Sciences (XE) 20202020
1 questions in this view		2020
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Official documents
Official question paperOriginal authority-issued PDF Official Download
Engineering Sciences (XE) 20192019
1 questions in this view		2019
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Official documents
Official question paperOriginal authority-issued PDF Official Download
Engineering Sciences (XE) 20182018
1 questions in this view		2018
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Official documents
Official question paperOriginal authority-issued PDF Official Download
Engineering Sciences (XE) 20172017
1 questions in this view		2017
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Official documents
Official question paperOriginal authority-issued PDF Official Download
Engineering Sciences (XE) 20162016
1 questions in this view		2016
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Official documents
Official question paperOriginal authority-issued PDF Official Download
Engineering Sciences (XE) 20152015
1 questions in this view		2015
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Official documents
Official question paperOriginal authority-issued PDF Official Download
Engineering Sciences (XE) 20142014
1 questions in this view		2014
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Official documents
Official question paperOriginal authority-issued PDF Official Download
Engineering Sciences (XE) 20132013
1 questions in this view		2013
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Official documents
Official question paperOriginal authority-issued PDF Official Download
Engineering Sciences (XE) 20122012
2 questions in this view		2012
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Official documents
Official question paperOriginal authority-issued PDF Official Download
Engineering Sciences (XE) 20112011
2 questions in this view		2011
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Official documents
Official question paperOriginal authority-issued PDF Official Download
Engineering Sciences (XE) 20092009
2 questions in this view		2009
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Official documents
Official question paperOriginal authority-issued PDF Official Download
Engineering Sciences (XE) 20082008
2 questions in this view		2008
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Official documents
Official question paperOriginal authority-issued PDF Official Download
Engineering Sciences (XE) 20072007
1 questions in this view		2007
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Official documents
Official question paperOriginal authority-issued PDF Official Download

Sample previous year questions

A varied preview from the papers represented in this selection, with every available option.

1
2007 · Engineering Sciences · Vector Calculus · Vector Derivatives and Line Integrals
Engineering Sciences (XE) 2007
The value of \( \oint_C (xy^2+2x)dx + (x^2y+4x)dy \) along the circle \( C: x^2+y^2=4 \) in the anticlockwise direction is
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2
2008 · Engineering Sciences · Vector Calculus · Vector Derivatives and Line Integrals
Engineering Sciences (XE) 2008
The directional derivative at the point \(P(1,2,3)\) to the surface \(x^2 + \frac{y^2}{4} + \frac{z^2}{9} = 3\) in the direction of the vector \(\overrightarrow{OP}\), where \(O\) denotes the origin, is
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3
2009 · Engineering Sciences · Vector Calculus · Vector Derivatives and Line Integrals
Engineering Sciences (XE) 2009
Let C be the boundary of the square given by 0 ≤ x ≤ 1, 0 ≤ y ≤ 1. Then \[ \oint_C (x dy - y dx) \] equals
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4
2011 · Engineering Sciences · Vector Calculus · Vector Derivatives and Line Integrals
Engineering Sciences (XE) 2011
A vector field is called solenoidal if its divergence is zero. Consider the vector fields $\vec{P}$ and $\vec{Q}$ given by
$\vec{P}(x, y, z) = (2x^2 + 8xy^2 z)\hat{i} + (3x^3 y - 3xy)\hat{j} - (4y^2 z^2 + 2x^2 z)\hat{k}$ and
$\vec{Q}(x, y, z) = xyz^2 \vec{P}(x, y, z)$.
Then
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5
2012 · Engineering Sciences · Vector Calculus · Vector Derivatives and Line Integrals
Engineering Sciences (XE) 2012
For \( f = x^4 - 5xy^2 \), the direction of maximum increase of \( f(x,y) \) at the point \( (2,2) \) is along
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6
2013 · Engineering Sciences · Vector Calculus · Vector Derivatives and Line Integrals
Engineering Sciences (XE) 2013
The work done by the force \(\vec{F}=(x+x^{2}) \hat{i}+(x^{2}+y^{3}) \hat{j}\) in moving a particle once along the triangle with vertices (0,0),(1,0) and (0,1) in the anti-clockwise direction is
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