Previous year question hub

Complex Variables - Engineering Mathematics - Mechanical Engineering Previous Year Questions

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

23Papers

16Years

27Questions

1Topics

Complex Variables 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.

27questions

Easy 19 70.4%

Medium 8 29.6%

Question type distribution

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

27questions

MCQ 22 81.5%

Numerical Answer Type (NAT) 5 18.5%

Subject weightage

Top subjects by unique question coverage.

Mechanical Engineering

27 Qs

Most asked topics

Top topics across the included previous year papers.

Engineering Mathematics

27 Qs

Subtopic coverage

Top subtopics inside this exact selection.

Complex Variables

27 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

1 Qs

Mechanical Engineering (ME) 2024

1 Qs

Mechanical Engineering (ME) 2023

1 Qs

Mechanical Engineering (ME) 2021 [Session 1]

1 Qs

Mechanical Engineering (ME) 2020 [Session 1]

3 Qs

Mechanical Engineering (ME) 2020 [Session 2]

1 Qs

Mechanical Engineering (ME) 2019 [Session 1]

1 Qs

Mechanical Engineering (ME) 2019 [Session 2]

1 Qs

Mechanical Engineering (ME) 2018 [Session 1]

1 Qs

Mechanical Engineering (ME) 2018 [Session 2]

1 Qs

Mechanical Engineering (ME) 2017 [Session 2]

1 Qs

Mechanical Engineering (ME) 2016 [Session 1]

2 Qs

Mechanical Engineering (ME) 2016 [Session 2]

2 Qs

Mechanical Engineering (ME) 2014 [Session 1]

1 Qs

Mechanical Engineering (ME) 2014 [Session 2]

1 Qs

Mechanical Engineering (ME) 2014 [Session 3]

1 Qs

Mechanical Engineering (ME) 2014 [Session 4]

1 Qs

Mechanical Engineering (ME) 2011

1 Qs

Mechanical Engineering (ME) 2010

1 Qs

Mechanical Engineering (ME) 2009

1 Qs

Mechanical Engineering (ME) 2008

1 Qs

Mechanical Engineering (ME) 2007

1 Qs

Included previous year papers

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

Paper name	Year	PDF
Mechanical Engineering (ME) 20262026 1 questions in this view	2026	ExamElite PDFs ExamElite solutions Official documents Official question paperOriginal authority-issued PDF Official Download Official answer keyOriginal authority-issued PDF Official Download
Mechanical Engineering (ME) 20252025 1 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
Mechanical Engineering (ME) 20242024 1 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
Mechanical Engineering (ME) 20232023 1 questions in this view	2023	ExamElite PDFs ExamElite solutions Official documents Official question paperOriginal authority-issued PDF Official Download Official answer keyOriginal authority-issued PDF Official Download
Mechanical Engineering (ME) 2021 [Session 1]2021 1 questions in this view	2021	ExamElite PDFs ExamElite solutions Official documents Official question paperOriginal authority-issued PDF Official Download Official answer keyOriginal authority-issued PDF Official Download
Mechanical Engineering (ME) 2020 [Session 1]2020 3 questions in this view	2020	ExamElite PDFs ExamElite solutions Official documents Official question paperOriginal authority-issued PDF Official Download
Mechanical Engineering (ME) 2020 [Session 2]2020 1 questions in this view	2020	ExamElite PDFs ExamElite solutions Official documents Official question paperOriginal authority-issued PDF Official Download
Mechanical Engineering (ME) 2019 [Session 1]2019 1 questions in this view	2019	ExamElite PDFs ExamElite solutions Official documents Official question paperOriginal authority-issued PDF Official Download
Mechanical Engineering (ME) 2019 [Session 2]2019 1 questions in this view	2019	ExamElite PDFs ExamElite solutions Official documents Official question paperOriginal authority-issued PDF Official Download
Mechanical Engineering (ME) 2018 [Session 1]2018 1 questions in this view	2018	ExamElite PDFs ExamElite solutions Official documents Official question paperOriginal authority-issued PDF Official Download
Mechanical Engineering (ME) 2018 [Session 2]2018 1 questions in this view	2018	ExamElite PDFs ExamElite solutions Official documents Official question paperOriginal authority-issued PDF Official Download
Mechanical Engineering (ME) 2017 [Session 2]2017 1 questions in this view	2017	ExamElite PDFs ExamElite solutions Official documents Official question paperOriginal authority-issued PDF Official Download
Mechanical Engineering (ME) 2016 [Session 1]2016 2 questions in this view	2016	ExamElite PDFs ExamElite solutions Official documents Official question paperOriginal authority-issued PDF Official Download
Mechanical Engineering (ME) 2016 [Session 2]2016 2 questions in this view	2016	ExamElite PDFs ExamElite solutions Official documents Official question paperOriginal authority-issued PDF Official Download
Mechanical Engineering (ME) 2014 [Session 1]2014 1 questions in this view	2014	ExamElite PDFs ExamElite solutions Official documents Official question paperOriginal authority-issued PDF Official Download
Mechanical Engineering (ME) 2014 [Session 2]2014 1 questions in this view	2014	ExamElite PDFs ExamElite solutions Official documents Official question paperOriginal authority-issued PDF Official Download
Mechanical Engineering (ME) 2014 [Session 3]2014 1 questions in this view	2014	ExamElite PDFs ExamElite solutions Official documents Official question paperOriginal authority-issued PDF Official Download
Mechanical Engineering (ME) 2014 [Session 4]2014 1 questions in this view	2014	ExamElite PDFs ExamElite solutions Official documents Official question paperOriginal authority-issued PDF Official Download
Mechanical Engineering (ME) 20112011 1 questions in this view	2011	ExamElite PDFs ExamElite solutions Official documents Official question paperOriginal authority-issued PDF Official Download
Mechanical Engineering (ME) 20102010 1 questions in this view	2010	ExamElite PDFs ExamElite solutions Official documents Official question paperOriginal authority-issued PDF Official Download
Mechanical Engineering (ME) 20092009 1 questions in this view	2009	ExamElite PDFs ExamElite solutions Official documents Official question paperOriginal authority-issued PDF Official Download
Mechanical Engineering (ME) 20082008 1 questions in this view	2008	ExamElite PDFs ExamElite solutions Official documents Official question paperOriginal authority-issued PDF Official Download
Mechanical Engineering (ME) 20072007 1 questions in this view	2007	ExamElite PDFs ExamElite solutions Official documents Official question paperOriginal authority-issued PDF Official Download

All Complex Variables previous year questions

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

2007 · Mechanical Engineering · Engineering Mathematics · Complex Variables

Mechanical Engineering (ME) 2007

If $ \phi(x,y) $ and $ \psi(x,y) $ are functions with continuous second derivatives, then $ \phi(x,y) + i\psi(x,y) $ can be expressed as an analytic function of $ x + iy $ ($ i = \sqrt{-1} $), when

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2008 · Mechanical Engineering · Engineering Mathematics · Complex Variables

Mechanical Engineering (ME) 2008

The integral $\oint f(z) \, dz$ evaluated around the unit circle on the complex plane for $f(z) = \frac{\cos z}{z}$ is

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2009 · Mechanical Engineering · Engineering Mathematics · Complex Variables

Mechanical Engineering (ME) 2009

An analytic function of a complex variable $ z = x + iy $ is expressed as $ f(z) = u(x, y) + i v(x, y) $ where $ i = \sqrt{-1} $. If $ u = xy $, the expression for $ v $ should be

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2010 · Mechanical Engineering · Engineering Mathematics · Complex Variables

Mechanical Engineering (ME) 2010

The modulus of the complex number $ \left( \frac{3 + 4i}{1 - 2i} \right) $ is

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2011 · Mechanical Engineering · Engineering Mathematics · Complex Variables

Mechanical Engineering (ME) 2011

The product of two complex numbers $1 + i$ and $2 - 5i$ is

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2014 · Mechanical Engineering · Engineering Mathematics · Complex Variables

Mechanical Engineering (ME) 2014 [Session 1]

The argument of the complex number \[ \frac{1+i}{1-i} \], where \[ i = \sqrt{-1} \], is

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2014 · Mechanical Engineering · Engineering Mathematics · Complex Variables

Mechanical Engineering (ME) 2014 [Session 2]

An analytic function of a complex variable $z = x + iy$ is expressed as $f(z) = u(x,y) + i v(x,y)$, where $i = \sqrt{-1}$. If $u(x,y) = 2xy$, then $v(x,y)$ must be

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2014 · Mechanical Engineering · Engineering Mathematics · Complex Variables

Mechanical Engineering (ME) 2014 [Session 3]

An analytic function of a complex variable $z = x + iy$ is expressed as $f(z) = u(x, y) + i v(x, y)$, where $i = \sqrt{-1}$. If $u(x, y) = x^2 - y^2$, then expression for $v(x, y)$ in terms of $x, y$ and a general constant $c$ would be

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2014 · Mechanical Engineering · Engineering Mathematics · Complex Variables

Mechanical Engineering (ME) 2014 [Session 4]

If z is a complex variable, the value of ∫₅^{2i} dz/z is

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2016 · Mechanical Engineering · Engineering Mathematics · Complex Variables

Mechanical Engineering (ME) 2016 [Session 1]

The value of the integral \[\int_{-\infty}^{\infty} \frac{\sin x}{x^{2}+2 x+2} d x\] evaluated using contour integration and the residue theorem is

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2016 · Mechanical Engineering · Engineering Mathematics · Complex Variables

Mechanical Engineering (ME) 2016 [Session 1]

$ f(z) = u(x,y) + i\, v(x,y) $ is an analytic function of complex variable $ z = x + iy $ where $ i = \sqrt{-1} $. If $ u(x,y) = 2xy $, then $ v(x,y) $ may be expressed as

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2016 · Mechanical Engineering · Engineering Mathematics · Complex Variables

Mechanical Engineering (ME) 2016 [Session 2]

The value of $\oint_{\Gamma} \frac{3 z - 5}{(z-1)(z-2)} dz$ along a closed path $\Gamma$ is equal to $(4 \pi i)$, where $z = x + iy$ and $i = \sqrt{-1}$. The correct path $\Gamma$ is

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2016 · Mechanical Engineering · Engineering Mathematics · Complex Variables

Mechanical Engineering (ME) 2016 [Session 2]

A function f of the complex variable z = x + i y, is given as f(x,y) = u(x,y) + i v(x,y), where u(x,y) = 2kxy and v(x,y) = x² - y². The value of k, for which the function is analytic, is __________.

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2018 · Mechanical Engineering · Engineering Mathematics · Complex Variables

Mechanical Engineering (ME) 2018 [Session 1]

$F(z)$ is a function of the complex variable $z = x + iy$ given by $F(z) = i z + k \, Re(z) + i \, Im(z)$. For what value of $k$ will $F(z)$ satisfy the Cauchy-Riemann equations?

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2018 · Mechanical Engineering · Engineering Mathematics · Complex Variables

Mechanical Engineering (ME) 2018 [Session 2]

Let $ z $ be a complex variable. For a counter-clockwise integration around a unit circle $ C $, centred at origin, \[ \oint_C \frac{1}{5z-4} dz = A\pi i \] , the value of $ A $ is

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2019 · Mechanical Engineering · Engineering Mathematics · Complex Variables

Mechanical Engineering (ME) 2019 [Session 1]

A harmonic function is analytic if it satisfies the Laplace equation.
If $u(x, y) = 2x^2 - 2y^2 + 4xy$ is a harmonic function, then its conjugate harmonic function $v(x, y)$ is

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2019 · Mechanical Engineering · Engineering Mathematics · Complex Variables

Mechanical Engineering (ME) 2019 [Session 2]

An analytic function $f(z)$ of complex variable $z = x + iy$ may be written as $f(z) = u(x, y) + iv(x, y)$. Then, $u(x, y)$ and $v(x, y)$ must satisfy

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2020 · Mechanical Engineering · Engineering Mathematics · Complex Variables

Mechanical Engineering (ME) 2020 [Session 1]

An analytic function of a complex variable z = x + iy (i = √−1) is defined as f(z) = x² − y² + i ψ(x,y), where ψ(x,y) is a real function. The value of the imaginary part of f(z) at z = (1 + i) is __________ (round off to 2 decimal places).

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2020 · Mechanical Engineering · Engineering Mathematics · Complex Variables

Mechanical Engineering (ME) 2020 [Session 1]

An analytic function of a complex variable $z = x + iy$ ($i = \sqrt{-1}$) is defined as $f(z) = x^2 - y^2 + i \psi(x,y)$, where $\psi(x,y)$ is a real function. The value of the imaginary part of $f(z)$ at $z = (1 + i)$ is ______________ (round off to 2 decimal places).

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2020 · Mechanical Engineering · Engineering Mathematics · Complex Variables

Mechanical Engineering (ME) 2020 [Session 1]

Which of the following function $f(z)$, of the complex variable z, is NOT analytic at all the points of the complex plane?

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Complex Variables - Engineering Mathematics - Mechanical Engineering Previous Year Questions