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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.

22Papers
15Years
26Questions
1Topics

Complex Variables question pattern

Every graph below is calculated only from this selection.

Questions by year

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

Difficulty distribution

How the classified questions are distributed by difficulty.

Easy 18 69.2%
Medium 8 30.8%

Question type distribution

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

MCQ 21 80.8%
Numerical Answer Type (NAT) 5 19.2%

Subject weightage

Top subjects by unique question coverage.

Mechanical Engineering
26 Qs

Most asked topics

Top topics across the included previous year papers.

Engineering Mathematics
26 Qs

Subtopic coverage

Top subtopics inside this exact selection.

Complex Variables
26 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) 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. Sort by year, question coverage or name.

PaperYear / sessionQuestions in this viewOpen
Mechanical Engineering (ME) 202620261View paper
Mechanical Engineering (ME) 202520251View paper
Mechanical Engineering (ME) 202420241View paper
Mechanical Engineering (ME) 202320231View paper
Mechanical Engineering (ME) 2021 [Session 1]20211View paper
Mechanical Engineering (ME) 2020 [Session 1]20203View paper
Mechanical Engineering (ME) 2020 [Session 2]20201View paper
Mechanical Engineering (ME) 2019 [Session 1]20191View paper
Mechanical Engineering (ME) 2019 [Session 2]20191View paper
Mechanical Engineering (ME) 2018 [Session 1]20181View paper
Mechanical Engineering (ME) 2018 [Session 2]20181View paper
Mechanical Engineering (ME) 2016 [Session 1]20162View paper
Mechanical Engineering (ME) 2016 [Session 2]20162View paper
Mechanical Engineering (ME) 2014 [Session 1]20141View paper
Mechanical Engineering (ME) 2014 [Session 2]20141View paper
Mechanical Engineering (ME) 2014 [Session 3]20141View paper
Mechanical Engineering (ME) 2014 [Session 4]20141View paper
Mechanical Engineering (ME) 201120111View paper
Mechanical Engineering (ME) 201020101View paper
Mechanical Engineering (ME) 200920091View paper
Mechanical Engineering (ME) 200820081View paper
Mechanical Engineering (ME) 200720071View paper

All Complex Variables previous year questions

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

1
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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2
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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3
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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4
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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5
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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6
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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7
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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8
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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9
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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10
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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11
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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12
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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13
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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14
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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15
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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16
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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17
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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18
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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19
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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20
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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Showing 20 of 26 questions