Gujarat Technological UniversitySummer 2026 examination

GTU BE02000011 Mathematics – 2 Summer 2026 Question Paper & PDF

B.E. · Common Engineering · Semester 2 · Subject code BE02000011GTU also lists this paper as BE02R00011
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Total
70 marks
To pass
23 marks (33%)
Duration
2.5 Hours 10:30 AM – 1:30 PM
Questions
5 with internal choice
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Q.1

14 Marks
(a)
3 marks
Define Analytic function & write two examples of analytic function.
(b)
4 marks
Solve dydx+y=x\dfrac{dy}{dx} + y = x .
(c)
7 marks
Define Eigen value, Eigen vector and compute it for the matrix A=[466132−1−5−2]A = \begin{bmatrix} 4 & 6 & 6 \\ 1 & 3 & 2 \\ -1 & -5 & -2 \end{bmatrix}

Q.2

14 Marks
(a)
3 marks
State Cauchy-Goursat theorem.
(b)
4 marks
Solve y′′+y′−2y=0,y(0)=4,y′(0)=−5y'' + y' - 2y = 0, y(0) = 4, y'(0) = -5.
(c)
7 marks
Compute ∫Czˉ dz\displaystyle\int_C \bar{z}\,dz from 00 to 4+2i4+2i along the curve C:z=t2+tiC : z = t^2 + ti.
(c)
7 marks
Prove that cos⁡(z)\cos(z) is analytic at everywhere.

Q.3

14 Marks
(a)
3 marks
Define Exact Differential equation.
(b)
4 marks
Use Gauss Jordan elimination method to solve the following linear system :

x−2y+3z=2,−x+y−2z=−2,2x−y+3z=4x - 2y + 3z = 2, -x + y - 2z = -2, 2x - y + 3z = 4 .

(c)
7 marks
Define Harmonic function. Check whether u(x,y)=excos⁡yu(x, y) = e^x\cos y is harmonic or not. If so, construct the analytic function f(z)=u+ivf(z) = u + iv.
(a)
3 marks
Write the necessary and sufficient conditions for the Exact differential equation.
(b)
4 marks
Define Rank of the matrix and find the Rank of the matrix A=[1234357936912−1−2−3−4]A = \begin{bmatrix} 1 & 2 & 3 & 4 \\ 3 & 5 & 7 & 9 \\ 3 & 6 & 9 & 12 \\ -1 & -2 & -3 & -4 \end{bmatrix}
(c)
7 marks
Write definition of Differentiation for complex Function. Using the definition, find the derivative of f(z)=z3−2zf(z) = z^3 - 2z at z=−1z = -1.

Q.4

14 Marks
(a)
3 marks
Solve (x2+y2+x) dx+xy dy=0(x^2 + y^2 + x)\,dx + xy\,dy = 0.
(b)
4 marks
Use Gauss Jordan method to calculate the inverse of the matrix A=[2111311−10]A = \begin{bmatrix} 2 & 1 & 1 \\ 1 & 3 & 1 \\ 1 & -1 & 0 \end{bmatrix}
(c)
7 marks

Expand f(z)=1(z+1)(z+3)f(z) = \dfrac{1}{(z + 1)(z + 3)} in a Laurent series for the region

a1<∣z∣<31 < |z| < 3
b∣z+1∣<2|z + 1| < 2.
(a)
3 marks
Write Bernoulli’s Equation and solve dydx=y3−yx\dfrac{dy}{dx} = y^3 - \dfrac{y}{x}.
(b)
4 marks
State Cayley-Hamilton theorem & Find inverse of the matrix A using it, where A=[4172]A = \begin{bmatrix} 4 & 1 \\ 7 & 2 \end{bmatrix}.
(c)
7 marks
State Cauchy’s Integral formula and Compute ∮Cezz(1−z)3 dz\oint_C \dfrac{e^z}{z(1 - z)^3}\,dz where C:∣z−1∣=12C : |z - 1| = \dfrac{1}{2}.

Q.5

14 Marks
(a)
3 marks
Solve xp2−(x−1)2=0xp^2 - (x - 1)^2 = 0.
(b)
4 marks
Solve x2y′′−xy′+y=sin⁡(log⁡x)x^2 y'' - xy' + y = \sin(\log x).
(c)
7 marks
Use method of Variation of parameter to solve y′′+4y=sec⁡(2x)y'' + 4y = \sec(2x).
(a)
3 marks
Define Clairaut’s equation and solve tan⁡(y−px)=p\tan(y - px) = p.
(b)
4 marks
Use undetermined coefficient method to solve y′′+y′−12y=exy'' + y' - 12y = e^x
(c)
7 marks
Find the power series solution of (1+x2)y′′+xy′−9y=0(1 + x^2) y'' + xy' - 9y = 0 about x=0x = 0.

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About this paper

Official Gujarat Technological University (GTU) examination paper for Mathematics – 2 (Summer 2026, B.E. · Common Engineering, Sem 2). Features complete 70-mark regular & remedial examination pattern, official marking distribution across all 5 questions, and direct 1-click official PDF download.

Transcribed for student exam preparation from Gujarat Technological University official examination archives. Questions, syllabus guidelines, and curriculum marking schemes remain the intellectual property of Gujarat Technological University.

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