Gujarat Technological UniversitySummer 2025 examination

GTU BE02000011 Mathematics – 2 Summer 2025 Question Paper & PDF

B.E. · Common Engineering · Semesters 1 and 2 · Subject code BE02000011
Download official PDFView PDF here
Share with your class
Total
70 marks
To pass
23 marks (33%)
Duration
2.5 Hours 10:30 AM – 1:30 PM
Questions
5 with internal choice
No solutions on this paper yetNeed them for your exam? Ask once. Papers that students ask for are solved first, and we aim to add them within 24 hours.

Q.1

14 Marks
(a)
3 marks
Prove that f(z)=1zf(z) = \frac{1}{z} is not differentiable at z=0z = 0, by definition.
(b)
4 marks
Solve dxdy+xy=x3\frac{dx}{dy} + \frac{x}{y} = x^3.
(c)
7 marks

Check the whether the given matrix A=[−14−2−340−313]A = \begin{bmatrix} -1 & 4 & -2 \\ -3 & 4 & 0 \\ -3 & 1 & 3 \end{bmatrix} is diagonalizable? If so, then find matrix PP such that P−1AP=DP^{-1}AP = D.

Q.2

14 Marks
(a)
3 marks
State Rouche’s Theorem. Evaluate ∫Cezdz\int_C e^z dz if CC is the circle ∣z∣=99|z| = 99.
(b)
4 marks
Solve y′′+4y′+4y=0,y(0)=1,y′(0)=1y'' + 4y' + 4y = 0, y(0) = 1, y'(0) = 1.
(c)
7 marks
1Evaluate ∫C3z2+zz2−1dz\int_C \frac{3z^2+z}{z^2-1} dz where CC is the circle ∣z−1∣=1|z - 1| = 1.
2Define entire function. Prove that eze^z is analytic at everywhere.
(c)
7 marks
1Evaluate ∫CRe(z)dz\int_C Re(z)dz from 1+i1 + i to 3+2i3 + 2i along the straight line 2y=x+12y = x + 1.
2Find real part and imaginary part of the following functions
isin⁡z\sin z
iiln⁡z\ln z.

Q.3

14 Marks
(a)
3 marks
Solve dydx+2ytan⁡x=sin⁡x,y(0)=2\frac{dy}{dx} + 2y \tan x = \sin x, y(0) = 2.
(b)
4 marks
Solve the following linear system by Gauss elimination method:

x−2y+3z=−2,−x+y−2z=3,2x−y+3z=−7x - 2y + 3z = -2, -x + y - 2z = 3, 2x - y + 3z = -7.

(c)
7 marks
Define Harmonic function. Check whether v=3x2y−y3v = 3x^2y - y^3 is harmonic or not. If so, construct the analytic function f(z)=u+ivf(z) = u + iv.
(a)
3 marks
Test for exactness and solve 2xydx+x2dy=02xydx + x^2dy = 0.
(b)
4 marks
Find the rank of the matrix A=[12−10−130−4213−2111−1]A = \begin{bmatrix} 1 & 2 & -1 & 0 \\ -1 & 3 & 0 & -4 \\ 2 & 1 & 3 & -2 \\ 1 & 1 & 1 & -1 \end{bmatrix}.
(c)
7 marks
Check whether u=3x−2xyu = 3x - 2xy is harmonic or not. If so, find the harmonic conjugate vv of uu.

Q.4

14 Marks
(a)
3 marks
Solve x2ydx−(x3+xy2)dy=0x^2ydx - (x^3 + xy^2)dy = 0.
(b)
4 marks
Find the inverse of the matrix A=[133143134]A = \begin{bmatrix} 1 & 3 & 3 \\ 1 & 4 & 3 \\ 1 & 3 & 4 \end{bmatrix} using Gauss Jordan method.
(c)
7 marks
Find all the Taylor’s and Laurent series of f(z)=−2z+3z2−3z+2f(z) = \frac{-2z+3}{z^2-3z+2} with center 0.
(a)
3 marks
Solve xex(dx−dy)+exdx+yeydy=0xe^x(dx - dy) + e^xdx + ye^ydy = 0.
(b)
4 marks
Find inverse of the matrix A=[2−12−12−11−12]A = \begin{bmatrix} 2 & -1 & 2 \\ -1 & 2 & -1 \\ 1 & -1 & 2 \end{bmatrix} by Cayley-Hamilton theorem.
(c)
7 marks
State Cauchy Residue theorem. Evaluate ∫Cz2(z−1)2(z+2)dz\int_C \frac{z^2}{(z-1)^2(z+2)} dz where CC is the circle ∣z∣=3|z| = 3 using Cauchy Residue theorem.

Q.5

14 Marks
(a)
3 marks
Solve x2p2+3xyp+2y2=0x^2p^2 + 3xyp + 2y^2 = 0.
(b)
4 marks
Solve xy′′+y′=12log⁡xxxy'' + y' = \frac{12 \log x}{x}.
(c)
7 marks
Solve y′′−2y′+y=xexsin⁡xy'' - 2y' + y = xe^x \sin x by using the method of variation of parameter.
(a)
3 marks
Solve (xdydx−y)(1−dydx)=dydx(x\frac{dy}{dx} - y)(1 - \frac{dy}{dx}) = \frac{dy}{dx}.
(b)
4 marks
Solve y′′+2y′+4y=2x2+3e−xy'' + 2y' + 4y = 2x^2 + 3e^{-x} by undetermined coefficient method.
(c)
7 marks
Find the power series solution of y′′+xy′+x2y=0y'' + xy' + x^2y = 0 about x=0x = 0.

More Mathematics – 2 papers

Questions repeat across sessions. Working through two or three papers shows you which topics GTU asks most.

Summer 202670 marks · 5 questions
Winter 202570 marks · 5 questions

Other Semester 2 subjects

BE Common

BE02000021
English for Technical Communication
BE02000031
Intellectual Property Rights
BE02000041
Fundamental of AI
BE02000061
Industrial Safety and Standards

Preparing with friends?

Send this paper to your class group. Every question has its own link.

About this paper

Official Gujarat Technological University (GTU) examination paper for Mathematics – 2 (Summer 2025, 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.

Download official PDF All Mathematics – 2 Papers (3) →Report a typo or correction
ViewDownload PDF