Gujarat Technological UniversitySummer 2025 examination

GTU 3110015 Mathematics - 2 (Maths 2) Summer 2025 Question Paper & PDF

B.E. · Common Engineering · Semesters 1 and 2 · Subject code 3110015
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.

2 of 25 questions on this paper were also asked in other years. 23 more are types of question GTU sets again with new data. Each is marked below with the years it appeared.See all 27 repeated 3110015 questions, most asked first

Q.1

14 Marks
(a)
3 marksSame type asked in 4 of 6 papers
Show that F⃗=(y2−z2+3yz−2x)i^+(3xz+2xy)j^+(3xy−2xz+2z)k^\vec{F} = (y^2 - z^2 + 3yz - 2x)\hat{i} + (3xz + 2xy)\hat{j} + (3xy - 2xz + 2z)\hat{k} is both solenoidal and irrotational.

Also asked in Winter 2025 Q1b, Winter 2023 Q1b, Summer 2023 Q1b

(b)
4 marksSame type asked in 4 of 6 papers
Find Fourier integral representation of function
f(x)={1∣x∣<10∣x∣>1f(x) = \begin{cases} 1 & |x| < 1 \\ 0 & |x| > 1 \end{cases}
Hence, evaluate
∫0∞sin⁡ωcos⁡ωxω dω\int_0^\infty \frac{\sin \omega \cos \omega x}{\omega} \, d\omega

Also asked in Winter 2025 Q3c OR, Summer 2024 Q2b, Summer 2023 Q3c OR

(c)
7 marksSame type asked in 6 of 6 papers
Verify Green’s theorem in the plane for
∫C[(3x2−8y2) dx+(4y−6xy) dy]\int_C \left[ (3x^2 - 8y^2) \, dx + (4y - 6xy) \, dy \right]
where CC is the boundary of the region bounded by x=0,y=0,x+y=1x = 0, y = 0, x + y = 1.

Also asked in Winter 2025 Q1c, Winter 2024 Q1c, Summer 2024 Q1c, Winter 2023 Q1c, Summer 2023 Q1c

Q.2

14 Marks
(a)
3 marksAsked in 2 of 6 papers
Solve yex dx+(2y+ex) dy=0y e^x \, dx + (2y + e^x) \, dy = 0.

Also asked in Winter 2024 Q1b

(b)
4 marksSame type asked in 2 of 6 papers
Find the directional derivative of ϕ=xy2+yz2\phi = x y^2 + y z^2 at the point (2,−1,1)(2, -1, 1) in the direction of the vector i^+2j^+2k^\hat{i} + 2\hat{j} + 2\hat{k}.

Also asked in Summer 2023 Q1a

(c)
7 marksSame type asked in 6 of 6 papers
Find the power series solution of
d2ydx2+xy=0\frac{d^2 y}{dx^2} + x y = 0

Also asked in Winter 2025 Q5b, Winter 2025 Q5c OR, Winter 2024 Q2c, Summer 2024 Q5c, Winter 2023 Q5b, Winter 2023 Q5c, Winter 2023 Q5b OR, Summer 2023 Q2c

(c)
7 marksAsked in 2 of 6 papers
Find the series solution of (1−x2)y′′−2xy′+2y=0(1 - x^2) y'' - 2x y' + 2y = 0.

Also asked in Winter 2025 Q5c

Q.3

14 Marks
(a)
3 marksSame type asked in 6 of 6 papers
Solve (4D2−4D+1)y=ex2(4D^2 - 4D + 1)y = e^{\frac{x}{2}}.

Also asked in Winter 2025 Q4c, Winter 2025 Q4c OR, Winter 2024 Q4b, Summer 2024 Q3a, Summer 2024 Q4b OR, Summer 2024 Q5b, Winter 2023 Q3b, Winter 2023 Q4a, Winter 2023 Q4a OR, Winter 2023 Q4b OR, Summer 2023 Q4b, Summer 2023 Q4b OR, Summer 2023 Q5a, Summer 2023 Q5a OR, Summer 2023 Q5c

(b)
4 marksSame type asked in 6 of 6 papers
Solve (D2+6D+8)y=cos⁡2x(D^2 + 6D + 8)y = \cos^2 x.

Also asked in Winter 2025 Q4c, Winter 2025 Q4c OR, Winter 2024 Q4b, Summer 2024 Q3a, Summer 2024 Q4b OR, Summer 2024 Q5b, Winter 2023 Q3b, Winter 2023 Q4a, Winter 2023 Q4a OR, Winter 2023 Q4b OR, Summer 2023 Q4b, Summer 2023 Q4b OR, Summer 2023 Q5a, Summer 2023 Q5a OR, Summer 2023 Q5c

(c)
7 marksSame type asked in 4 of 6 papers
Solve (D2−2D+3)y=x3+sin⁡x(D^2 - 2D + 3)y = x^3 + \sin x by using the method of undetermined coefficients.

Also asked in Winter 2024 Q2c OR, Winter 2023 Q4c, Summer 2023 Q5b, Summer 2023 Q5b OR

(a)
3 marksSame type asked in 6 of 6 papers
Solve (D2+a2)y=cos⁡ax(D^2 + a^2)y = \cos ax.

Also asked in Winter 2025 Q4c, Winter 2025 Q4c OR, Winter 2024 Q4b, Summer 2024 Q3a, Summer 2024 Q4b OR, Summer 2024 Q5b, Winter 2023 Q3b, Winter 2023 Q4a, Winter 2023 Q4a OR, Winter 2023 Q4b OR, Summer 2023 Q4b, Summer 2023 Q4b OR, Summer 2023 Q5a, Summer 2023 Q5a OR, Summer 2023 Q5c

(b)
4 marksSame type asked in 6 of 6 papers
Solve
d2ydx2+2dydx+2y=exsin⁡x+7\frac{d^2 y}{dx^2} + 2\frac{dy}{dx} + 2y = e^x \sin x + 7

Also asked in Winter 2025 Q4c, Winter 2025 Q4c OR, Winter 2024 Q4b, Summer 2024 Q3a, Summer 2024 Q4b OR, Summer 2024 Q5b, Winter 2023 Q3b, Winter 2023 Q4a, Winter 2023 Q4a OR, Winter 2023 Q4b OR, Summer 2023 Q4b, Summer 2023 Q4b OR, Summer 2023 Q5a, Summer 2023 Q5a OR, Summer 2023 Q5c

(c)
7 marksSame type asked in 5 of 6 papers
Solve
x2d2ydx2+xdydx+y=log⁡x⋅sin⁡(log⁡x)x^2 \frac{d^2 y}{dx^2} + x \frac{dy}{dx} + y = \log x \cdot \sin(\log x)
by Cauchy’s linear equation.

Also asked in Winter 2025 Q4b, Winter 2024 Q5b OR, Summer 2024 Q5a, Winter 2023 Q4b

Q.4

14 Marks
(a)
3 marksSame type asked in 6 of 6 papers
Find the Laplace Transform of f(t)=sinh⁡atf(t) = \sinh at.

Also asked in Winter 2025 Q2b, Winter 2025 Q3a, Winter 2024 Q2a, Winter 2024 Q3b, Winter 2024 Q4b OR, Winter 2024 Q5a OR, Summer 2024 Q2a, Summer 2024 Q3b OR, Summer 2024 Q4a OR, Winter 2023 Q2b, Summer 2023 Q3a, Summer 2023 Q3a OR

(b)
4 marksSame type asked in 6 of 6 papers
Find the Laplace Transform of te4tcos⁡2tt e^{4t} \cos 2t.

Also asked in Winter 2025 Q2b, Winter 2025 Q3a, Winter 2024 Q2a, Winter 2024 Q3b, Winter 2024 Q4b OR, Winter 2024 Q5a OR, Summer 2024 Q2a, Summer 2024 Q3b OR, Summer 2024 Q4a OR, Winter 2023 Q2b, Summer 2023 Q3a, Summer 2023 Q3a OR

(c)
7 marksSame type asked in 6 of 6 papers
Solve the differential equation using initial value problem:
y′′+6y′=1,y(0)=2,  y′(0)=0y'' + 6y' = 1, \quad y(0) = 2, \; y'(0) = 0

Also asked in Winter 2025 Q3c, Winter 2024 Q3c OR, Summer 2024 Q2c OR, Winter 2023 Q2c, Summer 2023 Q3c

(a)
3 marksSame type asked in 6 of 6 papers
Find the inverse Laplace transform of
log⁡s2+b2s2+a2\log \frac{s^2 + b^2}{s^2 + a^2}

Also asked in Winter 2025 Q3a OR, Winter 2024 Q3a OR, Winter 2024 Q3c, Winter 2024 Q4a, Summer 2024 Q2c, Summer 2024 Q3b, Winter 2023 Q2a, Summer 2023 Q3b, Summer 2023 Q3b OR

(b)
4 marksSame type asked in 6 of 6 papers
Find the Laplace Transform of
e−2tsin⁡2tcosh⁡tt\frac{e^{-2t} \sin 2t \cosh t}{t}

Also asked in Winter 2025 Q2b, Winter 2025 Q3a, Winter 2024 Q2a, Winter 2024 Q3b, Winter 2024 Q4b OR, Winter 2024 Q5a OR, Summer 2024 Q2a, Summer 2024 Q3b OR, Summer 2024 Q4a OR, Winter 2023 Q2b, Summer 2023 Q3a, Summer 2023 Q3a OR

(c)
7 marksSame type asked in 6 of 6 papers
Find the Inverse Laplace Transform of
5s+3(s−1)(s2+2s+5)\frac{5s + 3}{(s - 1)(s^2 + 2s + 5)}

Also asked in Winter 2025 Q3a OR, Winter 2024 Q3a OR, Winter 2024 Q3c, Winter 2024 Q4a, Summer 2024 Q2c, Summer 2024 Q3b, Winter 2023 Q2a, Summer 2023 Q3b, Summer 2023 Q3b OR

Q.5

14 Marks
(a)
3 marksSame type asked in 5 of 6 papers
Solve
dydx+ycot⁡x=2cos⁡x\frac{dy}{dx} + y \cot x = 2 \cos x

Also asked in Winter 2025 Q4a, Winter 2024 Q5a, Winter 2023 Q3a, Winter 2023 Q3a OR, Summer 2023 Q4c

(b)
4 marksSame type asked in 6 of 6 papers
Solve 3x4p2−xp−y=03x^4 p^2 - xp - y = 0.

Also asked in Winter 2025 Q4a OR, Winter 2024 Q3b OR, Summer 2024 Q3c, Winter 2023 Q3c, Winter 2023 Q3c OR, Summer 2023 Q4c OR

(c)
7 marksSame type asked in 6 of 6 papers
Using the method variation of parameter solve the differential equation (D2+1)y=xsin⁡x(D^2 + 1)y = x \sin x.

Also asked in Winter 2025 Q2c OR, Winter 2024 Q4c, Summer 2024 Q4c, Winter 2023 Q4c OR, Summer 2023 Q5c OR

(a)
3 marksSame type asked in 4 of 6 papers
Solve (xy−2y2) dx−(x2−3xy) dy=0(xy - 2y^2) \, dx - (x^2 - 3xy) \, dy = 0.

Also asked in Winter 2025 Q3b, Winter 2025 Q3b OR, Summer 2024 Q3a OR, Summer 2023 Q4a, Summer 2023 Q4a OR

(b)
4 marksSame type asked in 5 of 6 papers
Solve
dydx+1xy=y2x2\frac{dy}{dx} + \frac{1}{x} y = \frac{y^2}{x^2}

Also asked in Winter 2025 Q4a, Winter 2024 Q5a, Winter 2023 Q3a, Winter 2023 Q3a OR, Summer 2023 Q4c

(c)
7 marksSame type asked in 6 of 6 papers
Solve (D4−16)y=e2x+x4(D^4 - 16)y = e^{2x} + x^4.

Also asked in Winter 2025 Q4c, Winter 2025 Q4c OR, Winter 2024 Q4b, Summer 2024 Q3a, Summer 2024 Q4b OR, Summer 2024 Q5b, Winter 2023 Q3b, Winter 2023 Q4a, Winter 2023 Q4a OR, Winter 2023 Q4b OR, Summer 2023 Q4b, Summer 2023 Q4b OR, Summer 2023 Q5a, Summer 2023 Q5a OR, Summer 2023 Q5c

More Mathematics - 2 papers

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

Winter 202570 marks · 5 questions
Winter 202470 marks · 5 questions
Summer 202470 marks · 5 questions
Winter 202370 marks · 5 questions

Other Semester 1 subjects

BE Common

3110001
Chemistry
3110002
English
3110003
Programming for Problem Solving
3110004
Basic Civil Engineering

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 (Maths 2) (Summer 2025, B.E. · Common Engineering, Sem 1). 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 (6) →Report a typo or correction
ViewDownload PDF