What is the exam pattern and passing mark for GTU Mathematics - 2 (3110015)?

The GTU theory examination carries 70 total marks with a duration of 2.5 Hours. Minimum passing criteria is 23 marks (33%). The paper consists of 5 main questions with official marking breakdown and internal choices.

Where can I download the official GTU 3110015 Summer 2023 question paper PDF?

The official GTU question paper PDF is linked directly from Gujarat Technological University's official examination archive. You can view the full paper online or download the original file.

How can I practice solutions for these GTU questions?

Every question on UnFoldPrep includes deep-linking and one-click AI prompt buttons for ChatGPT, Claude, and Perplexity that instantly formulate structured exam prompts with standard mark breakdowns and academic rubrics.

Gujarat Technological UniversitySummer 2023 examination

GTU 3110015 Mathematics - 2 (Maths 2) Summer 2023 Question Paper & PDF

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

Download official PDF View 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.

25 of 25 questions 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 2 of 6 papers

Find the directional derivative of

f(x, y, z) = x^2 + 5y^2 + 3z^2

at point

(1, 1, 1)

in the direction

3\hat{i} + 4\hat{j} + 5\hat{k}

Also asked in Summer 2025 Q2b

(b)

4 marksSame type asked in 4 of 6 papers

A vector field is given by

\vec{F} = 3x^2 yz \hat{i} + x^3 z \hat{j} + x^3 y \hat{k}

, show that

f

is irrotational and find the scalar

\phi

such that

\vec{F} = \nabla \phi

Also asked in Winter 2025 Q1b, Summer 2025 Q1a, Winter 2023 Q1b

(c)

7 marksSame type asked in 6 of 6 papers

Verify the Greens theorem for

\vec{F} = x^2 \hat{i} + x y^2 \hat{j}

, along the square bounded by

x = 0, x = 1, y = 0

and

y = 1

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

Q.2

14 Marks

(a)

3 marksSame type asked in 3 of 6 papers

Discuss about ordinary point, singular point, regular singular point and irregular singular point of differential equation

(x^2 - 1)y'' + 3xy' + 5x^2 y = 0

Also asked in Winter 2025 Q5a, Winter 2025 Q5a OR, Winter 2023 Q5a, Winter 2023 Q5a OR

(b)

4 marksSame type asked in 3 of 6 papers

Express

f(x) = x^3 + 2x^2 + 3x - 1

in terms of Legendre’s polynomial.

Also asked in Summer 2024 Q5c OR, Winter 2023 Q5c OR

(c)

7 marksSame type asked in 6 of 6 papers

Find a power series solution of

y'' - 25y = 0

near an ordinary point

x = 0

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

(c)

7 marksSame type asked in 3 of 6 papers

Prove that

P_n(x) = \frac{1}{n! 2^n} \frac{d^n}{dx^n} (x^2 - 1)^n

Also asked in Summer 2024 Q5c OR, Winter 2023 Q5c OR

Q.3

14 Marks

(a)

3 marksSame type asked in 6 of 6 papers

Find the Laplace transform of:

e^{3t} t^5

t \cos 3t

iii

\frac{\sin^2 5t}{t}

Also asked in Winter 2025 Q2b, Winter 2025 Q3a, Summer 2025 Q4a, Summer 2025 Q4b, Summer 2025 Q4b OR, 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

(b)

4 marksSame type asked in 6 of 6 papers

Find the Inverse Laplace transform of:

\frac{1}{(s-1)(s-2)(s-3)}

\frac{1}{s^4 - 9s^2}

iii

\frac{s+1}{s^2 + 2s + 10}

\tan^{-1}\left(\frac{s}{4}\right)

Also asked in Winter 2025 Q3a OR, Summer 2025 Q4a OR, Summer 2025 Q4c OR, Winter 2024 Q3a OR, Winter 2024 Q3c, Winter 2024 Q4a, Summer 2024 Q2c, Summer 2024 Q3b, Winter 2023 Q2a

(c)

7 marksSame type asked in 6 of 6 papers

Solve the initial value problem using Laplace transformation:

y'' - 5y' - 6y = e^{3t} \quad \text{with } y(0) = 3 \text{ and } y'(0) = 2

Also asked in Winter 2025 Q3c, Summer 2025 Q4c, Winter 2024 Q3c OR, Summer 2024 Q2c OR, Winter 2023 Q2c

(a)

3 marksSame type asked in 6 of 6 papers

Find the Laplace transform of:

e^{4t} u(t - 2)

(t^2 + 1) u(t - 1)

iii

\sin 3t \, u(t - \pi)

(b)

4 marksSame type asked in 6 of 6 papers

Using convolution theorem find the Inverse Laplace transform of

\frac{1}{(s^2 - 4)(s^2 - 9)}

Also asked in Winter 2025 Q3a OR, Summer 2025 Q4a OR, Summer 2025 Q4c OR, Winter 2024 Q3a OR, Winter 2024 Q3c, Winter 2024 Q4a, Summer 2024 Q2c, Summer 2024 Q3b, Winter 2023 Q2a

(c)

7 marksSame type asked in 4 of 6 papers

Find the Fourier integral of

f(x) = \begin{cases} 0 & |x| < 5 \\ 5 & |x| > 5 \end{cases}

Also asked in Winter 2025 Q3c OR, Summer 2025 Q1b, Summer 2024 Q2b

Q.4

14 Marks

(a)

3 marksSame type asked in 4 of 6 papers

Solve the Differential equation

e^x \cos y \, dx - e^x \sin y \, dy = 0

Also asked in Winter 2025 Q3b, Winter 2025 Q3b OR, Summer 2025 Q5a OR, Summer 2024 Q3a OR

(b)

4 marksSame type asked in 6 of 6 papers

Solve

\frac{d^2 y}{dx^2} + 6\frac{dy}{dx} + 9y = 0, \quad y(0) = 1, \; y'(0) = 2

Also asked in Winter 2025 Q4c, Winter 2025 Q4c OR, Summer 2025 Q3a, Summer 2025 Q3b, Summer 2025 Q3a OR, Summer 2025 Q3b OR, Summer 2025 Q5c 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

(c)

7 marksSame type asked in 5 of 6 papers

Solve:

\frac{dy}{dx} + y \tan x = \sin 2x, \quad y(0) = 2

(x^3 + y^3) \, dx - x y^2 \, dy = 0

Also asked in Winter 2025 Q4a, Summer 2025 Q5a, Summer 2025 Q5b OR, Winter 2024 Q5a, Winter 2023 Q3a, Winter 2023 Q3a OR

(a)

3 marksSame type asked in 4 of 6 papers

Solve

(x^2 - y^2) \, dx + xy \, dy = 0

Also asked in Winter 2025 Q3b, Winter 2025 Q3b OR, Summer 2025 Q5a OR, Summer 2024 Q3a OR

(b)

4 marksSame type asked in 6 of 6 papers

Solve

\frac{d^2 y}{dx^2} - 5\frac{dy}{dx} - 14y = 0, \quad y(0) = 3, \; y'(0) = 1

(c)

7 marksSame type asked in 6 of 6 papers

Solve:

(y - px)(p^2 + 1) = \tan^{-1} p

p^2 x^2 = x^2 + p^2

Also asked in Winter 2025 Q4a OR, Summer 2025 Q5b, Winter 2024 Q3b OR, Summer 2024 Q3c, Winter 2023 Q3c, Winter 2023 Q3c OR

Q.5

14 Marks

(a)

3 marksSame type asked in 6 of 6 papers

Solve

\frac{d^2 y}{dx^2} + \frac{dy}{dx} - 12y = e^{-4x} - 12x

(b)

4 marksSame type asked in 4 of 6 papers

Using method of undetermined coefficient obtain the solution of

\frac{d^2 y}{dx^2} + 4y = \sin x

Also asked in Summer 2025 Q3c, Winter 2024 Q2c OR, Winter 2023 Q4c

(c)

7 marksSame type asked in 6 of 6 papers

Find the solution of differential equations:

\frac{d^2 y}{dx^2} + \frac{dy}{dx} + y = x^2 e^x

x^2 \frac{d^2 y}{dx^2} - 3x \frac{dy}{dx} + 4y = \cos(\log x)

(a)

3 marksSame type asked in 6 of 6 papers

Solve

\frac{d^4 y}{dx^4} + 8\frac{d^2 y}{dx^2} + 16y = \cos 2x

(b)

4 marksSame type asked in 4 of 6 papers

Using method of undetermined coefficient:

\frac{d^2 y}{dx^2} + \frac{dy}{dx} - 6y = x^2

Also asked in Summer 2025 Q3c, Winter 2024 Q2c OR, Winter 2023 Q4c

(c)

7 marksSame type asked in 6 of 6 papers

iUsing method of variation of parameters find the solution of differential equation

\frac{d^2 y}{dx^2} + 16y = \cot 4x

iiFind the solution of differential equation

x^2 \frac{d^2 y}{dx^2} - 6x \frac{dy}{dx} + 6y = x^2 + \frac{1}{x^2}

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

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

Summer 202570 marks · 5 questions

Winter 202470 marks · 5 questions

Summer 202470 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 2023, 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