What is the exam pattern and passing mark for GTU Mathematics 3 (Mechanical) (BE03000211)?

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 BE03000211 Summer 2026 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 2026 examination

GTU BE03000211 Mathematics 3 (Mechanical) Summer 2026 Question Paper & PDF

B.E. · Mechanical Engineering · Semester 3 · Subject code BE03000211

Download official PDF View PDF here

Share with your class

Total: 70 marks
To pass: 23 marks (33%)
Duration: 2.5 Hours 2:30 PM – 5:00 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

Evaluate

\displaystyle\int_0^1 e^x\,dx

, with

n = 10

using trapezoidal rule.

(b)

4 marks

Compute

f(0.56)

form the following table using Newton’s forward difference formula:

$x$	0.5	0.6	0.7	0.8
$f(x)$	1.127626	1.185465	1.255169	1.337435

(c)

7 marks

Using Laplace transform, solve the differential equation

y'' - 2y' + 2y = 0

y(0) = 1, y'(0) = 1

Q.2

14 Marks

(a)

3 marks

Form a PDE from the equation

z = ax + by + ab

by eliminating arbitrary constants

a

and

b

(b)

4 marks

Find the Fourier cosine series of

f(x) = e^x, 0 < x < 2

(c)

7 marks

Find the Fourier series of

f(x) = 1 - \dfrac{2|x|}{\pi}, -\pi \le x \le \pi

. Hence prove that

\dfrac{\pi^2}{8} = \dfrac{1}{1^2} + \dfrac{1}{3^2} + \dfrac{1}{5^2} + \cdots

(c)

7 marks

Find the Fourier series of

f(x) = x^2, 0 \le x \le 2\pi

Q.3

14 Marks

(a)

3 marks

A solid which is formed by rotating about the x-axis, the area between the x-axis, the lines $x = 0$ and $x = 1$ and a curve through the points with the following co-ordinates: Estimate the volume of the solid formed using Simpson’s 1/3rd rule.

$x$	0	0.25	0.5	0.75	1
$y$	1	0.9896	0.9589	0.9089	0.8415

(b)

4 marks

Given that Find $\dfrac{d^2 y}{dx^2}$ at $x = 2$ .

$x$	1.2	1.4	1.6	1.8	2
$y$	3.3201	4.0552	4.9530	6.0496	7.3891

(c)

7 marks

Find a second degree polynomial

f(x)

passing through the points

(0, 0)

(1, 1)

and

(2, 20)

using Langrange’s interpolation. Also find

f(1.5)

(a)

3 marks

Evaluate

\displaystyle\int_0^6 \dfrac{dx}{1 + x^2}

by using Simpson’s 3/8th rule.

(b)

4 marks

Given that Find $\dfrac{dy}{dx}$ at $x = 1.2$ .

$x$	1.2	1.4	1.6	1.8	2
$y$	3.3201	4.0552	4.9530	6.0496	7.3891

(c)

7 marks

Using Newton’s divided difference formula, calculate the value of

f(1)

from the following table:

$x$	0	2	3	4	7	9
$f(x)$	4	26	58	112	466	922

Q.4

14 Marks

(a)

3 marks

Find

L\left\{ \dfrac{1 - \cos t}{t} \right\}

(b)

4 marks

Find

L^{-1}\left\{ \ln\left( \dfrac{s + a}{s + b} \right) \right\}

(c)

7 marks

Write formula for Picard's method. Apply Euler's method to find

y

x = 0.1

in five steps given that

y' = \dfrac{y - x}{y + x}, y(0) = 1

(a)

3 marks

Find

L\{e^{-2t}\sin^2 t\}

(b)

4 marks

Find

L^{-1}\left\{ \dfrac{1}{s(s^2 + 4)} \right\}

by convolution theorem.

(c)

7 marks

Apply fourth order Runge-Kutta method to calculate

y(0.2)

with

h = 0.1

given that

y' = x + y, y(0) = 1

Q.5

14 Marks

(a)

3 marks

Find the complete integral of

(p - q)(z - px - qy) = 1

(b)

4 marks

Solve the PDE

x^2 p + y^2 q + z^2 = 0

(c)

7 marks

Solve one dimensional heat equation

u_t = c^2 u_{xx}

with boundary conditions

u(0, t) = u(l.t) = 0, \forall t

and initial condition

u(x, 0) = f(x), 0 < x < l

(a)

3 marks

Solve

\dfrac{\partial^2 z}{\partial x^2} - 6\dfrac{\partial^2 z}{\partial x\partial y} + 9\dfrac{\partial^2 z}{\partial y^2} = 0

(b)

4 marks

Find a complete integral of

(p^2 + q^2)y = qz

by Charpit's method.

(c)

7 marks

Find the solution of

u_{xx} + u_{yy} = 0

by method of separation of variables.

More Mathematics 3 (Mechanical) papers

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

Winter 202570 marks · 5 questions

Other Semester 3 subjects

BE Mechanical

3131904

Material Science and Metallurgy

3131905

Engineering Thermodynamics

3131906

Kinematics and Theory of Machines

BE03000201

Engineering Thermodynamics

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 3 (Mechanical) (Summer 2026, B.E. · Mechanical Engineering, Sem 3). 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 3 (Mechanical) Papers (2) →Report a typo or correction