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.

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Gujarat Technological UniversityWinter 2023 examination

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

B.E. · Common Engineering · Semester 1 · Subject code 3110015

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Total: 70 marks
To pass: 23 marks (33%)
Duration: 2.5 Hours 2:30 PM – 5:30 PM
Questions: 5 with internal choice

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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 marksAsked in 2 of 6 papers

Define Solenoidal Vector field. Find the constant

a

such that the vector

(x + 3)\hat{i} + (y - 2z)\hat{j} + (x + az)\hat{k}

is solenoidal.

Also asked in Winter 2024 Q1a

(b)

4 marksSame type asked in 4 of 6 papers

If $\vec{F} = 3x^2 y \hat{i} + (x^3 - 2yz^2)\hat{j} + (3z^2 - 2y^2 z)\hat{k}$ is conservative, then find:

iits scalar potential

\phi

iithe work done in moving from

(2, 1, 1)

(3, 0, 1)

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

(c)

7 marksSame type asked in 6 of 6 papers

Verify Green’s theorem in the plane for

\oint_C (xy^2 - 2xy) \, dx + (x^2 y + 3) \, dy

where

C

is the region bounded by the rectangle with vertices

(-1, 0), (1, 0), (1, 1)

and

(-1, 1)

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

Q.2

14 Marks

(a)

3 marksSame type asked in 6 of 6 papers

State first shifting theorem for Laplace transform. Evaluate:

\mathcal{L}[e^{-t} t^5]

\mathcal{L}^{-1}\left[\frac{1}{s^2 + 2s + 2}\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, Summer 2023 Q3b, Summer 2023 Q3b OR

(b)

4 marksSame type asked in 6 of 6 papers

Find:

\mathcal{L}\left[\frac{1 - \cos 2t}{t}\right]

\mathcal{L}^{-1}\left[\frac{54}{(s^2 + 9)(s^2 - 9)}\right]

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, Summer 2023 Q3a, Summer 2023 Q3a OR

(c)

7 marksSame type asked in 6 of 6 papers

Using Laplace transform solve the initial value problem:

y'' - y = t, \quad \text{with } y(0) = 1, \; y'(0) = -1

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

(c)

7 marksAsked in 2 of 6 papers

Find the Fourier sine integral of

f(x) = e^{-bx}

and show that

\frac{\pi}{2} e^{-bx} = \int_0^\infty \frac{\lambda \sin \lambda x}{\lambda^2 + b^2} \, d\lambda

Also asked in Winter 2024 Q2b

Q.3

14 Marks

(a)

3 marksSame type asked in 5 of 6 papers

Define linear differential equation. Solve:

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

, given that

y(1) = 1

Also asked in Winter 2025 Q4a, Summer 2025 Q5a, Summer 2025 Q5b OR, Winter 2024 Q5a, Summer 2023 Q4c

(b)

4 marksSame type asked in 6 of 6 papers

Solve: (i)

(D^2 + 7D - 18)y = 0

, (ii)

y'' + y' + 2y = 0

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, Summer 2023 Q4b, Summer 2023 Q4b OR, Summer 2023 Q5a, Summer 2023 Q5a OR, Summer 2023 Q5c

(c)

7 marksSame type asked in 6 of 6 papers

iSolve:

(x + y - 1) \, dx + (2x + 2y - 3) \, dy = 0

iiSolve:

x^2 p^2 - 4y^2 = 0

Also asked in Winter 2025 Q4a OR, Summer 2025 Q5b, Winter 2024 Q3b OR, Summer 2024 Q3c, Summer 2023 Q4c OR

(a)

3 marksSame type asked in 5 of 6 papers

Solve:

y^2 \frac{dx}{dy} + yx = y^3 x^2

Also asked in Winter 2025 Q4a, Summer 2025 Q5a, Summer 2025 Q5b OR, Winter 2024 Q5a, Summer 2023 Q4c

(b)

4 marksSame type asked in 2 of 6 papers

Determine a second solution of

x^2 \frac{d^2 y}{dx^2} - 2y = 0, x > 0

, where first solution is

y_1 = \frac{1}{x}

Also asked in Winter 2024 Q5b

(c)

7 marksSame type asked in 6 of 6 papers

iSolve:

p = \sin(y - px)

iiSolve:

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

Also asked in Winter 2025 Q4a OR, Summer 2025 Q5b, Winter 2024 Q3b OR, Summer 2024 Q3c, Summer 2023 Q4c OR

Q.4

14 Marks

(a)

3 marksSame type asked in 6 of 6 papers

Solve:

(D^2 + 3D + 2)y = \sin 2x

(b)

4 marksSame type asked in 5 of 6 papers

Solve:

x^3 y''' + x^2 y'' = x^3

Also asked in Winter 2025 Q4b, Summer 2025 Q3c OR, Winter 2024 Q5b OR, Summer 2024 Q5a

(c)

7 marksSame type asked in 4 of 6 papers

Using the method of undetermined coefficients solve

y'' + 9y = 2x^2

Also asked in Summer 2025 Q3c, Winter 2024 Q2c OR, Summer 2023 Q5b, Summer 2023 Q5b OR

(a)

3 marksSame type asked in 6 of 6 papers

Solve:

(D^2 + 4D)y = x + x^2

(b)

4 marksSame type asked in 6 of 6 papers

Solve:

(D^2 - 6D + 9)y = x^2 e^{3x}

(c)

7 marksSame type asked in 6 of 6 papers

Using the method of variation of parameters solve:

y'' - 2y' + y = x e^x \sin x

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

Q.5

14 Marks

(a)

3 marksSame type asked in 3 of 6 papers

Determine the singular points of the differential equation

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

and classify them as regular or irregular.

Also asked in Winter 2025 Q5a, Winter 2025 Q5a OR, Summer 2023 Q2a

(b)

4 marksSame type asked in 6 of 6 papers

Find the series solution of

y'' - y' = 0

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

(c)

7 marksSame type asked in 6 of 6 papers

Solve the differential equation

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

by using Frobenius method.

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

(a)

3 marksSame type asked in 3 of 6 papers

Discuss about the ordinary points, regular singular points and irregular singular points for the differential equation

x^3 y'' + 5xy' + 3y = 0

Also asked in Winter 2025 Q5a, Winter 2025 Q5a OR, Summer 2023 Q2a

(b)

4 marksSame type asked in 6 of 6 papers

Find the power series solution of

y' + 2xy = 0

in powers of

x

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

(c)

7 marksSame type asked in 3 of 6 papers

iExpress

J_3(x)

in terms of

J_1(x)

and

J_2(x)

iiExpress

f(x) = 4x^3 + 6x^2 + 7x + 1

in terms of Legendre’s polynomials.

Also asked in Summer 2024 Q5c OR, Summer 2023 Q2b, Summer 2023 Q2c 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

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About this paper

Official Gujarat Technological University (GTU) examination paper for Mathematics - 2 (Maths 2) (Winter 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.

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