Gujarat Technological UniversityWinter 2025 examination

GTU 130001 Mathematics-III (Maths 3) Winter 2025 Question Paper & PDF

B.E. · Computer Engineering · Semester 3 · Subject code 130001
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Total
70 marks
To pass
23 marks (33%)
Duration
2.5 Hours 10:30 AM – 1:30PM
Questions
5 with internal choice
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12 of 17 questions are types of question GTU sets again with new data. Each is marked below with the years it appeared.See all 11 repeated 130001 questions, most asked first

Q.1

14 Marks
(a)
7 marksSame type asked in 2 of 2 papers
Compute β(92,72)\beta\left(\frac{9}{2}, \frac{7}{2}\right).

Also asked in Summer 2025 Q1a

(b)
7 marksSame type asked in 2 of 2 papers
Find the series solution of y′−2xy=0y' - 2xy = 0.

Also asked in Summer 2025 Q4b OR

Q.2

14 Marks
(a)
7 marksSame type asked in 2 of 2 papers
Solve y′′+y′−12y=e6xy'' + y' - 12y = e^{6x}.

Also asked in Summer 2025 Q3b, Summer 2025 Q3b OR

(b)
7 marksSame type asked in 2 of 2 papers
Test the exactness and solve (x4−2xy2+y4)dx−(2x2y−4xy3+sin⁡y)dy=0(x^4 - 2xy^2 + y^4)dx - (2x^2 y - 4xy^3 + \sin y)dy = 0.

Also asked in Summer 2025 Q2b

(b)
7 marksSame type asked in 2 of 2 papers
Solve dydx+ysin⁡x=ecos⁡x\frac{dy}{dx} + y\sin x = e^{\cos x}.

Also asked in Summer 2025 Q2b OR

Q.3

14 Marks
(a)
7 marksSame type asked in 2 of 2 papers
Solve y′′+y=sin⁡xy'' + y = \sin x by using method of variation of parameters.

Also asked in Summer 2025 Q3a OR

(b)
7 marks
Find the half range sine series of f(x)=x2f(x) = x^2 in the interval (0,π)(0, \pi).
(a)
7 marksSame type asked in 2 of 2 papers
Solve x2y′′−20y=0x^2 y'' - 20y = 0.

Also asked in Summer 2025 Q5a OR

(b)
7 marksSame type asked in 2 of 2 papers
Find the Fourier series of f(x)=xf(x) = x in the interval (0,2π)(0, 2\pi).

Also asked in Summer 2025 Q1b, Summer 2025 Q2a

Q.4

14 Marks
(a)
7 marksSame type asked in 2 of 2 papers
Find L{tcos⁡at}\mathcal{L}\{t \cos at\}.

Also asked in Summer 2025 Q4a

(b)
7 marksSame type asked in 2 of 2 papers
Find L−1{s+2s(s+1)(s+3)}\mathcal{L}^{-1}\left\{\frac{s+2}{s(s+1)(s+3)}\right\}.

Also asked in Summer 2025 Q4b, Summer 2025 Q4a OR

(a)
7 marksSame type asked in 2 of 2 papers
Find L{∫0te−2tt3 dt}\mathcal{L}\left\{\int_0^t e^{-2t} t^3 \, dt\right\}.

Also asked in Summer 2025 Q4a

(b)
7 marks
Solve dydt+2y=e−3t\frac{dy}{dt} + 2y = e^{-3t}, y(0)=1y(0) = 1 by using Laplace transform.

Q.5

14 Marks
(a)
7 marks
Solve xp+yq=3zxp + yq = 3z.
(b)
7 marks
Solve p2+q2=x2+y2p^2 + q^2 = x^2 + y^2.
(a)
7 marks
Solve ∂2z∂x2−2∂2z∂x∂y+∂2z∂y2=ex+4y\frac{\partial^2 z}{\partial x^2} - 2\frac{\partial^2 z}{\partial x \partial y} + \frac{\partial^2 z}{\partial y^2} = e^{x+4y}.
(b)
7 marksSame type asked in 2 of 2 papers
Using the method of separation of variables, solve ∂u∂x=2∂u∂t+u\frac{\partial u}{\partial x} = 2\frac{\partial u}{\partial t} + u given that u(x,0)=6e−3xu(x, 0) = 6e^{-3x}.

Also asked in Summer 2025 Q5a

More Mathematics-III papers

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

Summer 202570 marks · 5 questions

Other Semester 3 subjects

BE Computer

3130004
Effective Technical Communication
3130006
Probability and Statistics
3130702
Data Structures
3130703
DATABASE MANAGEMENT SYSTEM

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About this paper

Official Gujarat Technological University (GTU) examination paper for Mathematics-III (Maths 3) (Winter 2025, B.E. · Computer 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.

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