Gujarat Technological UniversityWinter 2024 examination

GTU 3110015 Mathematics - 2 (Maths 2) Winter 2024 Question Paper & PDF

B.E. · Common Engineering · Semesters 1 and 2 · Subject code 3110015
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Total
70 marks
To pass
23 marks (33%)
Duration
2.5 Hours 10:30 AM – 1:30 PM
Questions
5 with internal choice
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5 of 25 questions on this paper were also asked in other years. 19 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
Find aa such that (x+3y)i^+(y−2z)j^+(x+az)k^(x+3y)\hat{i} + (y-2z)\hat{j} + (x+az)\hat{k} is solenoidal.

Also asked in Winter 2023 Q1a

(b)
4 marksAsked in 2 of 6 papers
Solve yex dx+(2y+ex) dy=0y e^x \, dx + (2y + e^x) \, dy = 0.

Also asked in Summer 2025 Q2a

(c)
7 marksSame type asked in 6 of 6 papers
Verify Green’s theorem in a plane for the integral
∫C[(x−2y) dx+x dy]\int_C [(x - 2y) \, dx + x \, dy]
taken around the circle x2+y2=4x^2 + y^2 = 4.

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

Q.2

14 Marks
(a)
3 marksSame type asked in 6 of 6 papers
Find the Laplace transform of (sin⁡2t−cos⁡2t)2(\sin 2t - \cos 2t)^2.

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

(b)
4 marksAsked in 2 of 6 papers
Find the Fourier sine integral of f(x)=e−bxf(x) = e^{-bx}.

Also asked in Winter 2023 Q2c OR

(c)
7 marksSame type asked in 6 of 6 papers
Using the Frobenius method, obtain the series solution for
2x(1−x)y′′+(1−x)y′+3y=0about x0=02x(1-x)y'' + (1-x)y' + 3y = 0 \quad \text{about } x_0 = 0

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

(c)
7 marksSame type asked in 4 of 6 papers
Using the method of undetermined coefficients, solve
(D2−9)y=x+e2x−sin⁡2x(D^2 - 9)y = x + e^{2x} - \sin 2x

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

Q.3

14 Marks
(a)
3 marks
Find the arc length of the curve r⃗(t)=t2i^+t3j^\vec{r}(t) = t^2 \hat{i} + t^3 \hat{j} between (1,1)(1, 1) and (4,8)(4, 8).
(b)
4 marksSame type asked in 6 of 6 papers
Find the Laplace transform of
e−tsin⁡tt\frac{e^{-t} \sin t}{t}

Also asked in Winter 2025 Q2b, Winter 2025 Q3a, Summer 2025 Q4a, Summer 2025 Q4b, Summer 2025 Q4b 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
State the convolution theorem and verify it for f(t)=tf(t) = t and g(t)=e2tg(t) = e^{2t}.

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

(a)
3 marksSame type asked in 6 of 6 papers
Find the inverse Laplace transform of tan⁡−1s\tan^{-1} s.

Also asked in Winter 2025 Q3a OR, Summer 2025 Q4a OR, Summer 2025 Q4c OR, 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
Solve x2p2+3xyp+2y2=0x^2 p^2 + 3xyp + 2y^2 = 0.

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

(c)
7 marksSame type asked in 6 of 6 papers
Solve the initial value problem using Laplace transformation:
y′′−3y′+2y=4twith y(0)=1,  y′(0)=−1y'' - 3y' + 2y = 4t \quad \text{with } y(0) = 1, \; y'(0) = -1

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

Q.4

14 Marks
(a)
3 marksSame type asked in 6 of 6 papers
Find the inverse Laplace transform of
e−πss2−2s+2\frac{e^{-\pi s}}{s^2 - 2s + 2}

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

(c)
7 marksSame type asked in 6 of 6 papers
Using method of variation of parameters, solve (D2−2D+2)y=extan⁡x(D^2 - 2D + 2)y = e^x \tan x.

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

(a)
3 marksAsked in 2 of 6 papers
Classify the singular points of the equation x3(x−2)y′′+x3y′+6y=0x^3 (x - 2) y'' + x^3 y' + 6y = 0.

Also asked in Summer 2024 Q5a OR

(b)
4 marksSame type asked in 6 of 6 papers
Find the Laplace transform of sin⁡t\sin \sqrt{t}.

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

(c)
7 marksAsked in 2 of 6 papers
Find the series solution of (1+x2)y′′+xy′−9y=0(1 + x^2) y'' + xy' - 9y = 0.

Also asked in Summer 2024 Q3c OR

Q.5

14 Marks
(a)
3 marksSame type asked in 5 of 6 papers
Solve dr+(2rcot⁡θ+sin⁡2θ) dθ=0dr + (2r \cot \theta + \sin 2\theta) \, d\theta = 0.

Also asked in Winter 2025 Q4a, Summer 2025 Q5a, Summer 2025 Q5b OR, Winter 2023 Q3a, Winter 2023 Q3a OR, Summer 2023 Q4c

(b)
4 marksSame type asked in 2 of 6 papers
If y1=sin⁡xxy_1 = \frac{\sin x}{x} is one of the solution of xy′′+2y′+xy=0x y'' + 2y' + xy = 0, find the second solution.

Also asked in Winter 2023 Q3b OR

(c)
7 marksSame type asked in 3 of 6 papers
Show that:
i
J12(x)=2πxsin⁡xJ_{\frac{1}{2}}(x) = \sqrt{\frac{2}{\pi x}} \sin x
ii
J−12(x)=2πxcos⁡xJ_{-\frac{1}{2}}(x) = \sqrt{\frac{2}{\pi x}} \cos x

Also asked in Winter 2025 Q5b OR, Summer 2024 Q5b OR

(a)
3 marksSame type asked in 6 of 6 papers
Find the Laplace transform of
∫0t∫0tsin⁡at dt dt\int_0^t \int_0^t \sin at \, dt \, dt

Also asked in Winter 2025 Q2b, Winter 2025 Q3a, Summer 2025 Q4a, Summer 2025 Q4b, Summer 2025 Q4b 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 5 of 6 papers
Solve (x2D2−xD+2)y=6(x^2 D^2 - xD + 2)y = 6.

Also asked in Winter 2025 Q4b, Summer 2025 Q3c OR, Summer 2024 Q5a, Winter 2023 Q4b

(c)
7 marksSame type asked in 3 of 6 papers
Prove that
J02(x)+2[J12(x)+J22(x)+J32(x)+… ]=1J_0^2(x) + 2\left[ J_1^2(x) + J_2^2(x) + J_3^2(x) + \dots \right] = 1

Also asked in Winter 2025 Q5b OR, Summer 2024 Q5b 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
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

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About this paper

Official Gujarat Technological University (GTU) examination paper for Mathematics - 2 (Maths 2) (Winter 2024, 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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