Gujarat Technological UniversityWinter 2024 examination

GTU 3110014 Mathematics - 1 (Maths 1) Winter 2024 Question Paper & PDF

B.E. · Common Engineering · Semesters 1 and 2 · Subject code 3110014
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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. 12 more are types of question GTU sets again with new data. Each is marked below with the years it appeared.See all 35 repeated 3110014 questions, most asked first

Q.1

14 Marks
(a)
3 marksSame type asked in 5 of 7 papers
Find the equation of tangent plane and normal line to the surface xyz=6xyz = 6 at (1,2,3)(1, 2, 3).

Also asked in Winter 2025 Q3b, Summer 2025 Q3b, Winter 2023 Q3b OR, Summer 2023 Q2b

(b)
4 marksAsked in 2 of 7 papers
Evaluate
lim⁡x→0(1x2−1sin⁡2x)\lim_{x \to 0} \left( \frac{1}{x^2} - \frac{1}{\sin^2 x} \right)

Also asked in Summer 2025 Q1a

(c)
7 marksSame type asked in 6 of 7 papers
Solve the following system by Gauss Elimination method:

x+y+2z=92x+4y−3z=13x+6y−5z=0\begin{aligned} x + y + 2z &= 9 \\ 2x + 4y - 3z &= 1 \\ 3x + 6y - 5z &= 0 \end{aligned}

Also asked in Summer 2026 Q5c, Winter 2025 Q5c, Summer 2024 Q4b OR, Winter 2023 Q1c, Summer 2023 Q5b

Q.2

14 Marks
(a)
3 marksSame type asked in 5 of 7 papers
Find the directional derivative of f(x,y,z)=xy2+yz3f(x, y, z) = xy^2 + yz^3 at the point (2,−1,1)(2, -1, 1) in the direction i^+2j^+2k^\hat{i} + 2\hat{j} + 2\hat{k}.

Also asked in Summer 2026 Q3b, Summer 2025 Q3b OR, Summer 2024 Q4a OR, Winter 2023 Q3b

(b)
4 marksSame type asked in 2 of 7 papers
Expand x4−3x3+2x2−x+1x^4 - 3x^3 + 2x^2 - x + 1 in powers of (x−3)(x - 3).

Also asked in Summer 2024 Q2b

(c)
7 marksSame type asked in 5 of 7 papers
Find the Fourier series of
f(x)={x20<x<π0π<x<2πf(x) = \begin{cases} x^2 & 0 < x < \pi \\ 0 & \pi < x < 2\pi \end{cases}

Also asked in Winter 2025 Q2c, Winter 2025 Q2c OR, Summer 2024 Q1c, Winter 2023 Q2c OR, Summer 2023 Q2c, Summer 2023 Q2c OR

(c)
7 marksSame type asked in 5 of 7 papers
Find the Fourier series of f(x)=x+∣x∣f(x) = x + |x| in the interval −π<x<π-\pi < x < \pi.

Also asked in Winter 2025 Q2c, Winter 2025 Q2c OR, Summer 2024 Q1c, Winter 2023 Q2c OR, Summer 2023 Q2c, Summer 2023 Q2c OR

Q.3

14 Marks
(a)
3 marksAsked in 3 of 7 papers
Show that the sequence {un}\{u_n\}, where un=sin⁡nnu_n = \frac{\sin n}{n} converges to zero.

Also asked in Summer 2025 Q5a OR, Summer 2024 Q2a

(b)
4 marksSame type asked in 2 of 7 papers
Evaluate
∫03dx(x−1)23\int_0^3 \frac{dx}{(x - 1)^{\frac{2}{3}}}

Also asked in Summer 2024 Q3a OR

(c)
7 marksAsked in 2 of 7 papers
A rectangular box without a lid is to be made from 12 m212\text{ m}^2 of cardboard. Find the maximum volume of such box.

Also asked in Summer 2023 Q4c OR

(a)
3 marks
Evaluate
∫01(log⁡x)5 dx\int_0^1 (\log x)^5 \, dx
(b)
4 marksSame type asked in 2 of 7 papers
Find the cosine series for f(x)=π−xf(x) = \pi - x in the interval 0<x<π0 < x < \pi.

Also asked in Summer 2024 Q4b

(c)
7 marksSame type asked in 7 of 7 papers
Find the extreme values of the function x3+xy2+21x−12x2−2y2x^3 + xy^2 + 21x - 12x^2 - 2y^2.

Also asked in Summer 2026 Q3b OR, Winter 2025 Q3c OR, Summer 2025 Q3c, Summer 2024 Q4c, Winter 2023 Q3c, Summer 2023 Q4c

Q.4

14 Marks
(a)
3 marks
Test the convergence of the series
∑n=1∞nn2+1\sum_{n=1}^\infty \frac{\sqrt{n}}{n^2 + 1}
(b)
4 marks
Evaluate the integral
∫0π2∫01−sin⁡θr2cos⁡θ dr dθ\int_0^{\frac{\pi}{2}} \int_0^{1-\sin \theta} r^2 \cos \theta \, dr \, d\theta
(c)
7 marksSame type asked in 3 of 7 papers
Find the length of the parabola x2=4yx^2 = 4y which lies inside the circle x2+y2=6yx^2 + y^2 = 6y.

Also asked in Summer 2024 Q2c OR, Summer 2023 Q3b OR

(a)
3 marksAsked in 2 of 7 papers
Evaluate
∫02∫1z∫0yzxyz dx dy dz\int_0^2 \int_1^z \int_0^{yz} xyz \, dx \, dy \, dz

Also asked in Summer 2025 Q4a OR

(b)
4 marks
Test the convergence of the series
∑(n+1)nxnnn+1\sum \frac{(n+1)^n x^n}{n^{n+1}}
(c)
7 marksSame type asked in 7 of 7 papers
Change the order of integration and evaluate:
∫0∞∫x∞e−yy dy dx\int_0^\infty \int_x^\infty \frac{e^{-y}}{y} \, dy \, dx

Also asked in Summer 2026 Q4b, Winter 2025 Q4c, Summer 2025 Q4c, Summer 2025 Q4b OR, Summer 2024 Q4c OR, Winter 2023 Q4b, Summer 2023 Q5c

Q.5

14 Marks
(a)
3 marks
Test the convergence of the series
∑n=1∞n2e−n3\sum_{n=1}^\infty n^2 e^{-n^3}
(b)
4 marks
Find aa and bb such that
A=[a41b]A = \begin{bmatrix} a & 4 \\ 1 & b \end{bmatrix}
has 33 and −2-2 as eigenvalues.
(c)
7 marks
If u=f(y−xxy,z−xxz)u = f\left(\frac{y-x}{xy}, \frac{z-x}{xz}\right), show that
x2∂u∂x+y2∂u∂y+z2∂u∂z=0x^2 \frac{\partial u}{\partial x} + y^2 \frac{\partial u}{\partial y} + z^2 \frac{\partial u}{\partial z} = 0
(a)
3 marksAsked in 2 of 7 papers
Evaluate
∫0∞dv(1+v2)(1+tan⁡−1v)\int_0^\infty \frac{dv}{(1+v^2)(1+\tan^{-1} v)}

Also asked in Summer 2024 Q3a

(b)
4 marksSame type asked in 3 of 7 papers
Using Gauss Jordan method find inverse of
A=[843211121]A = \begin{bmatrix} 8 & 4 & 3 \\ 2 & 1 & 1 \\ 1 & 2 & 1 \end{bmatrix}

Also asked in Summer 2025 Q2c OR, Summer 2024 Q5b OR

(c)
7 marks
Show that the matrix
A=[1−20122123]A = \begin{bmatrix} 1 & -2 & 0 \\ 1 & 2 & 2 \\ 1 & 2 & 3 \end{bmatrix}
is not diagonalizable.

More Mathematics - 1 papers

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

Summer 202670 marks · 5 questions · Solved
Winter 202570 marks · 5 questions · Solved
Summer 202570 marks · 5 questions · Solved
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 - 1 (Maths 1) (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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