Gujarat Technological UniversitySummer 2024 examination

GTU 3110014 Mathematics - 1 (Maths 1) Summer 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 2:30 PM – 5:30 PM
Questions
5 with internal choice
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4 of 25 questions on this paper were also asked in other years. 16 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
Using L’ Hospital’s rule, evaluate
lim⁡x→1x−xx1+log⁡x−x\lim_{x \to 1} \frac{x - x^x}{1 + \log x - x}

Also asked in Summer 2026 Q1a, Winter 2025 Q1a, Winter 2023 Q1a, Summer 2023 Q1a

(b)
4 marksSame type asked in 2 of 7 papers
Define Beta function and evaluate
∫01x3(1−x)5 dx\int_0^1 x^3 (1 - \sqrt{x})^5 \, dx

Also asked in Summer 2023 Q3a OR

(c)
7 marksSame type asked in 5 of 7 papers
Find the Fourier series of
f(x)={π+x−π<x<0π−x0<x<πf(x) = \begin{cases} \pi + x & -\pi < x < 0 \\ \pi - x & 0 < x < \pi \end{cases}

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

Q.2

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, Winter 2024 Q3a

(b)
4 marksSame type asked in 2 of 7 papers
Express f(x)=2x3+3x2−8x+7f(x) = 2x^3 + 3x^2 - 8x + 7 in terms of (x−2)(x - 2).

Also asked in Winter 2024 Q2b

(c)
7 marksSame type asked in 2 of 7 papers
Find the area of the surface of revolution of a quadrant of a circular arc as obtained by revolving it about a tangent at one of its ends.

Also asked in Summer 2025 Q2b

(c)
7 marksSame type asked in 3 of 7 papers
Find the length of the loop of the curve
9ay2=(x−2a)(x−5a)29ay^2 = (x - 2a)(x - 5a)^2

Also asked in Winter 2024 Q4c, Summer 2023 Q3b OR

Q.3

14 Marks
(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 Winter 2024 Q5a OR

(b)
4 marks
Test the convergence of the series
∑n=1∞2n+1n2(n+1)2\sum_{n=1}^\infty \frac{2n + 1}{n^2 (n+1)^2}
(c)
7 marks
If θ=tne−r24t\theta = t^n e^{-\frac{r^2}{4t}} then find nn so that
1r2∂∂r(r2∂θ∂r)=∂θ∂t\frac{1}{r^2} \frac{\partial}{\partial r} \left( r^2 \frac{\partial \theta}{\partial r} \right) = \frac{\partial \theta}{\partial t}
(a)
3 marksSame type asked in 2 of 7 papers
Check the convergence of
∫051x2 dx\int_0^5 \frac{1}{x^2} \, dx

Also asked in Winter 2024 Q3b

(b)
4 marks
Evaluate
∫0∞3−4x2 dx\int_0^\infty 3^{-4x^2} \, dx
(c)
7 marksAsked in 2 of 7 papers
Find the Fourier series of f(x)=12(π−x)f(x) = \frac{1}{2}(\pi - x) in the interval (0,2π)(0, 2\pi). Hence, deduce that
π4=1−13+15−17+…\frac{\pi}{4} = 1 - \frac{1}{3} + \frac{1}{5} - \frac{1}{7} + \dots

Also asked in Summer 2026 Q2c

Q.4

14 Marks
(a)
3 marks
Prove that
tan⁡−1x=x−x33+x55−x77+…\tan^{-1} x = x - \frac{x^3}{3} + \frac{x^5}{5} - \frac{x^7}{7} + \dots
(b)
4 marksSame type asked in 2 of 7 papers
Find the Fourier sine series of f(x)=exf(x) = e^x in 0<x<π0 < x < \pi.

Also asked in Winter 2024 Q3b OR

(c)
7 marksSame type asked in 7 of 7 papers
Find the extreme values of the function f(x,y)=x3+y3−3x−12y+20f(x, y) = x^3 + y^3 - 3x - 12y + 20.

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

(a)
3 marksSame type asked in 5 of 7 papers
Find the directional derivative of f(x,y,z)=x2yz+4xz2f(x, y, z) = x^2 yz + 4xz^2 at (1,−2,−1)(1, -2, -1) in the direction of 2i^−j^−2k^2\hat{i} - \hat{j} - 2\hat{k}.

Also asked in Summer 2026 Q3b, Summer 2025 Q3b OR, Winter 2024 Q2a, Winter 2023 Q3b

(b)
4 marksSame type asked in 6 of 7 papers
Solve the following system by Gauss-Jordan method:

−2y+3z=13x+6y−3z=−26x+6y+3z=5\begin{aligned} -2y + 3z &= 1 \\ 3x + 6y - 3z &= -2 \\ 6x + 6y + 3z &= 5 \end{aligned}

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

(c)
7 marksSame type asked in 7 of 7 papers
Change the order of integration and evaluate:
∫01∫01−y2cos⁡−1x1−x21−x2−y2 dx dy\int_0^1 \int_0^{\sqrt{1-y^2}} \frac{\cos^{-1} x}{\sqrt{1-x^2}\sqrt{1-x^2-y^2}} \, dx \, dy

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

Q.5

14 Marks
(a)
3 marks
Evaluate
∫03∫01(x2+3y2) dy dx\int_0^3 \int_0^1 (x^2 + 3y^2) \, dy \, dx
(b)
4 marksSame type asked in 2 of 7 papers
Apply Cayley-Hamilton theorem to
A=[122−1]A = \begin{bmatrix} 1 & 2 \\ 2 & -1 \end{bmatrix}
and deduce that A8=625IA^8 = 625 I.

Also asked in Summer 2023 Q5b OR

(c)
7 marksAsked in 2 of 7 papers
Evaluate
∫02∫02x−x2xx2+y2 dy dx\int_0^2 \int_0^{\sqrt{2x-x^2}} \frac{x}{x^2+y^2} \, dy \, dx
by changing to polar coordinates.

Also asked in Summer 2025 Q4c OR

(a)
3 marksSame type asked in 4 of 7 papers
Evaluate
∫02∫12∫0yzxyz dx dy dz\int_0^2 \int_1^2 \int_0^{yz} xyz \, dx \, dy \, dz

Also asked in Summer 2026 Q4c OR, Winter 2025 Q4b OR, Summer 2023 Q2a

(b)
4 marksSame type asked in 3 of 7 papers
Using Gauss Jordan method, find inverse of
A=[234431124]A = \begin{bmatrix} 2 & 3 & 4 \\ 4 & 3 & 1 \\ 1 & 2 & 4 \end{bmatrix}

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

(c)
7 marksSame type asked in 5 of 7 papers
Find the eigen values and eigen vectors of the matrix
A=[466132−1−4−3]A = \begin{bmatrix} 4 & 6 & 6 \\ 1 & 3 & 2 \\ -1 & -4 & -3 \end{bmatrix}

Also asked in Summer 2026 Q5c OR, Summer 2025 Q2c, Winter 2023 Q2c, Summer 2023 Q1c

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
Winter 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) (Summer 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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