Gujarat Technological UniversityWinter 2023 examination

GTU 3110014 Mathematics - 1 (Maths 1) Winter 2023 Question Paper & PDF

B.E. · Common Engineering · Semester 1 · 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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14 of 25 questions 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
Evaluate
lim⁡x→0+xln⁡x\lim_{x \to 0^+} x \ln x

Also asked in Summer 2026 Q1a, Winter 2025 Q1a, Summer 2024 Q1a, Summer 2023 Q1a

(b)
4 marks
Define beta and gamma functions. What is the relationship between beta and gamma functions?
(c)
7 marksSame type asked in 6 of 7 papers
Solve the following system of linear equations using Gauss-Jordan elimination:

x3+x4+x5=0−x1−x2+2x3−3x4+x5=0x1+x2−2x3−x5=02x1+2x2−x3+x5=0\begin{aligned} x_3 + x_4 + x_5 &= 0 \\ -x_1 - x_2 + 2x_3 - 3x_4 + x_5 &= 0 \\ x_1 + x_2 - 2x_3 - x_5 &= 0 \\ 2x_1 + 2x_2 - x_3 + x_5 &= 0 \end{aligned}

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

Q.2

14 Marks
(a)
3 marksSame type asked in 3 of 7 papers
Define rank of the matrix. Find rank(A)\text{rank}(A) if
A=[1224]A = \begin{bmatrix} 1 & 2 \\ 2 & 4 \end{bmatrix}

Also asked in Summer 2026 Q5a, Winter 2025 Q5a OR

(b)
4 marks
Test the convergence of the series
∑n=1∞(11+n)n\sum_{n=1}^\infty \left(\frac{1}{1+n}\right)^n
(c)
7 marksSame type asked in 5 of 7 papers
Find eigenvalues and eigenvectors of the matrix
A=[−522−2]A = \begin{bmatrix} -5 & 2 \\ 2 & -2 \end{bmatrix}

Also asked in Summer 2026 Q5c OR, Summer 2025 Q2c, Summer 2024 Q5c OR, Summer 2023 Q1c

(c)
7 marksSame type asked in 5 of 7 papers
Find the Fourier series of the function f(x)=x+πf(x) = x + \pi if −π<x<π-\pi < x < \pi and f(x+2π)=f(x)f(x + 2\pi) = f(x).

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

Q.3

14 Marks
(a)
3 marksSame type asked in 3 of 7 papers
If w=x2+y2,x=r−s,y=r+sw = x^2 + y^2, x = r - s, y = r + s, using chain rule, prove that ∂w∂s=4s\frac{\partial w}{\partial s} = 4s.

Also asked in Summer 2026 Q3a OR, Winter 2025 Q3a OR

(b)
4 marksSame type asked in 5 of 7 papers
Find the directional derivative of f(x,y,z)=2x2+3y2+z2f(x, y, z) = 2x^2 + 3y^2 + z^2 at point (2,1,3)(2, 1, 3) in the direction of the vector i−2k\mathbf{i} - 2\mathbf{k}.

Also asked in Summer 2026 Q3b, Summer 2025 Q3b OR, Winter 2024 Q2a, Summer 2024 Q4a OR

(c)
7 marksSame type asked in 7 of 7 papers
Find local extreme values of the function f(x,y)=4x2+9y2+8x−36y+24f(x, y) = 4x^2 + 9y^2 + 8x - 36y + 24.

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

(a)
3 marks
Determine whether
lim⁡(x,y)→(0,0)2x2yx3+y3\lim_{(x, y) \to (0, 0)} \frac{2x^2 y}{x^3 + y^3}
exists and find it if exists.
(b)
4 marksSame type asked in 5 of 7 papers
Find the equation of the tangent plane to z=3x2−xyz = 3x^2 - xy at the point (1,2,1)(1, 2, 1).

Also asked in Winter 2025 Q3b, Summer 2025 Q3b, Winter 2024 Q1a, Summer 2023 Q2b

(c)
7 marksSame type asked in 4 of 7 papers
Find the maximum and minimum values of the function f(x,y)=3x+4yf(x, y) = 3x + 4y on the circle x2+y2=1x^2 + y^2 = 1.

Also asked in Summer 2026 Q3c, Winter 2025 Q3c, Summer 2025 Q3c OR

Q.4

14 Marks
(a)
3 marks
Calculate
∬Rf(x,y) dA\iint_R f(x, y) \, dA
for f(x,y)=100−6x2yf(x, y) = 100 - 6x^2 y and R:0≤x≤2,−1≤y≤1R: 0 \le x \le 2, -1 \le y \le 1.
(b)
4 marksSame type asked in 7 of 7 papers
Sketch the region of integration for the integral
∫02∫x22x(4x+2) dy dx\int_0^2 \int_{x^2}^{2x} (4x + 2) \, dy \, dx
and write an equivalent integral with the order of integration reversed.

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

(c)
7 marks
Calculate
∬Rsin⁡xx dA\iint_R \frac{\sin x}{x} \, dA
where RR is the triangle in the xyxy-plane bounded by the xx-axis, the line y=xy = x and the line x=1x = 1.
(a)
3 marks
Evaluate
∫1ln⁡8∫0ln⁡yex+y dx dy\int_1^{\ln 8} \int_0^{\ln y} e^{x+y} \, dx \, dy
(b)
4 marks
Find the area of the region RR bounded by y=xy = x and y=x2y = x^2 in the first quadrant.
(c)
7 marksSame type asked in 2 of 7 papers
Evaluate
∫01∫01−x2(x2+y2) dy dx\int_0^1 \int_0^{\sqrt{1-x^2}} (x^2 + y^2) \, dy \, dx
by changing into polar coordinates.

Also asked in Summer 2026 Q4b OR

Q.5

14 Marks
(a)
3 marksSame type asked in 4 of 7 papers
Find the Maclaurin series for cos⁡x\cos x.

Also asked in Summer 2026 Q5b OR, Winter 2025 Q5b, Summer 2025 Q5b

(b)
4 marks
Determine the convergence or divergence of the series
∑n=1∞ne−n2\sum_{n=1}^\infty n e^{-n^2}
(c)
7 marks
Test the convergence of the series
∑n=1∞(−1)n−1n2\sum_{n=1}^\infty \frac{(-1)^{n-1}}{n^2}
(a)
3 marks
Define monotonic sequence. Is the sequence {1n2}\{\frac{1}{n^2}\} monotonic?
(b)
4 marksSame type asked in 4 of 7 papers
Investigate the convergence of the series
∑n=0∞2n+53n\sum_{n=0}^\infty \frac{2^n + 5}{3^n}

Also asked in Summer 2026 Q2b, Winter 2025 Q2b, Summer 2023 Q4a

(c)
7 marks
Find the interval of convergence of the series
x−x22+x33−…x - \frac{x^2}{2} + \frac{x^3}{3} - \dots

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) (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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