Gujarat Technological UniversityWinter 2025 examination

GTU 3110019 Remedial Mathematics (Remedial Maths) Winter 2025 Question Paper & PDF

B.E. · Common Engineering · Semesters 1 and 2 · Subject code 3110019
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Total
70 marks
To pass
23 marks (33%)
Duration
2.5 Hours 2:30 PM – 5:00 PM
Questions
5 with internal choice
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1 of 25 questions on this paper were also asked in other years. 14 more are types of question GTU sets again with new data. Each is marked below with the years it appeared.See all 38 repeated 3110019 questions, most asked first

Q.1

14 Marks
(a)
3 marksSame type asked in 2 of 7 papers
Define slope of a line and find the slope of the line joining the points (2,3)(2, 3) and (−1,5)(-1, 5).

Also asked in Summer 2025 Q1a

(b)
4 marksSame type asked in 3 of 7 papers
Find the equation of a line passing through (2,−3)(2, -3) and perpendicular to the line 3x−4y+7=03x - 4y + 7 = 0.

Also asked in Summer 2025 Q1b, Winter 2024 Q2a, Winter 2024 Q2b

(c)
7 marksSame type asked in 2 of 7 papers
Find the distance of the point (4,−3)(4, -3) from the line 3x+4y−5=03x + 4y - 5 = 0.

Also asked in Summer 2023 Q2a

Q.2

14 Marks
(a)
3 marks
Define real-valued function with examples.
(b)
4 marks
Express sin⁡3x\sin 3x and cos⁡3x\cos 3x.
(c)
7 marks
Prove sin⁡(x+y)sin⁡(x−y)=sin⁡2x−sin⁡2y\sin(x+y)\sin(x-y) = \sin^2 x - \sin^2 y.
(c)
7 marksSame type asked in 3 of 7 papers
Find lim⁡x→0sin⁡3xx\lim_{x \to 0} \frac{\sin 3x}{x}. Also Define limits and continuity of function.

Also asked in Summer 2025 Q3a, Summer 2023 Q3a OR

Q.3

14 Marks
(a)
3 marksSame type asked in 3 of 7 papers
Check continuity of f(x)={x2x<13x−2x≥1f(x) = \begin{cases} x^2 & x < 1 \\ 3x - 2 & x \ge 1 \end{cases} at x=1x = 1.

Also asked in Summer 2026 Q4a OR, Summer 2023 Q4a OR

(b)
4 marksSame type asked in 3 of 7 papers
If y=x2sin⁡xy = x^2\sin x, find dydx\frac{dy}{dx} and d2ydx2\frac{d^2 y}{dx^2}.

Also asked in Summer 2024 Q4b OR, Winter 2023 Q4b OR

(c)
7 marks
Differentiate the function sin⁡(3x+5)cos⁡x\frac{\sin(3x + 5)}{\cos x}.
(a)
3 marks
Find ∫(sin⁡x+cos⁡2x) dx\int (\sin x + \cos 2x) \, dx.
(b)
4 marks
Find ∫12(4x3−5x2+6x+9) dx\int_1^2 (4x^3 - 5x^2 + 6x + 9) \, dx.
(c)
7 marksAsked in 2 of 7 papers
Integrate the function ∫x(x+1)(x+2) dx\int \frac{x}{(x+1)(x+2)} \, dx.

Also asked in Summer 2025 Q4b OR

Q.4

14 Marks
(a)
3 marks
Find the transpose of the given matrix (1208)\begin{pmatrix} 1 & 2 \\ 0 & 8 \end{pmatrix}.
(b)
4 marks
Write Minors and Cofactors of the determinant ∣2−403∣\begin{vmatrix} 2 & -4 \\ 0 & 3 \end{vmatrix}.
(c)
7 marksSame type asked in 2 of 7 papers
Find the inverse of the matrix (123024005)\begin{pmatrix} 1 & 2 & 3 \\ 0 & 2 & 4 \\ 0 & 0 & 5 \end{pmatrix}.

Also asked in Summer 2026 Q5c OR

(a)
3 marksSame type asked in 6 of 7 papers
Compute the products [1−223](123231)\begin{bmatrix} 1 & -2 \\ 2 & 3 \end{bmatrix} \begin{pmatrix} 1 & 2 & 3 \\ 2 & 3 & 1 \end{pmatrix}.

Also asked in Summer 2026 Q2b, Winter 2024 Q3b OR, Summer 2024 Q2b, Winter 2023 Q2b, Summer 2023 Q1b

(b)
4 marks
If A and B are symmetric matrices, prove that AB−BAAB - BA is a skew symmetric matrix.
(c)
7 marksSame type asked in 2 of 7 papers
Solve system of linear equation, using matrix method: 4x−3y=34x - 3y = 3 and 3x−5y=73x - 5y = 7.

Also asked in Winter 2023 Q1b

Q.5

14 Marks
(a)
3 marksSame type asked in 6 of 7 papers
Find the degree of the differential equations:
1y′′+sin⁡x−5=0y'' + \sin x - 5 = 0
2dydx=sin⁡(2x−8)\frac{dy}{dx} = \sin(2x - 8)

Also asked in Summer 2026 Q4a, Winter 2024 Q4a, Summer 2024 Q4a, Winter 2023 Q4a, Summer 2023 Q4b

(b)
4 marksSame type asked in 2 of 7 papers
Find the solution of the differential equation x5dydx=−y5x^5 \frac{dy}{dx} = -y^5.

Also asked in Summer 2025 Q3c OR

(c)
7 marksSame type asked in 3 of 7 papers
Find a particular solution of the differential equation dydx+ycot⁡x=4xcosec⁡x\frac{dy}{dx} + y\cot x = 4x\operatorname{cosec} x given that y=0y = 0 when x=0x = 0.

Also asked in Winter 2024 Q4b, Winter 2024 Q4b OR, Winter 2023 Q4b

(a)
3 marks
Is y=x2+2x+cy = x^2 + 2x + c a solution of y′−2x−2=0y' - 2x - 2 = 0?
(b)
4 marksSame type asked in 2 of 7 papers
Find the particular solution of the differential equation: x(x2−1)dydx=1x(x^2 - 1)\frac{dy}{dx} = 1; y=0,x=2y = 0, x = 2.

Also asked in Summer 2025 Q3c OR

(c)
7 marksSame type asked in 3 of 7 papers
Find the solution of the differential equation dydx+2ytan⁡x=sin⁡x\frac{dy}{dx} + 2y\tan x = \sin x when y=0,x=0y = 0, x = 0.

Also asked in Winter 2024 Q4b, Winter 2024 Q4b OR, Winter 2023 Q4b

More Remedial Mathematics papers

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

Summer 202670 marks · 5 questions
Summer 202570 marks · 5 questions
Winter 202470 marks · 5 questions
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 Remedial Mathematics (Remedial Maths) (Winter 2025, 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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