Gujarat Technological UniversitySummer 2025 examination

GTU 3110019 Remedial Mathematics (Remedial Maths) Summer 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 10:30 AM – 1:00 PM
Questions
5 with internal choice
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1 of 25 questions on this paper were also asked in other years. 10 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
Find the slope of the line passing through the points (3,−2)(3, -2) and (3,4)(3, 4).

Also asked in Winter 2025 Q1a

(b)
4 marksSame type asked in 3 of 7 papers
Find the equation of line passing through (−4,3)(-4, 3) with slope -5.

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

(c)
7 marks
1Find the distance between the parallel lines 3x−4y+7=03x - 4y + 7 = 0 and 3x−4y+5=03x - 4y + 5 = 0. (3 marks)
2Find the angles between the lines 3x+y=1\sqrt{3}x + y = 1 and x+3y=1x + \sqrt{3}y = 1. (4 marks)

Q.2

14 Marks
(a)
3 marks
State domain and range of the function f(x)=cos⁡xf(x) = \cos x.
(b)
4 marks
Deduce trigonometric identity cos⁡2x=1−tan⁡2x1+tan⁡2x\cos 2x = \frac{1 - \tan^2 x}{1 + \tan^2 x}.
(c)
7 marks
1Find d2ydx2\frac{d^2 y}{dx^2} if y=cos⁡2xy = \cos 2x. (3 marks)
2Find derivative of cos⁡x1+sin⁡x\frac{\cos x}{1 + \sin x}. (4 marks)
(c)
7 marks
1Find derivative of y=sin⁡xcos⁡xy = \sin x \cos x. (3 marks)
2Find dydx\frac{dy}{dx} if y=x1+tan⁡xy = \frac{x}{1 + \tan x}. (4 marks)

Q.3

14 Marks
(a)
3 marksSame type asked in 3 of 7 papers
Evaluate lim⁡x→0sin⁡4xsin⁡2x\lim_{x \to 0} \frac{\sin 4x}{\sin 2x}.

Also asked in Winter 2025 Q2c OR, Summer 2023 Q3a OR

(b)
4 marks
If y=sin⁡−1xy = \sin^{-1} x, show that (1−x2)d2ydx2−xdydx=0(1 - x^2)\frac{d^2 y}{dx^2} - x\frac{dy}{dx} = 0.
(c)
7 marks
Find the solution of the following:
1dydx=x+12−y\frac{dy}{dx} = \frac{x+1}{2-y}; (y≠2)(y \neq 2) (3 marks)
2dydx+3y=e−3x\frac{dy}{dx} + 3y = e^{-3x} (4 marks)
(a)
3 marksSame type asked in 3 of 7 papers
Evaluate lim⁡x→2x3−2x2x2−5x+6\lim_{x \to 2} \frac{x^3 - 2x^2}{x^2 - 5x + 6}.

Also asked in Winter 2024 Q1a, Winter 2024 Q4a OR, Summer 2023 Q3a

(b)
4 marks
Find dydx\frac{dy}{dx} if x=cos⁡tx = \cos t and y=cos⁡2ty = \cos 2t.
(c)
7 marksSame type asked in 2 of 7 papers
Solve the following:
1xydydx=(x+2)(y+2)xy \frac{dy}{dx} = (x + 2)(y + 2) (3 marks)
2dydx=x+xy\frac{dy}{dx} = x + xy (4 marks)

Also asked in Winter 2025 Q5b, Winter 2025 Q5b OR

Q.4

14 Marks
(a)
3 marks
Find ∫(1+log⁡x)2x dx\int \frac{(1 + \log x)^2}{x} \, dx.
(b)
4 marks
Find ∫dxx2+2x+2\int \frac{dx}{x^2 + 2x + 2}.
(c)
7 marks
Evaluate the following:
1∫04(x+e2x) dx\int_0^4 (x + e^{2x}) \, dx (3 marks)
2∫0π/4(2sec⁡2x+x3+2) dx\int_0^{\pi/4} (2\sec^2 x + x^3 + 2) \, dx (4 marks)
(a)
3 marks
Find ∫sin⁡−1x1−x2 dx\int \frac{\sin^{-1} x}{\sqrt{1 - x^2}} \, dx.
(b)
4 marksAsked in 2 of 7 papers
Find ∫x(x+1)(x+2) dx\int \frac{x}{(x+1)(x+2)} \, dx.

Also asked in Winter 2025 Q3c OR

(c)
7 marks
Evaluate the following:
1∫01xex2 dx\int_0^1 x e^{x^2} \, dx (3 marks)
2∫0πsin⁡3x dx\int_0^\pi \sin^3 x \, dx (4 marks)

Q.5

14 Marks
(a)
3 marksSame type asked in 4 of 7 papers
Evaluate the determinant ∣3−1−200−13−50∣\begin{vmatrix} 3 & -1 & -2 \\ 0 & 0 & -1 \\ 3 & -5 & 0 \end{vmatrix}.

Also asked in Summer 2026 Q2a, Winter 2023 Q2a, Summer 2023 Q1a

(b)
4 marksSame type asked in 2 of 7 papers
If A=[31−12]A = \begin{bmatrix} 3 & 1 \\ -1 & 2 \end{bmatrix}, Show that A2−5A+7I=0A^2 - 5A + 7I = 0. Hence find A−1A^{-1}.

Also asked in Summer 2026 Q5c

(c)
7 marksSame type asked in 2 of 7 papers
Solve the system of linear equations:

3x−2y+3z=83x - 2y + 3z = 8 2x+y−z=12x + y - z = 1 4x−3y+2z=44x - 3y + 2z = 4

Also asked in Winter 2024 Q3c, Winter 2024 Q3c OR

(a)
3 marksSame type asked in 2 of 7 papers
Find the value of xx, if ∣x218x∣=∣62186∣\begin{vmatrix} x & 2 \\ 18 & x \end{vmatrix} = \begin{vmatrix} 6 & 2 \\ 18 & 6 \end{vmatrix}.

Also asked in Winter 2024 Q3a

(b)
4 marks
By using the properties of determinants prove ∣1aa21bb21cc2∣=(a−b)(b−c)(c−a)\begin{vmatrix} 1 & a & a^2 \\ 1 & b & b^2 \\ 1 & c & c^2 \end{vmatrix} = (a-b)(b-c)(c-a).
(c)
7 marksSame type asked in 2 of 7 papers
Solve the system of linear equations:

x−y+z=4x - y + z = 4 2x+y−3z=02x + y - 3z = 0 x+y+z=2x + y + z = 2

Also asked in Winter 2024 Q3c, Winter 2024 Q3c OR

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
Winter 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) (Summer 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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