Gujarat Technological UniversitySummer 2026 examination

GTU 3110019 Remedial Mathematics (Remedial Maths) Summer 2026 Question Paper & PDF

B.E. · Common Engineering · Semester 1 · 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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6 of 25 questions on this paper were also asked in other years. 7 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 marksAsked in 2 of 7 papers
Define exponential function and logarithmic function.

Also asked in Winter 2023 Q1a

(b)
4 marksAsked in 2 of 7 papers
Find the limits: (a) lim⁡x→1x2+1x+99\lim_{x \to 1} \frac{x^2 + 1}{x + 99} (b) lim⁡x→1x15−1x10−1\lim_{x \to 1} \frac{x^{15} - 1}{x^{10} - 1}.

Also asked in Summer 2024 Q1b

(c)
7 marks
Solve (x4+y4)dx−xy3dy=0(x^4 + y^4)dx - xy^3 dy = 0.

Q.2

14 Marks
(a)
3 marksSame type asked in 4 of 7 papers
Evaluate the determinant A=∣1−2302401−1∣A = \begin{vmatrix} 1 & -2 & 3 \\ 0 & 2 & 4 \\ 0 & 1 & -1 \end{vmatrix}.

Also asked in Summer 2025 Q5a, Winter 2023 Q2a, Summer 2023 Q1a

(b)
4 marksSame type asked in 6 of 7 papers
Find A⋅BA \cdot B if A=[58−23]A = \begin{bmatrix} 5 & 8 \\ -2 & 3 \end{bmatrix} and B=[1−14320]B = \begin{bmatrix} 1 & -1 & 4 \\ 3 & 2 & 0 \end{bmatrix}.

Also asked in Winter 2025 Q4a OR, Winter 2024 Q3b OR, Summer 2024 Q2b, Winter 2023 Q2b, Summer 2023 Q1b

(c)
7 marksAsked in 2 of 7 papers
iSolve dydx+2ytan⁡x=sin⁡x\frac{dy}{dx} + 2y\tan x = \sin x.
iiDerive sin⁡2x=2sin⁡xcos⁡x\sin 2x = 2\sin x \cos x.

Also asked in Summer 2024 Q2c

(c)
7 marksAsked in 3 of 7 papers
iFind dydx\frac{dy}{dx}, if x=acos⁡θ,y=asin⁡θx = a\cos\theta, y = a\sin\theta.
iiDerive the trigonometry identity: cos⁡2x=cos⁡2x−sin⁡2x\cos 2x = \cos^2 x - \sin^2 x.

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

Q.3

14 Marks
(a)
3 marksAsked in 2 of 7 papers
Define the matrices: (a) Identity matrix (b) Scalar matrix (c) Diagonal matrix.

Also asked in Winter 2024 Q3a OR

(b)
4 marks
Find the coordinates of the point which divides the line segment joining the points (6,3)(6, 3) and (4,−5)(4, -5) in the ratio 3:23:2 (i) internally and (ii) externally.
(c)
7 marksSame type asked in 3 of 7 papers
iIf ∣2451∣=∣2x46x∣\begin{vmatrix} 2 & 4 \\ 5 & 1 \end{vmatrix} = \begin{vmatrix} 2x & 4 \\ 6 & x \end{vmatrix} then find the value of xx.
iiIf the angle between two lines is π4\frac{\pi}{4} and slope of one of the lines is 14\frac{1}{4}, find the slope of the other line.

Also asked in Summer 2024 Q3c OR, Winter 2023 Q3c OR

(a)
3 marksAsked in 3 of 7 papers
State the Quotient (division) rule of derivative and compute the derivative of f(x)=sin⁡xcos⁡xf(x) = \frac{\sin x}{\cos x}.

Also asked in Summer 2024 Q3a, Winter 2023 Q3a

(b)
4 marks
A quadrilateral has the vertices at the points (−4,2),(2,6),(8,5)(-4, 2), (2, 6), (8, 5) and (9,−7)(9, -7). Show that the mid points of the sides of this quadrilateral are the vertices of a parallelogram.
(c)
7 marks
iFind the angle between the lines y−3x−5=0y - \sqrt{3}x - 5 = 0 and 3y−x+6=0\sqrt{3}y - x + 6 = 0.
iiSolve the following system of linear equations by matrix method: x+y+2z=8x + y + 2z = 8 −x−2y+3z=1-x - 2y + 3z = 1 3x−7y+4z=103x - 7y + 4z = 10

Q.4

14 Marks
(a)
3 marksSame type asked in 6 of 7 papers
Determine the order of the following differential equations:
i(d3ydx3)3+5(d2ydx2)4+2y=0\left(\frac{d^3 y}{dx^3}\right)^3 + 5\left(\frac{d^2 y}{dx^2}\right)^4 + 2y = 0
ii(d4ydx4)4+(d2ydx2)+sin⁡y=0\left(\frac{d^4 y}{dx^4}\right)^4 + \left(\frac{d^2 y}{dx^2}\right) + \sin y = 0
iii(y′′)2+3(y′)5−y=0(y'')^2 + 3(y')^5 - y = 0

Also asked in Winter 2025 Q5a, Winter 2024 Q4a, Summer 2024 Q4a, Winter 2023 Q4a, Summer 2023 Q4b

(b)
4 marks
If y=(cos⁡x)log⁡xy = (\cos x)^{\log x} then find dydx\frac{dy}{dx}.
(c)
7 marks
Solve the differential equation by method of separation of variables: ∂u∂x+∂u∂y=2(x+y)u\frac{\partial u}{\partial x} + \frac{\partial u}{\partial y} = 2(x+y)u.
(a)
3 marksSame type asked in 3 of 7 papers
Test the function for continuity at x=0x = 0, where f(x)={xsin⁡1xx≠00x=0f(x) = \begin{cases} x \sin\frac{1}{x} & x \neq 0 \\ 0 & x = 0 \end{cases}.

Also asked in Winter 2025 Q3a, Summer 2023 Q4a OR

(b)
4 marks
Find dydx\frac{dy}{dx} of the following function: y=1+cos⁡xsin⁡xy = \frac{1 + \cos x}{\sin x}.
(c)
7 marks
Solve the differential equation by method of separation of variables: ∂u∂x=4∂u∂y\frac{\partial u}{\partial x} = 4\frac{\partial u}{\partial y}, given that u(0,y)=8e−3yu(0, y) = 8e^{-3y}.

Q.5

14 Marks
(a)
3 marks
Evaluate ∫x4tan⁡x5 dx\int x^4 \tan x^5 \, dx.
(b)
4 marks
Evaluate by partial fractions: ∫x+43+2x−x2 dx\int \frac{x+4}{3 + 2x - x^2} \, dx.
(c)
7 marksSame type asked in 2 of 7 papers
Show that the matrix A=[2−11−12−11−12]A = \begin{bmatrix} 2 & -1 & 1 \\ -1 & 2 & -1 \\ 1 & -1 & 2 \end{bmatrix} satisfies the equation A3−6A2+9A−4I=0A^3 - 6A^2 + 9A - 4I = 0. Hence find A−1A^{-1}.

Also asked in Summer 2025 Q5b

(a)
3 marks
Evaluate ∫sin⁡xsin⁡(x−a) dx\int \frac{\sin x}{\sin(x-a)} \, dx.
(b)
4 marks
Evaluate by partial fractions: ∫x(2x+1)(x2+1) dx\int \frac{x}{(2x+1)(x^2 + 1)} \, dx.
(c)
7 marksSame type asked in 2 of 7 papers
Find the inverse of the matrix A=[234431124]A = \begin{bmatrix} 2 & 3 & 4 \\ 4 & 3 & 1 \\ 1 & 2 & 4 \end{bmatrix}.

Also asked in Winter 2025 Q4c

More Remedial Mathematics papers

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

Winter 202570 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) (Summer 2026, 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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