Gujarat Technological UniversityWinter 2023 examination

GTU 3110019 Remedial Mathematics (Remedial Maths) Winter 2023 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 2:30 PM – 5:00 PM
Questions
5 with internal choice
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14 of 25 questions on this paper were also asked in other years. 8 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 Summer 2026 Q1a

(b)
4 marksSame type asked in 2 of 7 papers
Solve the following system by matrix method:

2x+5y=12x + 5y = 1 3x+2y=73x + 2y = 7

Also asked in Winter 2025 Q4c OR

(c)
7 marks
iFind dydx\frac{dy}{dx} if y=x5−cos⁡xsin⁡xy = \frac{x^5 - \cos x}{\sin x}. (3 marks)
iiFind 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}. (4 marks)

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 2026 Q2a, Summer 2025 Q5a, 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 Summer 2026 Q2b, Winter 2025 Q4a OR, Winter 2024 Q3b OR, Summer 2024 Q2b, Summer 2023 Q1b

(c)
7 marks
iFind dydx\frac{dy}{dx}, if yx+xy+xx=100y^x + x^y + x^x = 100. (5 marks)
iiDerive sin⁡2x=2sin⁡xcos⁡x\sin 2x = 2\sin x \cos x. (2 marks)
(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. (5 marks)
iiDerive the trigonometry identity: cos⁡2x=cos⁡2x−sin⁡2x\cos 2x = \cos^2 x - \sin^2 x. (2 marks)

Also asked in Summer 2026 Q2c OR, Summer 2024 Q2c OR

Q.3

14 Marks
(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 2026 Q3a OR, Summer 2024 Q3a

(b)
4 marksAsked in 2 of 7 papers

Find the distance (i) of the point (3,−1)(3, -1) from the line 3x−4y−26=03x - 4y - 26 = 0.

iibetween two parallel lines: 15x+8y−34=015x + 8y - 34 = 0 and 15x+8y+31=015x + 8y + 31 = 0.

Also asked in Summer 2024 Q3b

(c)
7 marksAsked in 2 of 7 papers
iDefine the matrices:(a)Identity matrix(b)Scalar matrix(c)Diagonal matrix. (3 marks)
iiFind 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. (4 marks)

Also asked in Summer 2024 Q3c

(a)
3 marksAsked in 2 of 7 papers
State the product rule of derivative and find the derivative of f(x)=x+3x2+5x3+7x4+9x5f(x) = x + 3x^2 + 5x^3 + 7x^4 + 9x^5 at x=1x = 1.

Also asked in Summer 2024 Q3a OR

(b)
4 marksAsked in 2 of 7 papers
Find the point on the x-axis which is at equidistance from the point (7,6)(7, 6) and (3,4)(3, 4).

Also asked in Summer 2024 Q3b OR

(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. (3 marks)
iiIf the angle between two lines is π4\frac{\pi}{4} and slope of one of the lines is 12\frac{1}{2}, find the slope of the other line. (4 marks)

Also asked in Summer 2026 Q3c, Summer 2024 Q3c OR

Q.4

14 Marks
(a)
3 marksSame type asked in 6 of 7 papers
Determine the order of the following differential equations:
id3ydx3+4(d2ydx2)3+2y=0\frac{d^3 y}{dx^3} + 4\left(\frac{d^2 y}{dx^2}\right)^3 + 2y = 0
ii(d4ydx4)2+(d2ydx2)+sin⁡y=0\left(\frac{d^4 y}{dx^4}\right)^2 + \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 Summer 2026 Q4a, Winter 2025 Q5a, Winter 2024 Q4a, Summer 2024 Q4a, Summer 2023 Q4b

(b)
4 marksSame type asked in 3 of 7 papers
Solve the differential equation xdydx+2y=x2x\frac{dy}{dx} + 2y = x^2.

Also asked in Winter 2025 Q5c, Winter 2025 Q5c OR, Winter 2024 Q4b, Winter 2024 Q4b OR

(c)
7 marksAsked in 3 of 7 papers
Solve the following equations:
idydx=1+y21+x2\frac{dy}{dx} = \frac{1 + y^2}{1 + x^2} (3 marks)
iixcos⁡(yx)dydx=ycos⁡(yx)+xx\cos\left(\frac{y}{x}\right)\frac{dy}{dx} = y\cos\left(\frac{y}{x}\right) + x (4 marks)

Also asked in Summer 2024 Q4c, Summer 2023 Q4c

(a)
3 marksSame type asked in 3 of 7 papers
Find all points of discontinuity for the function given by f(x)={x+2x<12x=1x−2x>1f(x) = \begin{cases} x+2 & x < 1 \\ 2 & x = 1 \\ x-2 & x > 1 \end{cases}.

Also asked in Summer 2024 Q4a OR, Summer 2023 Q4a

(b)
4 marksSame type asked in 3 of 7 papers
If y=xcos⁡xy = x\cos x then find d2ydx2\frac{d^2 y}{dx^2}.

Also asked in Winter 2025 Q3b, Summer 2024 Q4b OR

(c)
7 marksAsked in 3 of 7 papers
Solve the following equations:
ix dy=(2x2+1) dxx \, dy = (2x^2 + 1) \, dx (3 marks)
iixdydx+2y=x2x\frac{dy}{dx} + 2y = x^2 (x≠0)(x \neq 0) (4 marks)

Also asked in Summer 2024 Q4c OR, Summer 2023 Q4c OR

Q.5

14 Marks
(a)
3 marksAsked in 2 of 7 papers
Find ∫etan⁡−1x1+x2 dx\int \frac{e^{\tan^{-1} x}}{1 + x^2} \, dx.

Also asked in Winter 2024 Q5b OR

(b)
4 marksAsked in 2 of 7 papers
Evaluate the integrals:
i∫dxx2−81\int \frac{dx}{x^2 - 81}
ii∫x2−1x dx\int \frac{x^2 - 1}{x} \, dx.

Also asked in Summer 2024 Q5b

(c)
7 marksAsked in 2 of 7 papers
iEvaluate ∫121(x+1)(x+2) dx\int_1^2 \frac{1}{(x+1)(x+2)} \, dx (3 marks)
iiFind ∫1x2−6x+13 dx\int \frac{1}{x^2 - 6x + 13} \, dx (4 marks)

Also asked in Summer 2024 Q5c

(a)
3 marksAsked in 3 of 7 papers
State the integration by parts and find ∫xex dx\int x e^x \, dx.

Also asked in Summer 2024 Q5a OR, Summer 2023 Q5a

(b)
4 marksAsked in 2 of 7 papers
Find ∫sin⁡x(1+cos⁡x)2 dx\int \frac{\sin x}{(1 + \cos x)^2} \, dx.

Also asked in Summer 2024 Q5b OR

(c)
7 marks
iEvaluate ∫0π/2cos⁡x⋅esin⁡x dx\int_0^{\pi/2} \cos x \cdot e^{\sin x} \, dx (3 marks)
iiFind ∫2xx2+3x+2 dx\int \frac{2x}{x^2 + 3x + 2} \, dx (4 marks)

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
Summer 202570 marks · 5 questions
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 Remedial Mathematics (Remedial Maths) (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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