Gujarat Technological UniversitySummer 2023 examination

GTU 3110019 Remedial Mathematics (Remedial Maths) Summer 2023 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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4 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 marksSame type asked in 4 of 7 papers
Evaluate the determinant A=∣124−130410∣A = \begin{vmatrix} 1 & 2 & 4 \\ -1 & 3 & 0 \\ 4 & 1 & 0 \end{vmatrix}.

Also asked in Summer 2026 Q2a, Summer 2025 Q5a, Winter 2023 Q2a

(b)
4 marksSame type asked in 6 of 7 papers
Find A⋅BA \cdot B if A=[6923]A = \begin{bmatrix} 6 & 9 \\ 2 & 3 \end{bmatrix} and B=[260798]B = \begin{bmatrix} 2 & 6 & 0 \\ 7 & 9 & 8 \end{bmatrix}.

Also asked in Summer 2026 Q2b, Winter 2025 Q4a OR, Winter 2024 Q3b OR, Summer 2024 Q2b, Winter 2023 Q2b

(c)
7 marks
1If [x+3z+42y−7−6a−10b−3−210]=[063y−2−6−32c+22b+4−210]\begin{bmatrix} x+3 & z+4 & 2y-7 \\ -6 & a-1 & 0 \\ b-3 & -21 & 0 \end{bmatrix} = \begin{bmatrix} 0 & 6 & 3y-2 \\ -6 & -3 & 2c+2 \\ 2b+4 & -21 & 0 \end{bmatrix}, find a,b,c,x,ya, b, c, x, y and zz.
2Solve the following system of equations by matrix method: 2x+5y=12x + 5y = 1 3x+2y=73x + 2y = 7

Q.2

14 Marks
(a)
3 marksSame type asked in 2 of 7 papers
Find distance of the point (3,−5)(3, -5) from the line 3x−4y−26=03x - 4y - 26 = 0.

Also asked in Winter 2025 Q1c

(b)
4 marks
If 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.
(c)
7 marks
1Define modulus function and greatest integer function.
2Deduce trigonometric identity sin⁡3x=3sin⁡x−4sin⁡3x\sin 3x = 3\sin x - 4\sin^3 x.
(c)
7 marks
1Define exponential function and logarithmic function.
2Deduce trigonometric identity sin⁡2x=2tan⁡x1+tan⁡2x\sin 2x = \frac{2\tan x}{1+\tan^2 x}, x≠nπ+π2,n∈Zx \neq n\pi + \frac{\pi}{2}, n \in \mathbb{Z}.

Q.3

14 Marks
(a)
3 marksSame type asked in 3 of 7 papers
Evaluate: lim⁡x→2(x3−4x2+4xx2−4)\lim_{x \to 2} \left(\frac{x^3 - 4x^2 + 4x}{x^2 - 4}\right).

Also asked in Summer 2025 Q3a OR, Winter 2024 Q1a, Winter 2024 Q4a OR

(b)
4 marks
Find dydx\frac{dy}{dx} if y=x5−cos⁡xsin⁡xy = \frac{x^5 - \cos x}{\sin x}.
(c)
7 marks
1Find derivative of y=sin⁡(x2)y = \sin(x^2).
2If y=3e2x+2e3xy = 3e^{2x} + 2e^{3x}, prove that d2ydx2−5dydx+6y=0\frac{d^2 y}{dx^2} - 5\frac{dy}{dx} + 6y = 0.
(a)
3 marksSame type asked in 3 of 7 papers
Evaluate: lim⁡x→0(1−cos⁡xx)\lim_{x \to 0} \left(\frac{1 - \cos x}{x}\right).

Also asked in Winter 2025 Q2c OR, Summer 2025 Q3a

(b)
4 marks
Find dydx\frac{dy}{dx} if x=acos⁡θ,y=asin⁡θx = a\cos\theta, y = a\sin\theta.
(c)
7 marks
1Find derivative of y=cos⁡−1(ex)y = \cos^{-1}(e^x).
2Find d2ydx2\frac{d^2 y}{dx^2} if y=x3+tan⁡xy = x^3 + \tan x.

Q.4

14 Marks
(a)
3 marksSame type asked in 3 of 7 papers
Find all points of discontinuity for the function given by f(x)={x+2x<10x=1x−2x>1f(x) = \begin{cases} x+2 & x < 1 \\ 0 & x = 1 \\ x-2 & x > 1 \end{cases}.

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

(b)
4 marksSame type asked in 6 of 7 papers
Find order and degree of following differential equations:
1xyd2ydx2+x(dydx)2−ydydx=0xy \frac{d^2 y}{dx^2} + x\left(\frac{dy}{dx}\right)^2 - y\frac{dy}{dx} = 0
2(d3ydx3)2+(d2ydx2)3+(dydx)4+y5=0\left(\frac{d^3 y}{dx^3}\right)^2 + \left(\frac{d^2 y}{dx^2}\right)^3 + \left(\frac{dy}{dx}\right)^4 + y^5 = 0

Also asked in Summer 2026 Q4a, Winter 2025 Q5a, Winter 2024 Q4a, Summer 2024 Q4a, Winter 2023 Q4a

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

Also asked in Summer 2024 Q4c, Winter 2023 Q4c

(a)
3 marksSame type asked in 3 of 7 papers
Discuss the continuity of f(x)={x3+1x≠01x=0f(x) = \begin{cases} x^3 + 1 & x \neq 0 \\ 1 & x = 0 \end{cases} at x=0x = 0.

Also asked in Summer 2026 Q4a OR, Winter 2025 Q3a

(b)
4 marks

Find dydx\frac{dy}{dx} if:

1y+sin⁡y=cos⁡xy + \sin y = \cos x
2x−y=πx - y = \pi
(c)
7 marksAsked in 3 of 7 papers
Solve the following:
1x dy=(2x2+1) dxx \, dy = (2x^2 + 1) \, dx
2xdydx+2y=x2x \frac{dy}{dx} + 2y = x^2 (x≠0)(x \neq 0).

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

Q.5

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

Also asked in Summer 2024 Q5a OR, Winter 2023 Q5a OR

(b)
4 marks
Find the following integrals:
1∫x3−1x2 dx\int \frac{x^3 - 1}{x^2} \, dx
2∫(x2/3+1) dx\int (x^{2/3} + 1) \, dx
(c)
7 marks
Evaluate followings:
1∫121(x+1)(x+2) dx\int_1^2 \frac{1}{(x+1)(x+2)} \, dx
2∫12tan⁡−1x1+x2 dx\int_1^2 \frac{\tan^{-1} x}{1+x^2} \, dx.
(a)
3 marks
Find ∫1−sin⁡xcos⁡2x dx\int \frac{1 - \sin x}{\cos^2 x} \, dx.
(b)
4 marks
Find ∫1x2−6x+13 dx\int \frac{1}{x^2 - 6x + 13} \, dx.
(c)
7 marksAsked in 2 of 7 papers
Find ∫x2+x+1(x+1)(x2+1) dx\int \frac{x^2 + x + 1}{(x+1)(x^2 + 1)} \, dx.

Also asked in Summer 2024 Q5c 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
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) (Summer 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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