Gujarat Technological UniversityWinter 2024 examination

GTU 3110019 Remedial Mathematics (Remedial Maths) Winter 2024 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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2 of 25 questions on this paper were also asked in other years. 11 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 3 of 7 papers
Find lim⁡x→2(x2−6x+8x2−4)\lim_{x \to 2} \left(\frac{x^2 - 6x + 8}{x^2 - 4}\right).

Also asked in Summer 2025 Q3a OR, Summer 2023 Q3a

(b)
4 marks

Find dydx\frac{dy}{dx} for the following:

1y=ecot⁡xy = e^{\cot x}
2y=log⁡(sin⁡x2)y = \log(\sin x^2)
(c)
7 marks
Show that the function y=e3x+e2xy = e^{3x} + e^{2x} is a solution of differential equation d2ydx2−5dydx+6y=0\frac{d^2 y}{dx^2} - 5\frac{dy}{dx} + 6y = 0.

Q.2

14 Marks
(a)
3 marksSame type asked in 3 of 7 papers
Find the equation of a line passing through the points (1,−3)(1, -3) & (5,6)(5, 6).

Also asked in Winter 2025 Q1b, Summer 2025 Q1b

(b)
4 marksSame type asked in 3 of 7 papers
Find the equation of a line passing through (−3,5)(-3, 5) and perpendicular to the line through the points (2,5)(2, 5) and (−3,6)(-3, 6).

Also asked in Winter 2025 Q1b, Summer 2025 Q1b

(c)
7 marks
1If a line passing through the points (−2,5)(-2, 5) and (4,9)(4, 9) is perpendicular to the line passing through the points (6,8)(6, 8) and (x,20)(x, 20) then find the value of xx. (3 marks)
2Find the angle between two lines 3x−y+5=03x - y + 5 = 0 and 2x−4y+11=02x - 4y + 11 = 0. (4 marks)
(c)
7 marks
1Represent cos⁡(x+y)\cos(x+y) in terms of sine and cosine and hence prove that cos⁡(2x)=cos⁡2x−sin⁡2x\cos(2x) = \cos^2 x - \sin^2 x. (3 marks)
2Find the distance of the point (5,2)(5, 2) from the line 3x−4y+13=03x - 4y + 13 = 0. (4 marks)

Q.3

14 Marks
(a)
3 marksSame type asked in 2 of 7 papers
Find the value of xx, such that ∣x32x∣=∣14435∣\begin{vmatrix} x & 3 \\ 2 & x \end{vmatrix} = \begin{vmatrix} 14 & 4 \\ 3 & 5 \end{vmatrix}.

Also asked in Summer 2025 Q5a OR

(b)
4 marks
If A=[3124]A = \begin{bmatrix} 3 & 1 \\ 2 & 4 \end{bmatrix} & B=[−1205]B = \begin{bmatrix} -1 & 2 \\ 0 & 5 \end{bmatrix} then verify that AB≠BAAB \neq BA.
(c)
7 marksSame type asked in 2 of 7 papers
Solve the following system of linear equations:

x+y+2z=8x + y + 2z = 8 −x−2y+3z=1-x - 2y + 3z = 1 3x−7y+4z=103x - 7y + 4z = 10

Also asked in Summer 2025 Q5c, Summer 2025 Q5c OR

(a)
3 marksAsked in 2 of 7 papers
Define (a) Identity matrix (b) Scalar matrix and (c) Diagonal matrix.

Also asked in Summer 2026 Q3a

(b)
4 marksSame type asked in 6 of 7 papers
If A=[3124]A = \begin{bmatrix} 3 & 1 \\ 2 & 4 \end{bmatrix} & B=[−123054]B = \begin{bmatrix} -1 & 2 & 3 \\ 0 & 5 & 4 \end{bmatrix} then find A⋅BA \cdot B.

Also asked in Summer 2026 Q2b, Winter 2025 Q4a OR, Summer 2024 Q2b, Winter 2023 Q2b, Summer 2023 Q1b

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

x+2y−z=1x + 2y - z = 1 x+y+2z=9x + y + 2z = 9 2x+y−z=22x + y - z = 2

Also asked in Summer 2025 Q5c, Summer 2025 Q5c OR

Q.4

14 Marks
(a)
3 marksSame type asked in 6 of 7 papers
Determine the order and degree of following differential equations:
1d2ydx2−3(dydx)3+4y=0\frac{d^2 y}{dx^2} - 3\left(\frac{dy}{dx}\right)^3 + 4y = 0
2(d2ydx2)3−(d3ydx3)13−y=0\left(\frac{d^2 y}{dx^2}\right)^3 - \left(\frac{d^3 y}{dx^3}\right)^{\frac{1}{3}} - y = 0

Also asked in Summer 2026 Q4a, Winter 2025 Q5a, Summer 2024 Q4a, Winter 2023 Q4a, Summer 2023 Q4b

(b)
4 marksSame type asked in 3 of 7 papers
Solve: dydx+yx=x2\frac{dy}{dx} + \frac{y}{x} = x^2.

Also asked in Winter 2025 Q5c, Winter 2025 Q5c OR, Winter 2023 Q4b

(c)
7 marks
1Solve: x2dy=y(x2+x+1)dxx^2 dy = y(x^2 + x + 1)dx. (3 marks)
2If y=xe3xy = x e^{3x} find d2ydx2\frac{d^2 y}{dx^2}. (4 marks)
(a)
3 marksSame type asked in 3 of 7 papers
Evaluate: lim⁡x→1(x100−1x−1)\lim_{x \to 1} \left(\frac{x^{100} - 1}{x - 1}\right).

Also asked in Summer 2025 Q3a OR, Summer 2023 Q3a

(b)
4 marksSame type asked in 3 of 7 papers
Solve: dydx+3y=e−x\frac{dy}{dx} + 3y = e^{-x}.

Also asked in Winter 2025 Q5c, Winter 2025 Q5c OR, Winter 2023 Q4b

(c)
7 marks
1If y=exx2+1y = \frac{e^x}{x^2 + 1} then find dydx\frac{dy}{dx}. (3 marks)
2Solve: dydx=1+y21+x2\frac{dy}{dx} = \frac{1 + y^2}{1 + x^2}. (4 marks)

Q.5

14 Marks
(a)
3 marks
Evaluate: ∫(x2−7x+10x) dx\int \left(\frac{x^2 - 7x + 10}{x}\right) \, dx.
(b)
4 marks
Evaluate: ∫(e2x1+e2x) dx\int \left(\frac{e^{2x}}{1 + e^{2x}}\right) \, dx.
(c)
7 marks
Evaluate the following integrations:
1∫(2e3x+sin⁡2x+3) dx\int (2e^{3x} + \sin 2x + 3) \, dx (3 marks)
2∫021(x+1)(x+2) dx\int_0^2 \frac{1}{(x+1)(x+2)} \, dx (4 marks)
(a)
3 marks
Evaluate: ∫(1x3+1x2) dx\int \left(\frac{1}{x^3} + \frac{1}{x^2}\right) \, dx.
(b)
4 marksAsked in 2 of 7 papers
Evaluate: ∫(etan⁡−1x1+x2) dx\int \left(\frac{e^{\tan^{-1} x}}{1 + x^2}\right) \, dx.

Also asked in Winter 2023 Q5a

(c)
7 marks
Evaluate the integration:
1∫sin⁡3xcos⁡2x dx\int \sin 3x \cos 2x \, dx (3 marks)
2∫23(1x2−1) dx\int_2^3 \left(\frac{1}{x^2 - 1}\right) \, 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
Summer 202470 marks · 5 questions

Other Semester 1 subjects

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3110001
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3110002
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3110004
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About this paper

Official Gujarat Technological University (GTU) examination paper for Remedial Mathematics (Remedial Maths) (Winter 2024, 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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