GTU · First Year Common · Semesters 1 and 2

GTU 3110019 Remedial Mathematics (Remedial Maths) Old Question Papers PDF

Official Gujarat Technological University (GTU) old question papers PDF (Regular & Remedial) and step-by-step solved questions for Remedial Mathematics (Remedial Maths) across 2023 – 2026 examinations.

7 papers, 2023 – 202670 marks23 to pass2.5 hours
38 questions GTU asked more than onceAsked 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}.See list

Exam papers

Summer 20265 questions · 70 marks
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Winter 20255 questions · 70 marks
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Summer 20255 questions · 70 marks
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Winter 20245 questions · 70 marks
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Summer 20245 questions · 70 marks
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Winter 20235 questions · 70 marks
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Summer 20235 questions · 70 marks
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Most repeated questions

38 questions GTU set in two or more of 7 papers, most repeated first. Tap a year to open that paper at the question.

  1. 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}.

    4 marksSame type asked in 6 of 7 papers

    Summer 2026 Q2b Winter 2025 Q4a OR Winter 2024 Q3b OR Summer 2024 Q2b Winter 2023 Q2b Summer 2023 Q1b

  2. 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

    3 marksSame type asked in 6 of 7 papers

    Summer 2026 Q4a Winter 2025 Q5a Winter 2024 Q4a Summer 2024 Q4a Winter 2023 Q4a Summer 2023 Q4b

  3. Evaluate the determinant A=∣1−2302401−1∣A = \begin{vmatrix} 1 & -2 & 3 \\ 0 & 2 & 4 \\ 0 & 1 & -1 \end{vmatrix}.

    3 marksSame type asked in 4 of 7 papers

    Summer 2026 Q2a Summer 2025 Q5a Winter 2023 Q2a Summer 2023 Q1a

  4. (i) Find dydx\frac{dy}{dx}, if x=acos⁡θ,y=asin⁡θx = a\cos\theta, y = a\sin\theta. (ii) Derive the trigonometry identity: cos⁡2x=cos⁡2x−sin⁡2x\cos 2x = \cos^2 x - \sin^2 x.

    7 marksAsked in 3 of 7 papers

    Summer 2026 Q2c OR Summer 2024 Q2c OR Winter 2023 Q2c OR

  5. (i) If ∣2451∣=∣2x46x∣\begin{vmatrix} 2 & 4 \\ 5 & 1 \end{vmatrix} = \begin{vmatrix} 2x & 4 \\ 6 & x \end{vmatrix} then find the value of xx. (ii) If 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.

    7 marksSame type asked in 3 of 7 papers

    Summer 2026 Q3c Summer 2024 Q3c OR Winter 2023 Q3c OR

  6. Solve the following equations: (i) dydx=1+y21+x2\frac{dy}{dx} = \frac{1 + y^2}{1 + x^2} (3 marks) (ii) xcos⁡(yx)dydx=ycos⁡(yx)+xx\cos\left(\frac{y}{x}\right)\frac{dy}{dx} = y\cos\left(\frac{y}{x}\right) + x (4 marks)

    7 marksAsked in 3 of 7 papers

    Summer 2024 Q4c Winter 2023 Q4c Summer 2023 Q4c

  7. Solve the following equations: (i) x dy=(2x2+1) dxx \, dy = (2x^2 + 1) \, dx (3 marks) (ii) xdydx+2y=x2x\frac{dy}{dx} + 2y = x^2 (x≠0)(x \neq 0) (4 marks)

    7 marksAsked in 3 of 7 papers

    Summer 2024 Q4c OR Winter 2023 Q4c OR Summer 2023 Q4c OR

  8. Find a particular solution of the differential equation dydx+ycot⁡x=4xcosec⁡x\frac{dy}{dx} + y\cot x = 4x\operatorname{cosec} x given that y=0y = 0 when x=0x = 0.

    7 marksSame type asked in 3 of 7 papers

    Winter 2025 Q5c Winter 2025 Q5c OR Winter 2024 Q4b Winter 2024 Q4b OR Winter 2023 Q4b

  9. Find lim⁡x→0sin⁡3xx\lim_{x \to 0} \frac{\sin 3x}{x}. Also Define limits and continuity of function.

    7 marksSame type asked in 3 of 7 papers

    Winter 2025 Q2c OR Summer 2025 Q3a Summer 2023 Q3a OR

  10. If y=x2sin⁡xy = x^2\sin x, find dydx\frac{dy}{dx} and d2ydx2\frac{d^2 y}{dx^2}.

    4 marksSame type asked in 3 of 7 papers

    Winter 2025 Q3b Summer 2024 Q4b OR Winter 2023 Q4b OR

Show 28 more repeated questionsHide the 28 more

  1. Find the equation of a line passing through (2,−3)(2, -3) and perpendicular to the line 3x−4y+7=03x - 4y + 7 = 0.

    4 marksSame type asked in 3 of 7 papers

    Winter 2025 Q1b Summer 2025 Q1b Winter 2024 Q2a Winter 2024 Q2b

  2. State the Quotient (division) rule of derivative and compute the derivative of f(x)=sin⁡xcos⁡xf(x) = \frac{\sin x}{\cos x}.

    3 marksAsked in 3 of 7 papers

    Summer 2026 Q3a OR Summer 2024 Q3a Winter 2023 Q3a

  3. 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}.

    3 marksSame type asked in 3 of 7 papers

    Summer 2024 Q4a OR Winter 2023 Q4a OR Summer 2023 Q4a

  4. 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}.

    3 marksSame type asked in 3 of 7 papers

    Summer 2026 Q4a OR Winter 2025 Q3a Summer 2023 Q4a OR

  5. State the integration by parts and find ∫xex dx\int x e^x \, dx.

    3 marksAsked in 3 of 7 papers

    Summer 2024 Q5a OR Winter 2023 Q5a OR Summer 2023 Q5a

  6. Evaluate lim⁡x→2x3−2x2x2−5x+6\lim_{x \to 2} \frac{x^3 - 2x^2}{x^2 - 5x + 6}.

    3 marksSame type asked in 3 of 7 papers

    Summer 2025 Q3a OR Winter 2024 Q1a Winter 2024 Q4a OR Summer 2023 Q3a

  7. (i) Solve dydx+2ytan⁡x=sin⁡x\frac{dy}{dx} + 2y\tan x = \sin x. (ii) Derive sin⁡2x=2sin⁡xcos⁡x\sin 2x = 2\sin x \cos x.

    7 marksAsked in 2 of 7 papers

    Summer 2026 Q2c Summer 2024 Q2c

  8. (i) Define the matrices: (a) Identity matrix (b) Scalar matrix (c) Diagonal matrix. (3 marks) (ii) Find 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)

    7 marksAsked in 2 of 7 papers

    Summer 2024 Q3c Winter 2023 Q3c

  9. Find the distance of the point (4,−3)(4, -3) from the line 3x+4y−5=03x + 4y - 5 = 0.

    7 marksSame type asked in 2 of 7 papers

    Winter 2025 Q1c Summer 2023 Q2a

  10. (i) Evaluate ∫121(x+1)(x+2) dx\int_1^2 \frac{1}{(x+1)(x+2)} \, dx (3 marks) (ii) Find ∫1x2−6x+13 dx\int \frac{1}{x^2 - 6x + 13} \, dx (4 marks)

    7 marksAsked in 2 of 7 papers

    Summer 2024 Q5c Winter 2023 Q5c

  11. Find ∫x2+x+1(x+1)(x2+1) dx\int \frac{x^2 + x + 1}{(x+1)(x^2 + 1)} \, dx.

    7 marksAsked in 2 of 7 papers

    Summer 2024 Q5c OR Summer 2023 Q5c OR

  12. Integrate the function ∫x(x+1)(x+2) dx\int \frac{x}{(x+1)(x+2)} \, dx.

    7 marksAsked in 2 of 7 papers

    Winter 2025 Q3c OR Summer 2025 Q4b OR

  13. 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}.

    7 marksSame type asked in 2 of 7 papers

    Summer 2026 Q5c Summer 2025 Q5b

  14. Find the inverse of the matrix A=[234431124]A = \begin{bmatrix} 2 & 3 & 4 \\ 4 & 3 & 1 \\ 1 & 2 & 4 \end{bmatrix}.

    7 marksSame type asked in 2 of 7 papers

    Summer 2026 Q5c OR Winter 2025 Q4c

  15. 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

    7 marksSame type asked in 2 of 7 papers

    Summer 2025 Q5c Summer 2025 Q5c OR Winter 2024 Q3c Winter 2024 Q3c OR

  16. Solve system of linear equation, using matrix method: 4x−3y=34x - 3y = 3 and 3x−5y=73x - 5y = 7.

    7 marksSame type asked in 2 of 7 papers

    Winter 2025 Q4c OR Winter 2023 Q1b

  17. 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}.

    4 marksAsked in 2 of 7 papers

    Summer 2026 Q1b Summer 2024 Q1b

  18. Find the distance (i) of the point (3,−1)(3, -1) from the line 3x−4y−26=03x - 4y - 26 = 0. (ii) between two parallel lines: 15x+8y−34=015x + 8y - 34 = 0 and 15x+8y+31=015x + 8y + 31 = 0.

    4 marksAsked in 2 of 7 papers

    Summer 2024 Q3b Winter 2023 Q3b

  19. Find the point on the x-axis which is at equidistance from the point (7,6)(7, 6) and (3,4)(3, 4).

    4 marksAsked in 2 of 7 papers

    Summer 2024 Q3b OR Winter 2023 Q3b OR

  20. Find the solution of the differential equation x5dydx=−y5x^5 \frac{dy}{dx} = -y^5.

    4 marksSame type asked in 2 of 7 papers

    Winter 2025 Q5b Winter 2025 Q5b OR Summer 2025 Q3c OR

  21. Find ∫sin⁡x(1+cos⁡x)2 dx\int \frac{\sin x}{(1 + \cos x)^2} \, dx.

    4 marksAsked in 2 of 7 papers

    Summer 2024 Q5b OR Winter 2023 Q5b OR

  22. Evaluate the integrals: (i) ∫dxx2−81\int \frac{dx}{x^2 - 81} (ii) ∫x2−1x dx\int \frac{x^2 - 1}{x} \, dx.

    4 marksAsked in 2 of 7 papers

    Summer 2024 Q5b Winter 2023 Q5b

  23. Evaluate: ∫(etan⁡−1x1+x2) dx\int \left(\frac{e^{\tan^{-1} x}}{1 + x^2}\right) \, dx.

    4 marksAsked in 2 of 7 papers

    Winter 2024 Q5b OR Winter 2023 Q5a

  24. Define exponential function and logarithmic function.

    3 marksAsked in 2 of 7 papers

    Summer 2026 Q1a Winter 2023 Q1a

  25. Define the matrices: (a) Identity matrix (b) Scalar matrix (c) Diagonal matrix.

    3 marksAsked in 2 of 7 papers

    Summer 2026 Q3a Winter 2024 Q3a OR

  26. 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.

    3 marksAsked in 2 of 7 papers

    Summer 2024 Q3a OR Winter 2023 Q3a OR

  27. Define slope of a line and find the slope of the line joining the points (2,3)(2, 3) and (−1,5)(-1, 5).

    3 marksSame type asked in 2 of 7 papers

    Winter 2025 Q1a Summer 2025 Q1a

  28. Find the value of xx, if ∣x218x∣=∣62186∣\begin{vmatrix} x & 2 \\ 18 & x \end{vmatrix} = \begin{vmatrix} 6 & 2 \\ 18 & 6 \end{vmatrix}.

    3 marksSame type asked in 2 of 7 papers

    Summer 2025 Q5a OR Winter 2024 Q3a

Which branches take this subject

GTU's syllabus lists 3110019 for 6 branches. One set of papers serves all of them.

Semester 1: 6 branches

Bio-Technology, Biomedical Engineering, Food Engineering & Technology, Nano Technology, Rubber Technology, Textile Technology

Other Semester 1 subjects

3110001Chemistry7 papers3110002English7 papers3110003Programming for Problem Solving7 papers3110004Basic Civil Engineering7 papers3110005Basic Electrical Engineering7 papers3110006Basic Mechanical Engineering6 papers3110007Environmental Sciences7 papers3110011Physics7 papers3110013Engineering Graphics & Design7 papers3110014Mathematics - 17 papers

Common questions

Are these GTU 3110019 Remedial Mathematics papers valid for both Regular and Remedial exams?

Yes. Gujarat Technological University (GTU) follows the same 70-mark syllabus, exam blueprint, and 23-mark passing cutoff for both Regular and Remedial (ATKT/backlog) examinations. All 7 past exam sessions (2023 – 2026) serve as comprehensive preparation for either attempt.

How can I download GTU 3110019 Remedial Mathematics old question papers PDF?

You can download official GTU 3110019 original question paper PDFs directly from the table above with 1 click and zero deceptive ads or wait timers. Every paper also includes interactive online questions with AI study prompts.

What is the passing mark for GTU Remedial Mathematics (3110019)?

The external theory exam carries 70 marks. The minimum passing cutoff is 23 marks (33%). Exam duration is 2.5 hours.

What is the GTU exam pattern for 3110019?

The examination contains 5 main questions of 14 marks each, totaling 70 marks. Questions 2 through 5 provide internal OR choices, typically split into 3-mark, 4-mark, and 7-mark questions.