Explore: All CBSE Class 12 chapters · CBSE Class 12 Mathematics PYQs · CBSE Class 12 hub · Syllabus & pattern · Class 12 2026
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Application of Derivatives PYQs (previous year questions) for CBSE Class 12: Application of Derivatives (Mathematics) had 29 questions across the 50 official CBSE Class 12 papers we tagged (2016–2026), and appeared in 9 of them. Asked in 9 of 10 years. The concepts asked in the most papers: Maxima and Minima, Rate of Change, Tangents and Normals.
Year-wise question count
Asked in 9 of 10 years.
Most-asked concepts
Sorted by the number of papers a concept appeared in.
| Concept | Questions | Papers | Years |
|---|---|---|---|
| Maxima and Minima | 11 | 8 | 2026, 2025, 2024, 2023, 2020, 2019, 2018, 2017 |
| Rate of Change | 5 | 5 | 2026, 2025, 2024, 2023, 2017 |
| Tangents and Normals | 5 | 4 | 2020, 2019, 2018, 2016 |
| Increasing and Decreasing Functions | 4 | 3 | 2025, 2024, 2023 |
| Increasing Functions | 2 | 2 | 2017, 2016 |
| Marginal Cost | 1 | 1 | 2018 |
| Rolle's Theorem | 1 | 1 | 2017 |
How to practise Application of Derivatives PYQs
- Start with the concepts at the top of the table. They have come back the most.
- Solve one year’s Application of Derivatives questions from the official PDF against the clock, then check the answer listed below.
- Log every miss as a concept gap, a calculation slip or a misread. Each needs a different fix.
- Once a concept is clean in two papers, move to the next. Then sit a full paper from the year pages.
Questions by year
Each line gives the question number and paper, type, concept, our one-line summary, with a link to the official PDF.
CBSE Class 122026
- Q.7 (Mathematics (65/1/1)) · MCQ · Maxima and Minima: Least value of x^3 - 12x on [0, 3] PDF
- Q.22 (Mathematics (65/1/1)) · Very short answer · Rate of Change: Rate at which perfume level drops in a conical bottle PDF
- Q.36 (Mathematics (65/1/1)) · Case-based · Maxima and Minima: Case study: subscription fee increase and maximum revenue PDF
CBSE Class 122025
- Q.8 (Mathematics (65/1/1)) · MCQ · Maxima and Minima: Absolute maximum of x^3 - 3x + 2 on [0, 2] PDF
- Q.24 (Mathematics (65/1/1)) · Very short answer · Increasing and Decreasing Functions: Intervals where 5x^(3/2) - 3x^(5/2) increases or decreases PDF
- Q.26 (Mathematics (65/1/1)) · Short answer · Rate of Change: Rate of increase of area of an equilateral triangle PDF
- Q.33 (Mathematics (65/1/1)) · Long answer · Maxima and Minima: Absolute max and min of a cubic on [1, 5] PDF
- Q.36 (Mathematics (65/1/1)) · Case-based · Maxima and Minima: Case study: solar panel area with partition, maximise area PDF
CBSE Class 122024
- Q.4 (Mathematics (65/1/1)) · MCQ · Increasing and Decreasing Functions: Condition on f'(x) for a function to be strictly increasing PDF
- Q.22 (Mathematics (65/1/1)) · Very short answer · Maxima and Minima: Show a cubic has neither maxima nor minima PDF
- Q.36 (Mathematics (65/1/1)) · Case-based · Rate of Change: Case study: speed camera on a pole, rate of change of elevation angle PDF
CBSE Class 122023
- Q.16 (Mathematics (65/1/1)) · MCQ · Increasing and Decreasing Functions: Interval where a(x + sin x)-type function is strictly decreasing PDF
- Q.25 (Mathematics (65/1/1)) · Very short answer · Increasing and Decreasing Functions: Show a trigonometric function is strictly decreasing on an interval PDF
- Q.37 (Mathematics (65/1/1)) · Case-based · Rate of Change: Case study: water draining from a conical tank, rates of r and area PDF
- Q.38 (Mathematics (65/1/1)) · Case-based · Maxima and Minima: Case study: roller-coaster cubic, find a and f'(x) at x = 1 PDF
CBSE Class 122020
- Q.14 (Mathematics (65/1/1)) · Fill in the blank · Tangents and Normals: Equation of normal to y^2 = 8x at the origin PDF
- Q.23 (Mathematics (65/1/1)) · Short answer · Tangents and Normals: Points on a cubic where tangent is parallel to a given line PDF
- Q.35 (Mathematics (65/1/1)) · Long answer II · Maxima and Minima: Cylinder of max volume inscribed in a cone has height h/3 PDF
CBSE Class 122019
CBSE Class 122018
- Q.8 (Mathematics (65/1)) · Short answer · Marginal Cost: Marginal cost of a cubic cost function at 3 units PDF
- Q.16 (Mathematics (65/1)) · Long answer I · Tangents and Normals: Tangent and normal to an ellipse at a given point PDF
- Q.17 (Mathematics (65/1)) · Long answer I · Maxima and Minima: Open square-base tank costs least when depth is half width; values PDF
CBSE Class 122017
- Q.6 (Mathematics (65/1)) · Short answer · Rolle's Theorem: Value of c in Rolle's theorem for x^3 - 3x on an interval PDF
- Q.7 (Mathematics (65/1)) · Short answer · Rate of Change: Rate of change of cube surface area given volume rate PDF
- Q.8 (Mathematics (65/1)) · Short answer · Increasing Functions: Show a cubic is increasing on R PDF
- Q.26 (Mathematics (65/1)) · Long answer II · Maxima and Minima: Closed square-base cuboid of fixed volume has min surface as a cube PDF
CBSE Class 122016
Other Mathematics chapters
- Relations and Functions PYQs
- Inverse Trigonometric Functions PYQs
- Matrices PYQs
- Determinants PYQs
- Continuity and Differentiability PYQs
- Integrals PYQs
- Application of Integrals PYQs
- Differential Equations PYQs
- Vector Algebra PYQs
- Three Dimensional Geometry PYQs
- Linear Programming PYQs
- Probability PYQs
FAQ
How many Application of Derivatives questions come in CBSE Class 12?
In the official papers we tagged: 3 in 2026, 5 in 2025, 3 in 2024, 4 in 2023, 3 in 2020, 2 in 2019, 3 in 2018, 4 in 2017 and 2 in 2016. Not asked in the other year. That is 29 questions in all, about 9% of Mathematics.
Which Application of Derivatives topics repeat in CBSE Class 12?
Asked in the most papers: Maxima and Minima, Rate of Change, Tangents and Normals. The concept table lists every one with its count.
Are these official CBSE Class 12 questions?
Yes. Every question is from an official CBSE Class 12 paper hosted on our year pages. The one-line summaries are ours; open the PDF linked beside each question for the full text.