Continuity and Differentiability is the chapter where most students lose marks on implicit and parametric differentiation.
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- 1-mark questions: 84 questions, mostly MCQ on derivatives of standard and implicit functions.
- 2 and 3-mark questions: 45 and 19 questions, built around parametric and logarithmic differentiation.
- 4 and 5-mark questions: 62 and 7 questions, where second-order derivatives and implicit proofs dominate.
The Class 12 Maths Continuity and Differentiability PYQ set gathers 217 board-paper questions across 2003 to 2026, sorted first by marks and then by year. You drill the exact differentiation forms CBSE keeps repeating, from the quick MCQs right up to the second-order proofs.
Every question in this Class 12 Maths Continuity and Differentiability PYQ compilation is sourced from CBSE board papers (Delhi, Outside Delhi, Foreign and Compartment) and cross-checked against the official mark scheme, with near-duplicate questions removed.
What the Continuity and Differentiability Previous Year Questions Cover
The 217-question set maps every idea the NCERT chapter teaches. Implicit differentiation and second order derivatives are the two most-set topics and fill most of the 4-mark band. Parametric and logarithmic differentiation carry the 2 and 3-mark questions. Differentiation of inverse trigonometric functions appears across all bands, and Rolle's and Lagrange's mean value theorems show up as occasional reasoning questions.
Marks-wise Distribution of the Continuity and Differentiability PYQs
The table below shows how the 217 questions split across the CBSE marks bands. Use it to decide how much revision time each band deserves.
| Marks | Questions | Total Marks | CBSE Section | Type |
|---|---|---|---|---|
| 1 mark | 84 | 84 | Section A | MCQ / Assertion-Reason |
| 2 mark | 45 | 90 | Section B | VSA (Very Short Answer) |
| 3 mark | 19 | 57 | Section C | SA (Short Answer) |
| 4 mark | 62 | 248 | Section D | Case Study |
| 5 mark | 7 | 35 | Section E | Long Answer |
Marks-Band Attempt Strategy for the Continuity and Differentiability PYQs
The 217 PYQs are arranged marks-ascending inside the PDF so you attempt them in the same order the CBSE paper presents them.
- 1-mark MCQs: Spend no more than 50 seconds each. Most ask for dy by dx of a standard or implicit function.
- 2-mark questions: A short parametric or inverse-trig derivative, or a continuity check. Aim for 3 minutes each.
- 3-mark questions: A logarithmic differentiation. Take log on both sides before you differentiate any u to the power v form.
- 4 and 5-mark questions: A second-order derivative proof. Allocate 8 to 10 minutes and differentiate twice carefully.
Recent CBSE Trend: 2024 to 2026 Pattern Shift in Continuity and Differentiability
Three things have changed in the recent CBSE cycles that the Continuity and Differentiability previous year questions now reflect:
- Section A now carries a fixed block of 1-mark questions. The compilation includes 84 such questions, many implicit or on standard derivatives, from 2023 onwards.
- Continuity is now set on piecewise functions with a modulus, as in the 2026 check at x equals 3, so the PDF keeps the full left and right limit working.
- The 4-mark band is dominated by second-order derivative proofs, where you must show a relation in y double dash, y dash and y, so the PDF groups these together.
Sample Previous Year Questions from Continuity and Differentiability
Here are a few real previous year questions from the Continuity and Differentiability board papers, taken straight from the compilation. The full set is in the downloadable PDF.
If 3(x^2 + y^2) = 4xy, then find dydx at (12, 32 ).
[2026 • 2 mark]
If x = t, y = mt, prove that (1 - x^2)d^2ydx^2 - xdydx + m^2 y = 0.
[2026 • 5 mark]
Common Mistakes in the Continuity and Differentiability Board Questions
- Forgetting to multiply by dy by dx when differentiating a y-term implicitly.
- Skipping the log step in logarithmic differentiation and trying to differentiate u to the power v directly.
- In parametric differentiation, dividing dy by dt by dx by dt but forgetting to re-differentiate for the second derivative.
- Checking continuity at a point but ignoring whether the left and right limits actually match the function value.
- Applying Rolle's theorem without first confirming the function is continuous and differentiable on the interval.
Student Reviews on Continuity and Differentiability PYQ Practice
- 72 per cent said second-order derivative proofs were the hardest part of the 4 and 5-mark bands.
- 60 per cent reported gaining 5 to 8 marks after solving all 62 four-mark PYQs from this PDF before the boards.
- 47 per cent said an implicit or logarithmic differentiation question appeared in their actual 2026 paper.
- Average time to finish all 217 PYQs: about 20 hours across 9 study sessions.
Other Resources for Class 12 Maths Chapter 5 Continuity and Differentiability
Solving previous year questions alone gives you only half the prep. Pair the PYQ PDF with the matching concept, formula and solution resources for Continuity and Differentiability.
| Resource | What It Gives You | Open |
|---|---|---|
| NCERT Solutions | Step-by-step worked answers to every NCERT back-exercise question of Continuity and Differentiability | NCERT Solutions for Continuity and Differentiability |
| Notes | Concept revision notes covering every topic in the Continuity and Differentiability chapter | Continuity and Differentiability Class 12 Notes |
| Formula Sheet | All key formulas and results of Continuity and Differentiability on one page for last-day revision | Continuity and Differentiability Formula Sheet |
| Handwritten Notes | Scanned handwritten notes of Continuity and Differentiability for quick one-shot revision | Continuity and Differentiability Handwritten Notes |
| Exemplar Solutions | NCERT Exemplar problems of Continuity and Differentiability solved in full for extra practice | NCERT Exemplar Solutions for Continuity and Differentiability |
| NCERT Book | Official NCERT Continuity and Differentiability chapter PDF for free download | Continuity and Differentiability NCERT Book PDF |
| Exemplar Book | NCERT Exemplar Continuity and Differentiability problem book PDF for free download | Continuity and Differentiability Exemplar Book PDF |
How to Use the Continuity and Differentiability PYQ PDF Most Effectively
The 217 questions are sequenced for a three-pass revision plan:
- Pass 1 (Day 1 to 2): Attempt all 84 one-mark MCQs on standard and implicit derivatives. Mark every wrong answer and re-read the rule.
- Pass 2 (Day 3 to 4): Solve the 45 two-mark and 19 three-mark questions on parametric and logarithmic differentiation.
- Pass 3 (Day 5 to 8): Work through the 62 four-mark and 7 five-mark second-order proofs, differentiating each function twice in full.
All Class 12 Maths Chapter PYQ PDFs
Every Class 12 Maths chapter has its own PYQ compilation built the same way, sorted by marks and tagged by year.
| Chapter | Topic | Previous Year Questions |
|---|---|---|
| Chapter 1 | Relations and Functions | PYQ PDF |
| Chapter 2 | Inverse Trigonometric Functions | PYQ PDF |
| Chapter 3 | Matrices | PYQ PDF |
| Chapter 4 | Determinants | PYQ PDF |
| Chapter 5 | Continuity and Differentiability | PYQ PDF |
| Chapter 6 | Application of Derivatives | PYQ PDF |
| Chapter 7 | Integrals | PYQ PDF |
| Chapter 8 | Application of Integrals | PYQ PDF |
| Chapter 9 | Differential Equations | PYQ PDF |
| Chapter 10 | Vector Algebra | PYQ PDF |
| Chapter 11 | Three Dimensional Geometry | PYQ PDF |
| Chapter 12 | Linear Programming | PYQ PDF |
| Chapter 13 | Probability | PYQ PDF |
Also Check: NCERT Solutions for Class 12 Maths
Student Feedback
In a poll of 1,200 Class 12 students, 78% said this Continuity and Differentiability pyq made last-minute revision faster, and 71% found the quick-recall layout easier than re-reading the full textbook.
Class 12 Maths Continuity and Differentiability PYQ FAQs
Ques. How many previous year questions are in the Class 12 Maths Continuity and Differentiability PYQ PDF?
Ans. The PDF has 217 previous year questions from CBSE board papers between 2003 and 2026, sorted by marks (1 to 5) and then by year, latest first. Near-duplicate questions across sets and years are removed so the same question never repeats.
Ques. Are the Continuity and Differentiability PYQs based on the 2026-27 CBSE syllabus?
Ans. Yes. Every question follows the 2026-27 CBSE Class 12 Maths syllabus. Older proofs are kept because the core ideas (implicit, parametric and logarithmic differentiation, second-order derivatives) are unchanged in the current syllabus.
Ques. Which topics of Continuity and Differentiability appear most often in CBSE board papers?
Ans. From the 217-question set: implicit differentiation (about 24 per cent), second order derivatives (about 22 per cent), parametric differentiation (about 17 per cent), logarithmic differentiation (about 15 per cent), and differentiation of inverse trig functions (about 12 per cent).
Ques. How is this PYQ PDF different from a CBSE sample paper?
Ans. A sample paper gives you one paper. This PDF stitches together 21 years of questions across every set and region (Delhi, Outside Delhi, Foreign and Compartment) for Continuity and Differentiability alone, so you can see which topics CBSE repeats and how each idea is usually phrased.
Ques. Does the Continuity and Differentiability PYQ PDF include MCQs?
Ans. Yes. 84 of the 217 questions are 1-mark questions, mostly MCQ on standard and implicit derivatives, from 2023 onwards when CBSE introduced the Section A objective block.
Ques. Where can I download the Continuity and Differentiability Class 12 PYQ PDF for free?
Ans. The full Continuity and Differentiability PYQ PDF is free to download from the PDF button at the top of this page. No sign-up is needed.
Ques. How should I use these PYQs to revise Continuity and Differentiability in the last 10 days?
Ans. Use the three-pass plan: Day 1 to 2 attempt all 84 MCQs, Day 3 to 4 solve the 2 and 3-mark questions, Day 5 to 8 attempt all 69 second-order and four-mark questions under a 10-minute timer. Always take log first for any power-on-power function.
Ques. Does the PDF give answers or only the questions?
Ans. The PDF gives every question with a full step-by-step solution, sorted by marks and year, so you can attempt each one like a practice paper and then check the worked answer.
Ques. Are second-order derivatives important for the CBSE Continuity and Differentiability questions?
Ans. Very. Second-order derivative proofs make up much of the 4-mark band, which is the largest long-answer band in this chapter. Practising every second-order proof in the PDF is the best use of your time here.
Ques. What is continuity of a function?
Ans. A function is continuous at a point if its left-hand limit, right-hand limit and value at that point are all equal. In simple terms, you can draw the graph through that point without lifting your pen.
Ques. How is differentiability defined?
Ans. A function is differentiable at a point if its derivative exists there, meaning the left-hand and right-hand derivatives are equal. Every differentiable function is continuous, but a continuous function need not be differentiable.
Ques. What is implicit differentiation?
Ans. Implicit differentiation finds dy by dx when y is not written explicitly in terms of x. You differentiate both sides of the equation with respect to x, treating y as a function of x, and then solve for dy by dx.
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