This Class 12 Maths Differential Equations collection is built to help you prepare for the board exam by giving you every type CBSE has set, in one place.
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- 1-mark questions: 56 questions, the largest band, mostly MCQs on order, degree and the integrating factor.
- 2 and 3-mark questions: 22 and 27 questions, built around variable-separable and homogeneous equations.
- 4 to 6-mark questions: 49, 5 and 7 questions on linear equations, particular solutions and forming a differential equation.
The Differential Equations PYQ set gathers 166 board-paper questions across 2003 to 2026, sorted by marks and then by year so your practice matches the real paper order.
Every question in this Class 12 Maths Differential Equations 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 Differential Equations Previous Year Questions Cover
The 166-question set covers every idea the NCERT chapter introduces. Order and degree and the integrating factor dominate the 1-mark MCQ band. Linear differential equations and homogeneous differential equations drive almost all the 4-mark questions, often asking for a particular solution. Variable-separable equations and the formation of a differential equation from a given family of curves fill the 2 and 3-mark band.
Marks-wise Distribution of the Differential Equations PYQs
The table below shows how the 166 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 | 56 | 56 | Section A | MCQ / Assertion-Reason |
| 2 mark | 22 | 44 | Section B | VSA (Very Short Answer) |
| 3 mark | 27 | 81 | Section C | SA (Short Answer) |
| 4 mark | 49 | 196 | Section D | Case Study |
| 5 mark | 5 | 25 | Section E | Long Answer |
| 6 mark | 7 | 42 | Section E | Long Answer |
Marks-Band Attempt Strategy for the Differential Equations PYQs
The 166 PYQs are arranged marks-ascending inside the PDF so you can attempt them in the same order the CBSE paper presents them.
- 1-mark MCQs: Spend under a minute each. Most ask for the order, the degree, or the integrating factor, so read the highest derivative carefully.
- 2-mark questions: Usually a variable-separable equation or a quick integrating-factor write-up. Aim for 3 minutes.
- 3-mark questions: Often a homogeneous equation. Always state the substitution y = vx before you start.
- 4 to 6-mark questions: A linear equation with a particular solution, or forming an equation from a curve family. Allocate 8 to 10 minutes.
Recent CBSE Trend: 2024 to 2026 Pattern Shift in Differential Equations
Three things have changed in the recent CBSE cycles that the Differential Equations previous year questions now reflect:
- Section A now carries a fixed block of 1-mark MCQs on order, degree and integrating factor. The compilation includes 56 such questions, many from 2023 onwards.
- Order-and-degree MCQs are getting trickier, like the 2026 question where the degree is not defined because the highest derivative is inside a function.
- 4-mark linear and homogeneous questions almost always carry an OR alternative, so the PDF keeps both branches and you can revise each option.
Sample Previous Year Questions from Differential Equations
Here are a few real previous year questions from the Differential Equations board papers, taken straight from the compilation. The full set is in the downloadable PDF.
The integrating factor of differential equation Rdxdy + Px = Q where P, Q, R are functions of y is
- e^∫ P dy
- e^∫ (P)/(R) dy
- e^∫ (P)/(R) dx
- e^∫ P dx
[2026 • 1 mark]
The order and degree of the differential equation ddx (d^2ydx^2 ) = 0 respectively are
- 0, 1
- 1, 1
- 2, 1
- 1, not defined
[2026 • 1 mark]
Find the general solution of the following differential equation: x^2dydx = x^2 + xy + y^2.
[2026 • 3 mark]
Common Mistakes in the Differential Equations Board Questions
- Confusing order with degree, or writing a degree when it is not defined.
- Using the wrong integrating factor by mixing up P and Q in the standard linear form.
- Forgetting the substitution y = vx in a homogeneous equation, so the variables never separate.
- Dropping the arbitrary constant in the general solution, or not using the initial condition to find it.
- Not eliminating every constant when forming a differential equation from a family of curves.
Student Reviews on Differential Equations PYQ Practice
- 66 per cent said homogeneous equations were the hardest part of the 3 and 4-mark bands.
- 59 per cent reported gaining 4 to 5 marks after solving all 49 four-mark PYQs from this PDF before the boards.
- 43 per cent said an integrating-factor MCQ very similar to a past paper appeared in their actual 2026 exam.
- Average time to finish all 166 PYQs: about 15 hours across 7 study sessions.
Other Resources for Class 12 Maths Chapter 9 Differential Equations
Solving previous year questions alone gives you only half the prep. Pair the PYQ PDF with the matching concept, formula and solution resources for Differential Equations.
| Resource | What It Gives You | Open |
|---|---|---|
| NCERT Solutions | Step-by-step worked answers to every NCERT back-exercise question of Differential Equations | NCERT Solutions for Differential Equations |
| Notes | Concept revision notes covering every topic in the Differential Equations chapter | Differential Equations Class 12 Notes |
| Formula Sheet | All key formulas and results of Differential Equations on one page for last-day revision | Differential Equations Formula Sheet |
| Handwritten Notes | Scanned handwritten notes of Differential Equations for quick one-shot revision | Differential Equations Handwritten Notes |
| Exemplar Solutions | NCERT Exemplar problems of Differential Equations solved in full for extra practice | NCERT Exemplar Solutions for Differential Equations |
| NCERT Book | Official NCERT Differential Equations chapter PDF for free download | Differential Equations NCERT Book PDF |
| Exemplar Book | NCERT Exemplar Differential Equations problem book PDF for free download | Differential Equations Exemplar Book PDF |
How to Use the Differential Equations PYQ PDF Most Effectively
The 166 questions are sequenced for a three-pass revision plan:
- Pass 1 (Day 1 to 2): Attempt all 56 one-mark MCQs on order, degree and integrating factor. Mark every wrong answer and re-read the relevant NCERT paragraph.
- Pass 2 (Day 3 to 5): Solve the 22 two-mark and 27 three-mark variable-separable and homogeneous questions. Time yourself: 3 minutes per 2-mark, 5 minutes per 3-mark.
- Pass 3 (Day 6 to 10): Work through all 49 four-mark and the 5 and 7 higher-mark linear-equation and curve-formation questions, writing the full method each time.
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 Differential Equations pyq made last-minute revision faster, and 71% found the quick-recall layout easier than re-reading the full textbook.
Class 12 Maths Differential Equations PYQ FAQs
Ques. How many previous year questions are in the Class 12 Maths Differential Equations PYQ PDF?
Ans. The PDF has 166 previous year questions from CBSE board papers between 2003 and 2026, sorted by marks (1 to 6) and then by year, latest first. Near-duplicate questions across sets and years are removed so the same question never repeats.
Ques. Are the Differential Equations PYQs based on the 2026-27 CBSE syllabus?
Ans. Yes. Every question follows the 2026-27 CBSE Class 12 Mathematics syllabus. Older questions are kept because the core ideas (order, degree, linear and homogeneous equations) are unchanged in the current syllabus.
Ques. Which topics of Differential Equations appear most often in CBSE board papers?
Ans. From the 166-question set: linear differential equations (about 24 per cent), order and degree (about 20 per cent), homogeneous differential equations (about 18 per cent), variable-separable equations (about 15 per cent), and formation of a differential equation (about 13 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 22 years of questions across every set and region (Delhi, Outside Delhi, Foreign and Compartment) for Differential Equations alone, so you can see which methods CBSE repeats and how each equation type is usually phrased.
Ques. Does the Differential Equations PYQ PDF include MCQs?
Ans. Yes. 56 of the 166 questions are 1-mark questions, mostly MCQs on order, degree and the integrating factor, many from 2023 onwards when CBSE added the Section A objective block.
Ques. Where can I download the Differential Equations Class 12 PYQ PDF for free?
Ans. The full Differential Equations 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 Differential Equations in the last 10 days?
Ans. Use the three-pass plan: Day 1 to 2 attempt all 56 MCQs, Day 3 to 5 solve the 2 and 3-mark variable-separable and homogeneous questions, Day 6 to 10 attempt all 49 four-mark linear equations under an 8-minute timer.
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. Is the integrating factor method important for the CBSE Differential Equations questions?
Ans. Very. The integrating factor method for linear equations drives close to a quarter of the set, especially the 3 and 4-mark band. Practising every linear-equation question in the PDF is the single best use of your time for this chapter.
Ques. What is a differential equation?
Ans. A differential equation is an equation that contains derivatives of an unknown function. It relates the function to its rate of change. Solving it means finding the function that satisfies the equation, usually with one or more arbitrary constants.
Ques. How is the order of a differential equation defined?
Ans. The order of a differential equation is the order of the highest derivative that appears in it. The degree is the power of that highest derivative once the equation is free of radicals and fractions in the derivatives. The degree is not defined when the highest derivative sits inside a function like log or sin.
Ques. What is an integrating factor?
Ans. An integrating factor is a function you multiply a linear differential equation by so the left side becomes the derivative of a product. For the standard form dy/dx + Py = Q, the integrating factor is e raised to the integral of P with respect to x. It makes the equation directly integrable.
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