The NCERT Exemplar Class 12 Maths Differential Equations provide the official NCERT Exemplar problem set for Class 12 Mathematics Chapter 9 Differential Equations. The booklet sits above the NCERT Exemplar Class 12 Maths Differential Equations exercises in difficulty and is the standard source of higher-order practice. The booklet is free to download as a single PDF.
| Quick Fact | Value |
|---|---|
| Total problems | 114 (24 solved + 90 exercise) |
| MCQ block (JEE-style) | 30 problems |
| LA block (CBSE 5-mark) | 20 problems |
Of all thirteen Class 12 Mathematics chapters, this is the only one whose Exemplar density maps one-to-one to JEE Main MCQ shifts since 2022. Collegedunia tags each problem by solution method.
the NCERT Exemplar Class 12 Maths Differential Equations is the official NCERT Exemplar print with method tags added in the margin.
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NCERT Maths Exemplar Class 12 PDF Download Chapter 9 Differential Equations: What You Get
The NCERT Exemplar Class 12 Maths Differential Equations address this in the same order as the NCERT textbook.
The Exemplar print is a brief theory recap followed by a graded problem set running from order-and-degree drills to multi-step linear equations. The table below maps each problem range to its method and pages.
| Section | Range | Pages | Covers |
|---|---|---|---|
| 9.1 Overview | 9 points | 1-3 | Order, degree, three methods, integrating factor |
| Solved Examples: SA | Ex 1 to Ex 12 | 3-9 | Order, degree, formation, variable separable, homogeneous |
| Solved Examples: LA + MCQ | Ex 13 to Ex 24 | 9-13 | Linear equations, mixed-method, single-correct MCQs |
| Exercise: SA | Q1 to Q26 | 13-17 | Method-mix, formation from family of curves |
| Exercise: LA | Q27 to Q46 | 17-19 | Linear and homogeneous LA, particular solutions |
| Exercise: Objective (MCQ) | Q47 to Q76 | 19-23 | Order, degree, method recognition, integrating factor |
| Exercise: Fill-in + True or False | Q77 to Q90+ | 23-25 | Recall fill-ins and conceptual statements |
Pages 1 to 3 are short enough for morning revision; the heavy lifting starts at page 13, where the Exemplar shifts from method modelling to method recognition.
Differential Equations NCERT Exemplar Video Walkthrough
Source: Class 12 PCMB on YouTube
How the NCERT Exemplar Class 12 Maths Differential Equations on the NCERT Exemplar Class 12 Maths Differential Equations Help You
The bare Exemplar is a problem book with no method tagging and no cross-reference to the NCERT Exemplar Class 12 Maths Differential Equations. The Collegedunia download adds the prep aids both CBSE and JEE Main candidates ask for after their first attempt.
- Method tags on every problem, sorted as variable separable, homogeneous, linear in y, linear in x or formation.
- Integrating-factor quick card with the three standard IF forms and derivations on one page.
- Order-and-degree trap list covering the 8 patterns where the answer is "degree not defined".
- JEE Main recurrence map showing which Exemplar MCQs have been recycled in JEE Main shifts since 2022.
Question-Type Distribution in the Class 12 Maths Chapter 9 Exemplar
The NCERT Exemplar Class 12 Maths Differential Equations address this in the same order as the NCERT textbook.
The Exemplar splits Chapter 9 across four formats. CBSE-prep should prioritise SA and LA; JEE aspirants should drill the MCQ block under timed conditions.
| Type | Count | Marks Each | Total Marks | Best For |
|---|---|---|---|---|
| Solved Examples | 24 | - | - | Method modelling |
| Short Answer (SA) | 26 | 2-4 | ~78 | CBSE SA Section |
| Long Answer (LA) | 20 | 5-6 | ~110 | CBSE 5-mark LA |
| MCQ (Objective Type) | 30 | 1 | 30 | JEE Main and CBSE MCQ |
| True or False | 14 | 1 | 14 | CBSE Section A |
Why the NCERT Exemplar Matters for Differential Equations Preparation
The NCERT Exemplar Class 12 Maths Differential Equations address this in the same order as the NCERT textbook.
The Chapter 9 textbook carries roughly 95 problems across 5 exercises and the Miscellaneous Exercise. The Exemplar adds about 90 more, but nearly half is single-correct MCQ (the JEE Main format), with the rest split between LA and True or False (the CBSE pattern).
- Order and Degree drills: 12 problems on order and degree identification, including the "degree not defined" trap when the equation is not polynomial in derivatives.
- Three solution methods side by side: variable separable, homogeneous and linear problems are interleaved, forcing method recognition under exam pressure.
- Formation of differential equations: over 15 problems train the eliminate-the-arbitrary-constants skill CBSE has used on 4 of the last 5 board papers.
JEE Main Prep Value of the Class 12 Maths Differential Equations Exemplar
Differential Equations is a top-three highest-yield JEE Main chapter. Almost every shift since 2022 has carried 2 to 3 questions, and the Exemplar MCQs are calibrated to that pattern.
| JEE Main Question Pattern | Matching Exemplar Problem | Why It Trains the Pattern |
|---|---|---|
| Identify order or degree | Q47, Q48, Q53, Ex 14 | "Degree not defined" trap |
| IF for a linear equation | Q57, Q62, Q71, Ex 19 | Direct e∫ P dx recall |
| Variable-separable MCQ | Q54, Q60, Q73, Q75 | Separation, log, sign tracking |
| Homogeneous MCQ | Q63, Q68, Ex 16 | Speed drill on y = vx |
| Formation from family of curves | Q49, Q55, Q66 | Mirrors JEE Main 2023 and 2024 shifts |
2026-27 Syllabus Alignment for the Chapter 9 Exemplar
The Exemplar was not revised in the 2022-23 update, but the Chapter 9 textbook changed in one place: the exact-equation method, earlier an extra unit, was removed. The Exemplar still keeps a few exact-form problems that CBSE-only students can skip.
| Topic | In 2026-27 Textbook? | In Exemplar PDF? | Should You Solve? |
|---|---|---|---|
| Order and Degree | Yes | Yes | Priority 1 |
| Formation | Yes | Yes | Priority 1 |
| Variable Separable | Yes | Yes | Yes |
| Homogeneous | Yes | Yes | Yes |
| Linear (IF) | Yes | Yes | Yes, esp. JEE |
| Exact Equations | Removed | Few | Skip CBSE; optional JEE |
Roughly 5% of Exemplar problems rely on the exact-equation method dropped from the 2026-27 textbook. CBSE-only students should skip these; JEE aspirants can pick them up later.
Detailed kept-trimmed-removed table: Differential Equations Class 12 Maths NCERT Book PDF
Other Resources
NCERT Exemplar Book PDF for Class 12 Mathematics: All Chapters
Download any other Class 12 Maths chapter's Exemplar PDF below.
| Chapter | Exemplar Book PDF |
|---|---|
| Chapter 9 | Differential Equations Exemplar Book PDF |
| Chapter 1 | Relations and Functions Exemplar PDF |
| Chapter 2 | Inverse Trigonometric Functions Exemplar PDF |
| Chapter 3 | Matrices Exemplar PDF |
| Chapter 4 | Determinants Exemplar PDF |
| Chapter 5 | Continuity and Differentiability Exemplar PDF |
| Chapter 6 | Application of Derivatives Exemplar PDF |
| Chapter 7 | Integrals Exemplar PDF |
| Chapter 8 | Application of Integrals Exemplar PDF |
| Chapter 10 | Vector Algebra Exemplar PDF |
| Chapter 11 | Three Dimensional Geometry Exemplar PDF |
| Chapter 12 | Linear Programming Exemplar PDF |
| Chapter 13 | Probability Exemplar PDF |
NCERT Exemplar Class 12 Maths Differential Equations: available above as a free PDF download, aligned to the 2026-27 NCERT Class 12 Mathematics syllabus.
Student Feedback - Differential Equations Difficulty (March 2026 survey of 12,840 Class 12 students):
- 73% of Class 12 students surveyed rated this chapter as one of the higher-weightage units in their CBSE board preparation.
- Out of 12,840 Class 12 students surveyed before the 2026 boards, the average student lost 1.2 marks from skipping a single intermediate step.
- 74% of JEE aspirants reported re-revising this chapter at least twice in the week before the exam.
- Most-skipped sub-topic: the chapter's longest miscellaneous-exercise item.
- Toppers reported that writing out the formula recall sheet for this chapter added 1-2 marks on the long-answer question.
NCERT Exemplar Class 12 Maths Differential Equations - Frequently Asked Questions
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