The Continuity and Differentiability Class 12 Exemplar Solutions page compiles NCERT Class 12 Mathematics Chapter 5 into a single download-ready resource, aligned to the 2026-27 NCERT syllabus. The page covers definitions, solved examples, exam-weightage data and common mistakes, with every formula matched to the CBSE marking scheme used in recent board papers.
Use the resource above alongside the chapter breakdown below.
Use the resource above alongside the chapter breakdown below.
Use the resource above alongside the chapter breakdown below.
Use the resource above alongside the chapter breakdown below.
Use the resource above alongside the chapter breakdown below.
Use the resource above alongside the chapter breakdown below.
Use the resource above alongside the chapter breakdown below.
Use the resource above alongside the chapter breakdown below.
Use the resource above alongside the chapter breakdown below.
Use the resource above alongside the chapter breakdown below.
Use the resource above alongside the chapter breakdown below.
Use the resource above alongside the chapter breakdown below.
Use the resource above alongside the chapter breakdown below.
Use the resource above alongside the chapter breakdown below.
Use the resource above alongside the chapter breakdown below.
Use the resource above alongside the chapter breakdown below.
Use the resource above alongside the chapter breakdown below.
Use the resource above alongside the chapter breakdown below.
Use the resource above alongside the chapter breakdown below.
Use the resource above alongside the chapter breakdown below.
Use the resource above alongside the chapter breakdown below.
Use the resource above alongside the chapter breakdown below.
Use the resource above alongside the chapter breakdown below.
Use the resource above alongside the chapter breakdown below.
Use the resource above alongside the chapter breakdown below.
Use the resource above alongside the chapter breakdown below.
Use the resource above alongside the chapter breakdown below.
Use the resource above alongside the chapter breakdown below.
Use the resource above alongside the chapter breakdown below.
Use the resource above alongside the chapter breakdown below.
Use the resource above alongside the chapter breakdown below.
Use the resource above alongside the chapter breakdown below.
Use the resource above alongside the chapter breakdown below.
Use the resource above alongside the chapter breakdown below.
Use the resource above alongside the chapter breakdown below.
Use the resource above alongside the chapter breakdown below.
Use the resource above alongside the chapter breakdown below.
Use the resource above alongside the chapter breakdown below.
Use the resource above alongside the chapter breakdown below.
Use the resource above alongside the chapter breakdown below.
Use the resource above alongside the chapter breakdown below.
Use the resource above alongside the chapter breakdown below.
Use the resource above alongside the chapter breakdown below.
Use the resource above alongside the chapter breakdown below.
Use the resource above alongside the chapter breakdown below.
Use the resource above alongside the chapter breakdown below.
Use the resource above alongside the chapter breakdown below.
Use the resource above alongside the chapter breakdown below.
Use the resource above alongside the chapter breakdown below.
Use the resource above alongside the chapter breakdown below.
Use the resource above alongside the chapter breakdown below.
Use the resource above alongside the chapter breakdown below.
Use the resource above alongside the chapter breakdown below.
Use the resource above alongside the chapter breakdown below.
Use the resource above alongside the chapter breakdown below.
Use the resource above alongside the chapter breakdown below.
Use the resource above alongside the chapter breakdown below.
Use the resource above alongside the chapter breakdown below.
Use the resource above alongside the chapter breakdown below.
Use the resource above alongside the chapter breakdown below.
Use the resource above alongside the chapter breakdown below.
Use the resource above alongside the chapter breakdown below.
Use the resource above alongside the chapter breakdown below.
Use the resource above alongside the chapter breakdown below.
Use the resource above alongside the chapter breakdown below.
Use the resource above alongside the chapter breakdown below.
Use the resource above alongside the chapter breakdown below.
Use the resource above alongside the chapter breakdown below.
Use the resource above alongside the chapter breakdown below.
Use the resource above alongside the chapter breakdown below.
Use the resource above alongside the chapter breakdown below.
Use the resource above alongside the chapter breakdown below.
Use the resource above alongside the chapter breakdown below.
Use the resource above alongside the chapter breakdown below.
Use the resource above alongside the chapter breakdown below.
Use the resource above alongside the chapter breakdown below.
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- CBSE Weightage: 8 marks (typical 6-10 marks range)
- JEE Main Weightage: 6-8% of Mathematics section
- JEE Main Weightage: Not applicable for the NCERT Exemplar Class 12 Maths Continuity and Differentiability
Collegedunia's Class 12 Maths Exemplar Solutions for Chapter 5 walk through every objective and subjective question step by step, with each derivation written in full so that the chain rule, logarithmic differentiation, parametric forms, and second-order derivatives become muscle memory before exams.
NCERT Exemplar Solutions for Class 12 Maths Chapter 5 Continuity and Differentiability
The Exemplar for the NCERT Exemplar Class 12 Maths Continuity and Differentiability is organised into five solution categories that mirror the CBSE blueprint. Each category targets a different skill level - the MCQ block tests definition recall, the SA block tests calculation speed, and the LA block tests proof-style reasoning needed for the 5-mark questions on the board paper.
| Section | Question Type | Question Count | Marks Range |
|---|---|---|---|
| 5.3 Exercise (Short Answer) | SA | 20 | 2-3 marks |
| 5.3 Exercise (Long Answer) | LA | 13 | 4-5 marks |
| Objective Type - MCQ | MCQ | 15 | 1 mark each |
| Fill in the Blanks | VSA | 5 | 1 mark each |
| True / False | VSA | 5 | 1 mark each |
Continuity and Differentiability NCERT Exemplar Video Solutions
Source: Magnet Brains on YouTube
Key Concepts Tested in Class 12 Maths Chapter 5 Exemplar
The NCERT Exemplar Class 12 Maths Continuity and Differentiability address this in the same order as the NCERT textbook.
Before opening the Exemplar PDF, students should be confident with these six anchor concepts. The Exemplar problems are deliberately designed to combine two or three of them in a single question, so weak spots get exposed quickly.
- Continuity at a point using the three-step test: x → a- f(x) = x → a+ f(x) = f(a)
- Differentiability implies continuity, but the converse is false (Exemplar Q.28 tests this directly)
- Chain rule for composite functions: ddxf(g(x)) = f'(g(x)) · g'(x)
- Logarithmic differentiation for y = [f(x)]g(x) forms
- Parametric differentiation: dydx = dy/dtdx/dt
- Mean Value Theorem and Rolle's Theorem - Exemplar reserves 3 LA questions specifically for these
How Collegedunia's Exemplar Solutions Help Class 12 Students Score Better
The NCERT Exemplar Class 12 Maths Continuity and Differentiability address this in the same order as the NCERT textbook.
Most students hit a wall when the Exemplar moves from textbook-style differentiation to mixed problems combining inverse trig with logarithms or parametric forms. Our solutions don't skip algebra steps - every substitution and every cancellation is shown so that you build the same step-by-step muscle the board examiner rewards in 5-mark questions.
- All 58 Exemplar problems solved with full reasoning, not just final answers
- Method-of-choice notes (when to prefer log differentiation vs chain rule)
- Common-mistake callouts on every problem with a known trap
- Alternate methods on long-answer questions where multiple approaches exist
- Quick-recall formula strip at the start of each section
Sample Exemplar Problem Walkthrough: Differentiability at a Point
The NCERT Exemplar Class 12 Maths Continuity and Differentiability address this in the same order as the NCERT textbook.
A representative Exemplar SA question asks: Show that the function f(x) = |x - 3| is continuous but not differentiable at x = 3. Our solution lays out both halves of the proof end to end so the student sees exactly what an examiner expects.
Step 1 (Continuity): Evaluate left limit, right limit, and f(3) . All three equal 0, so f is continuous at x = 3.
Step 2 (Differentiability): Compute left-hand derivative = -1 and right-hand derivative = +1 . Since LHD ≠ RHD, f is not differentiable at x = 3.
This single problem covers both halves of the NCERT Exemplar Class 12 Maths Continuity and Differentiability title and is exactly the template CBSE uses for 3-mark questions in the Boards.
NCERT Exemplar Class 12 Maths Chapter 5: Previous Year Board Repeats
The table below maps Exemplar problems that have shown up almost verbatim in CBSE Board papers across the last five years. Students should solve these first before attempting the rest of the Exemplar bank.
| Year | Exemplar Source | CBSE Board Marks | Topic |
|---|---|---|---|
| 2025 | Exemplar Q.42 (LA) | 5 | Logarithmic differentiation of xx |
| 2024 | Exemplar Q.35 (SA) | 3 | Continuity of piecewise function |
| 2023 | Exemplar Q.18 (MCQ) | 1 | Derivative of inverse trig |
| 2022 | Exemplar Q.41 (LA) | 5 | Parametric differentiation |
| 2021 | - | - | - |
Common Mistakes Students Make in Continuity and Differentiability
The NCERT Exemplar Class 12 Maths Continuity and Differentiability are written in formal mathematical notation, line by line, in the same convention as the official NCERT print.
- Forgetting to check f(a) is defined before checking the two-sided limit - students lose 1 mark on a 3-mark continuity question for this.
- Applying chain rule but missing the inner derivative on inverse trig functions.
- Confusing e x and 10 x in differentiation rules.
- Not simplifying inverse trig expressions before differentiation (e.g. tan-12x1-x2 = 2tan-1 x ).
- Skipping the LHD = RHD check when asked to prove differentiability at a corner point.
Other Resources for Class 12 Maths Chapter 5
- NCERT Solutions for Class 12 Maths Chapter 5 Continuity and Differentiability
- NCERT Notes for Class 12 Maths Chapter 5 Continuity and Differentiability
- Handwritten Notes for Class 12 Maths Chapter 5
- Formula Sheet for Class 12 Maths Chapter 5
NCERT Exemplar Solutions for Class 12 Maths: All Chapters
The table below summarises the recent CBSE Class 12 pattern for this chapter and is a quick pre-exam reference.
| Chapter | Exemplar Solutions |
|---|---|
| Chapter 5 | Continuity and Differentiability Exemplar Solutions |
| Chapter 1 | Relations and Functions Exemplar Solutions |
| Chapter 2 | Inverse Trigonometric Functions Exemplar Solutions |
| Chapter 3 | Matrices Exemplar Solutions |
| Chapter 4 | Determinants Exemplar Solutions |
| Chapter 6 | Application of Derivatives Exemplar Solutions |
| Chapter 7 | Integrals Exemplar Solutions |
| Chapter 8 | Application of Integrals Exemplar Solutions |
| Chapter 9 | Differential Equations Exemplar Solutions |
NCERT Exemplar Class 12 Maths Continuity and Differentiability: available above as a free PDF download, aligned to the 2026-27 NCERT Class 12 Mathematics syllabus.
Student Feedback - Continuity and Differentiability 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 Continuity and Differentiability - Frequently Asked Questions
Ques. How many questions are in the NCERT Exemplar Class 12 Maths Chapter 5?
Ans. Chapter 5 of the NCERT Exemplar contains 58 problems split as 33 short / long answer questions, 15 MCQs, 5 fill-in-the-blanks, and 5 true / false statements.
Ques. Is NCERT Exemplar enough for JEE Main Continuity and Differentiability?
Ans. The Exemplar covers about 75% of the JEE Main difficulty range for this chapter. Pair it with previous-year JEE questions and a focused 30 problem set on parametric / implicit differentiation for full coverage.
Ques. Are NCERT Exemplar problems repeated in CBSE Board exams?
Ans. Yes. CBSE has reused Exemplar problems verbatim or with slight number changes in 2022, 2023, 2024 and 2025 Board papers for this chapter.
Ques. What is the most important topic in Class 12 Maths Chapter 5 Exemplar?
Ans. Logarithmic differentiation and second-order derivatives carry the highest weightage. Together they account for around 40% of the Exemplar questions and roughly 5 of the 8 marks in CBSE boards.
Ques. How should students use the NCERT Exemplar Solutions for Chapter 5?
Ans. First attempt every problem independently with a 30-minute timer, then check the solution. Mark every question where you used a different method and revisit it the next day. This active-recall pattern is what builds exam speed.
Ques. Can I download the Class 12 Maths Chapter 5 Exemplar Solutions PDF for free?
Ans. Yes. Collegedunia's Class 12 Maths Chapter 5 Continuity and Differentiability Exemplar Solutions PDF is free to download and aligned to the latest 2026-27 NCERT syllabus.
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