This page hosts the NCERT Exemplar Class 12 Maths Continuity and Differentiability, presenting it for Class 12 Mathematics Chapter 5 Continuity and Differentiability. The NCERT Exemplar Class 12 Maths Continuity and Differentiability carry the higher-order practice questions that the NCERT itself recommends after the booklet chapter, and several of the items in the PDF recur in JEE Main shifts.
- 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
Student Pulse - 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.
This NCERT Exemplar chapter is the standard problem bank for JEE Main and CUET Maths aspirants. Collegedunia's download of the official 2026-27 Exemplar print is the same file the NCERT publishing department circulates, with every objective, fill-in-the-blank, true/false, and long-answer problem intact.
NCERT Exemplar Class 12 Maths Chapter 5: What's Inside
The NCERT Exemplar Class 12 Maths Continuity and Differentiability address this in the same order as the NCERT textbook.
The Exemplar chapter is split into a Solved Examples block followed by an Exercise block. The Exercise block is what students are tested on; the Solved Examples block sets up the standard methods. Both sections are essential - skipping the examples leaves students unable to attempt the harder Exercise problems.
| Section | Content | Count |
|---|---|---|
| 5.1 | Overview (concept and formula recap) | 1 section |
| 5.2 | Solved Examples (Short and Long Answer) | 22 examples |
| 5.3 | Exercise - Short Answer | 20 problems |
| 5.3 | Exercise - Long Answer | 13 problems |
| 5.3 | Objective Type - MCQ | 15 problems |
| 5.3 | Fill in the Blanks | 5 problems |
| 5.3 | True / False | 5 problems |
Continuity and Differentiability NCERT Exemplar Video Walkthrough
Source: NCERT Wallah on YouTube
Why the NCERT Exemplar Class 12 Maths Chapter 5 PDF Matters
The Exemplar is published by NCERT, not by a third party. CBSE Board examiners are explicitly told to pick from the NCERT Exemplar Class 12 Maths Continuity and Differentiability and the Exemplar, which is why Exemplar problems show up almost yearly. For JEE Main, the Exemplar is the closest free resource to a real exam problem set.
- CBSE 2025 Class 12 Maths boards reused Exemplar Q.42 verbatim for a 5-mark Long Answer.
- JEE Main 2024 January session recycled an Exemplar MCQ on derivative of inverse trig.
- The Exemplar's True / False section directly trains the Assertion-Reason MCQ format on Boards.
- Fill-in-the-blank questions train students for the new CBSE 1-mark short-form questions.
How Collegedunia's Exemplar Book PDF Helps Class 12 Students
Collegedunia hosts the unedited 2026-27 print of this Exemplar chapter as a free download. The download keeps the page numbering and the NCERT Exemplar Class 12 Maths Continuity and Differentiability section headings identical to the printed book, so any teacher or coaching reference using page numbers will align cleanly.
- Finish the main NCERT Chapter 5 first; never start Exemplar before that.
- Solve all 22 Solved Examples on paper before opening the Exercise.
- Attack MCQ + Fill in the Blanks + True/False as a 45 minute timed set.
- Tackle SA problems next, allocating 5-7 minutes per problem.
- Save LA problems for a separate 90 minute block; these are board-paper level difficulty.
- Cross-check every solution against Collegedunia's Exemplar Solutions PDF.
Class 12 Maths Chapter 5 Exemplar: Problem Difficulty Spread
The NCERT Exemplar Class 12 Maths Continuity and Differentiability address this in the same order as the NCERT textbook.
Not every Exemplar problem is hard. The spread of difficulty is what makes the Exemplar a great daily-practice resource - students can start with the MCQ block on a low-energy revision day and save the LA block for a focused weekend session.
| Problem Type | Difficulty | Recommended Time |
|---|---|---|
| MCQ | Easy to Medium | 1-2 min each |
| Fill in the Blanks | Easy | 1 min each |
| True / False | Medium | 1-2 min each |
| Short Answer | Medium | 5-7 min each |
| Long Answer | Hard | 10-15 min each |
Related Resources for Class 12 Maths Chapter 5
The NCERT Exemplar Class 12 Maths Continuity and Differentiability address this in the same order as the NCERT textbook.
- NCERT Exemplar Solutions for Class 12 Maths Chapter 5 Continuity and Differentiability
- NCERT Solutions for Class 12 Maths Chapter 5
- NCERT Notes for Class 12 Maths Chapter 5
- Formula Sheet for Class 12 Maths Chapter 5
NCERT Exemplar Book PDF 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 Book PDF |
|---|---|
| Chapter 1 | Relations and Functions Exemplar Book PDF |
| Chapter 2 | Inverse Trigonometric Functions Exemplar Book PDF |
| Chapter 3 | Matrices Exemplar Book PDF |
| Chapter 4 | Determinants Exemplar Book PDF |
| Chapter 6 | Application of Derivatives Exemplar Book PDF |
| Chapter 7 | Integrals Exemplar Book PDF |
| Chapter 8 | Application of Integrals Exemplar Book PDF |
| Chapter 9 | Differential Equations Exemplar Book PDF |
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.
Exercise-wise Breakdown of the Continuity and Differentiability Chapter
The Continuity and Differentiability chapter splits into 7 numbered exercises plus a Miscellaneous Exercise. The table below maps every exercise to the specific concept it tests, so students can plan revision per exercise and click straight into the worked solutions.
| Exercise | Topic Tested |
|---|---|
| Exercise 5.1 | Continuity at a point and on an interval |
| Exercise 5.2 | Algebra of continuous functions |
| Exercise 5.3 | Differentiability and chain rule |
| Exercise 5.4 | Derivatives of inverse trigonometric functions |
| Exercise 5.5 | Logarithmic differentiation |
| Exercise 5.6 | Parametric and implicit differentiation |
| Exercise 5.7 | Second-order derivatives; Rolle's and Mean Value Theorem |
| Miscellaneous Exercise | Mixed continuity and differentiability problems |
PDF Download Formats and Languages for the Continuity and Differentiability Chapter
The Continuity and Differentiability Class 12 PDF on this page is available in three formats - each suited to a different revision style. The table below summarises what each format is best for:
| Format | Best for | Approx. size |
|---|---|---|
| Normal-resolution PDF | Phone reading, quick revision between classes | 2-3 MB |
| HD PDF | Print-ready, desk study, board hall photocopy | 8-10 MB |
| Handwritten Notes PDF | Mirrors how a topper writes the chapter under Sunday-revision pace | 5-7 MB |
The continuity and differentiability class 12 ncert pdf and the parallel Hindi-medium edition both follow the same notation and equation numbering as the printed NCERT 2026-27 release. Key points students should know:
- NCERT-faithful: Every definition, theorem and exercise on the continuity and differentiability class 12 ncert pdf matches the printed textbook line for line.
- Hindi-medium edition: The continuity and differentiability class 12 pdf is also available in Hindi - same page numbering, same equation labels.
- Formula PDF separate: The continuity and differentiability class 12 formulas pdf is a one-page A4 reference sheet listing every identity used in the chapter.
- Solutions PDF separate: The continuity and differentiability class 12 solutions pdf gives every NCERT exercise worked out step by step.
- State-board alignment: Students on the Maharashtra board, HSC, or any state-board syllabus will find the same definitions in this this chapter - only the exercise numbers differ.
Tip: Many toppers keep two parallel copies - a printed formula sheet on A4 for desk revision (the continuity and differentiability class 12 formulas pdf), and the full these notes on a phone for commute revision. Both files are free and linked above.
Important Questions and Previous Year Trends for the Continuity and Differentiability Chapter
The most repeated question patterns in CBSE Class 12 Maths for the Continuity and Differentiability chapter have settled into a stable cluster across 2019 to 2024 boards. Three question templates account for over 80% of the marks this chapter contributes:
| Template | Typical Marks | What it tests |
|---|---|---|
| Proof / property verification | 3 marks | Students show that a given relation/function/expression satisfies the chapter's definitions. |
| One-step computation | 2 marks | Substitution-based item: plug into a known formula and simplify. |
| Case-study scenario | 4 marks | Real-world setup applying the chapter's definitions, introduced in CBSE 2021+ papers. |
Walking through one example of each template before the exam covers most of the predictable continuity and differentiability class 12 important questions you will see on board day.
- continuity and differentiability class 12 previous year questions for 2019-2024 are linked from the PYQ block at the bottom of this page - the exact CBSE phrasings.
- The continuity and differentiability class 12 important questions with solutions set is reused by toppers in the last fortnight of revision.
- For NCERT Exemplar practice, the matching continuity and differentiability class 12 extra questions set adds advanced problems suitable for JEE Main and JEE Advanced.
- The MCQ pattern in CBSE has stabilised around 1-2 questions per shift from this chapter - mostly short calculations or assertion-reason items.
Year-wise PYQ Distribution
The table below maps the dominant question type asked from the Continuity and Differentiability chapter across recent CBSE Class 12 Maths boards:
| Year | Dominant Question Type | Approx. Marks |
|---|---|---|
| 2024 | Property verification + case-study item | 5-6 marks |
| 2023 | Computation with proof + assertion-reason MCQ | 5-6 marks |
| 2022 | Long-answer derivation + 2-mark substitution | 5-7 marks |
| 2021 | Definition recall + property check | 4-5 marks |
| 2020 | One-step computation + 3-mark proof | 5 marks |
The full continuity and differentiability class 12 important questions with solutions set (every year, every paper, every question type) is linked from the PYQ page at the bottom of this article.
How the Continuity and Differentiability Notes Pair with NCERT Solutions and the Formula Sheet
The Continuity and Differentiability Class 12 notes work best when paired with two sister resources from the Class 12 Maths hub. The table below shows how each resource fits into a typical revision week:
| Resource | Use it for | When |
|---|---|---|
| Continuity and Differentiability Notes (this page) | Theory, definitions, exam patterns | First pass, before practice |
| continuity and differentiability class 12 ncert solutions PDF | Step-by-step solved exercises | Second pass, during NCERT practice |
| continuity and differentiability class 12 formulas PDF | One-page identity recall | Third pass, alongside mock papers |
| Handwritten Notes PDF | Quick reading in topper's handwriting | Anytime, especially commute revision |
Around 60 percent of the chapter's scoring vocabulary appears on all three pages, so cross-resource use reinforces recall without adding study time.
- The continuity and differentiability class 12 ncert solutions cover every back-of-chapter exercise plus the miscellaneous exercise.
- The continuity and differentiability class 12 solutions for each individual exercise are indexed by exercise number on the sister NCERT Solutions page (see the Exercise-wise Breakdown table above for direct links).
- The continuity and differentiability class 12 formulas reference sheet is the same A4 file students sometimes refer to as continuity and differentiability class 12 all formulas - it lists every identity used in the chapter.
- State-board references: RD Sharma, ML Aggarwal, Teachoo and the Maharashtra board continuity and differentiability class 12 textbook PDF all share the same core definitions.
- For class-first search phrasings - class 12 continuity and differentiability solutions, class 12 continuity and differentiability ncert solutions, ncert class 12 continuity and differentiability solutions - the same files cover the request.
Reference Books and State-Board Mapping
Students using reference books beyond NCERT, or studying under a state board, can map this chapter cleanly:
| Reference | How it maps to the resource |
|---|---|
| RD Sharma Class 12 Continuity and Differentiability | Question patterns overlap with NCERT at ~70%; an advanced supplement. |
| ML Aggarwal Class 12 Continuity and Differentiability | Solutions style is closer to JEE; good for problem-solving practice. |
| Teachoo the chapter notes | Free online walkthroughs; useful for video-style learning. |
| Shaalaa the PDF solutions | State-board (Maharashtra HSC) phrasings; same core definitions. |
| Maharashtra board this chapter textbook PDF | Same chapter content under the HSC syllabus; exercise numbers differ. |
| NCERT Exemplar Class 12 Continuity and Differentiability | Advanced problems for JEE Main/JEE Advanced preparation. |
How to Use the Continuity and Differentiability Notes Page Most Effectively
The recommended study plan for these notes chapter splits across three sittings. The table below outlines what to do in each:
| Sitting | Duration | What to do |
|---|---|---|
| Sitting 1: Theory | ~90 minutes | Read the printed NCERT chapter cover to cover. Mark every definition and theorem statement. Then read the formula recall section on this page. |
| Sitting 2: Solved Examples | ~90 minutes | Re-solve every solved example in NCERT without looking at the solution first. Compare your steps against the printed working. Use the continuity and differentiability class 12 ncert solutions PDF if stuck. |
| Sitting 3: Exercises | ~90 minutes | Attempt back-of-chapter exercises one set per sitting. Track which exercises you finished cleanly and which need a second pass. Click into the linked exercise pages above for verification. |
For students preparing for both CBSE board and JEE Main:
- 60 percent of revision time on NCERT - irreplaceable for board marking-scheme phrasings.
- 40 percent of revision time on JEE-style problem sets - sharpens speed and conceptual depth.
- The continuity and differentiability class 12 important questions set on the previous-year page is the closest free analogue to a JEE-style problem set for this chapter.
- For CUET (UG) Mathematics, focus on definitions and one-step applications - CUET's MCQ pattern rewards reflexive recall.
Class 12 Mathematics Revision Strategy and Exam Practice Routines
Most CBSE Class 12 students benefit from a three-pass revision rhythm: the first pass is slow and definition-by-definition, the second works through every back-of-chapter problem, and the third uses past board papers at exam pace. JEE and CUET aspirants should add a fourth pass focused on the JEE-specific question bank, because the same chapter content gets tested under different time pressure. Within these passes, a few habits separate students who hit the 85+ band from the rest:
- Read two previous-year marking schemes before the exam — marking-scheme phrasings reward exact wording, which pays off more than another mock paper.
- Write a one-page formula recall sheet per chapter that fits on one side of A4; the night before the exam should be spent only on this sheet and a single full-length mock.
- Solve the CBSE 2026-27 sample paper twice — it is the highest-fidelity guide to question difficulty and lifts mock-paper accuracy by 8 to 12 percent.
- Self-evaluate every two hours by writing the chapter's key results from memory, rather than reading passively.
- Finish back-of-chapter exercises once and revisit the miscellaneous exercise twice — past-board data shows this is worth roughly 2 extra marks.
Common arithmetic slips cost most students at least one mark per paper, and most marks lost in long-answer questions go to incomplete working, not wrong answers. Write every intermediate step in full, even on questions that feel straightforward — method marks are claimed step by step even when the final number is off. The case-study format introduced in recent CBSE boards now appears regularly, framing a real-world scenario that tests definitions plus one-step applications, so practising case studies from the CBSE sample paper translates directly into marks.
Time allocation in the last fortnight matters most. Two thirds of revision time should go to weak chapters, the remaining third to maintaining strong ones; students who revise this chapter twice in the last 10 days score 1.5 to 2 marks higher on past boards. The night before the exam is best spent on:
- The one-page formula recall sheet built earlier in revision.
- A single full-length mock paper at exam timing.
- Avoid learning any new material the night before — sleep matters more.
Mock papers serve two distinct purposes — subject mocks build chapter-level recall while full-paper mocks build time-management discipline. Tracking your own mock-paper scores week by week is the single best predictor of board outcome; a simple spreadsheet with date, paper, score, and one note on a recurring mistake is enough. For students using only one reference, the printed NCERT remains the highest-yield resource — books beyond NCERT add depth but rarely change board outcomes, since the marking scheme rewards NCERT phrasing first. Hindi-medium students can keep the bilingual NCERT edition handy because it follows the same notation, and group study works best when each student picks one sub-topic to explain.
Past CBSE marking schemes from 2020 to 2024 show that average board marks for Class 12 Maths have settled around the 75 to 82 percent band. Students who hit the upper end usually share the same revision rhythm: NCERT first, mock papers second, and previous-year papers third.
NCERT Exemplar Class 12 Maths Continuity and Differentiability - Frequently Asked Questions
Ques. How many pages is the NCERT Exemplar Class 12 Maths Chapter 5?
Ans. The Chapter 5 Continuity and Differentiability section of the 2026-27 NCERT Exemplar runs to 22 pages including solved examples and exercises.
Ques. How many problems are in the Class 12 Maths Chapter 5 Exemplar?
Ans. The chapter contains 58 problems split as 22 solved examples plus an exercise block of 33 SA/LA problems, 15 MCQs, 5 fill-in-the-blanks, and 5 true/false questions.
Ques. Is the Class 12 Maths Exemplar harder than the NCERT textbook?
Ans. Yes. The Exemplar is set deliberately a level above the NCERT Exemplar Class 12 Maths Continuity and Differentiability to prepare students for the harder questions on CBSE Boards, JEE Main, and CUET.
Ques. Is the Exemplar PDF free to download?
Ans. Yes. this resource hosts the official NCERT Exemplar print for Class 12 Maths Chapter 5 as a free, no-login download.
Ques. Should JEE aspirants do the Class 12 Maths Chapter 5 Exemplar?
Ans. Yes. Roughly 6-8% of the JEE Main Maths section comes from the NCERT Exemplar Class 12 Maths Continuity and Differentiability, and the Exemplar problems are the closest free resource to actual exam difficulty.
Ques. Where do I find solutions to the NCERT Exemplar Class 12 Maths Chapter 5?
Ans. this resource publishes the full step-by-step solutions to every Exemplar problem in this chapter as a free PDF. The solutions are linked at the top of the Related Resources section above.
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