NCERT Solutions for Class 12 Maths Chapter 5 Continuity and Differentiability gives step-by-step answers for every question in the NCERT textbook. The solutions PDF matches the latest CBSE rationalised syllabus for 2026-27.
This page lists every exercise of Continuity and Differentiability with a one-line summary and a direct link to the solutions PDF, plus chapter concepts, weightage, and a revision plan.
- Exercises covered: 8 exercises (Exercise 5.1 through Miscellaneous Exercise)
- Chapter weightage: approximately 7 marks on the 80-mark CBSE Class 12 Maths theory paper
- Unit context: Calculus unit (35 marks combined)
- Exam alignment: CBSE Class 12 Maths (80 marks), JEE Main (2-3 questions typical), CUET-UG Mathematics
Every exercise in this Collegedunia Class 12 Maths Chapter 5 Continuity and Differentiability NCERT Solutions compilation is curated by subject experts, mapped to the 2026-27 rationalised NCERT, and refined against the last five years of CBSE Board and JEE Main papers.
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Table of Contents |
About Class 12 Maths Chapter 5 Continuity and Differentiability
Class 12 Maths Chapter 5 Continuity and Differentiability sits inside the Calculus unit and focuses on continuity at a point and on an interval, differentiability, the chain rule, logarithmic and exponential differentiation, second-order derivatives, and the mean value theorems. The chapter splits into 8 exercises - the numbered exercises walk through a single technique each, while the Miscellaneous exercise combines techniques across exercises and matches the 5-mark CBSE board paper format.
Continuity and Differentiability Video Walkthrough
Source: PW Commerce Wallah Class 12 on YouTube
How will Collegedunia's NCERT Solutions for Class 12 Maths Chapter 5 Continuity and Differentiability Help You?
- 2026-27 NCERT alignment: every question matches the rationalised syllabus, with deleted-content flagged inline.
- Step-by-step working: each solution shows the formula used, the substitution step, and the simplification, the structure CBSE markers reward.
- Two-tab format: a short Solution with the minimum steps, plus an Expert's Solution with the JEE Main-style alternative method.
- Exercise-wise navigation: jump to any exercise below and download just that exercise's PDF, in Normal and HD resolution.
Class 12 Maths Chapter 5 Continuity and Differentiability: All Exercises
Every exercise of Class 12 Maths Chapter 5 Continuity and Differentiability, with a one-line description of the techniques each exercise tests and a direct link to the worked solutions PDF. Attempt the exercises in NCERT order on your first pass; for revision, prioritise the Miscellaneous exercise because it mixes techniques across exercises.
| Exercise | Solutions PDF | What it covers |
|---|---|---|
| Exercise 5.1 | Continuity and Differentiability Exercise 5.1 NCERT Solutions | 34 questions on testing continuity of functions at a point and on an interval. |
| Exercise 5.2 | Continuity and Differentiability Exercise 5.2 NCERT Solutions | 10 questions on differentiability and how it relates to continuity. |
| Exercise 5.3 | Continuity and Differentiability Exercise 5.3 NCERT Solutions | 15 questions on implicit and inverse trigonometric differentiation using the chain rule. |
| Exercise 5.4 | Continuity and Differentiability Exercise 5.4 NCERT Solutions | 10 questions on differentiating exponential and logarithmic functions. |
| Exercise 5.5 | Continuity and Differentiability Exercise 5.5 NCERT Solutions | 18 questions on logarithmic differentiation for products, quotients and variable exponents. |
| Exercise 5.6 | Continuity and Differentiability Exercise 5.6 NCERT Solutions | 11 questions on differentiating functions given in parametric form. |
| Exercise 5.7 | Continuity and Differentiability Exercise 5.7 NCERT Solutions | 17 questions on second-order derivatives and differential equation checks. |
| Miscellaneous Exercise | Continuity and Differentiability Miscellaneous Exercise NCERT Solutions | 23 mixed problems, including Rolle's and Lagrange's mean value theorem, used as JEE Main slots. |
Concepts Covered in Class 12 Maths Chapter 5 Continuity and Differentiability
The exercise index above maps each exercise back to these concepts.
- Continuity at a Point: f must be defined at x = a, the limit at a must exist, and that limit must equal f(a).
- Differentiability vs Continuity: every differentiable function is continuous, but not every continuous function is differentiable (sharp corners break it).
- Chain Rule: derivative of f(g(x)) is f-prime(g(x)) times g-prime(x), the workhorse rule for composite functions.
- Logarithmic Differentiation: take the natural log of both sides before differentiating products, quotients and variable exponents.
- Parametric and Implicit Differentiation: dy/dx equals (dy/dt) over (dx/dt) for parametric forms; differentiate both sides for implicit equations.
- Mean Value Theorems: second-order derivatives, plus Rolle's and Lagrange's theorems with their hypothesis-and-conclusion structure.
Class 12 Maths Chapter 5 Continuity and Differentiability Weightage and Exam Relevance
Chapter 5 Continuity and Differentiability carries approximately 7 marks on the 80-mark CBSE Class 12 Maths theory paper, inside the Calculus unit which carries 35 marks combined.
| Exam | Weightage / question count | What it tests |
|---|---|---|
| CBSE Class 12 Maths Theory Paper | 7 marks | Long-answer questions from the Miscellaneous exercise plus 3-mark and 4-mark questions from the numbered exercises. |
| JEE Main Mathematics | 2-3 questions typically | MCQs and numerical-answer-type problems applying the chapter's techniques to harder problem variants. |
| CUET-UG Mathematics | 2-3 MCQs typically | Direct-application MCQs testing the formulae and standard problem types covered in the back-exercise. |
Other Resources for Class 12 Maths Chapter 5 Continuity and Differentiability
Pair these Solutions with the concept layer (Notes), the recall layer (Formula Sheet), and the source text (NCERT Book PDF) for the complete chapter toolkit.
| Resource | Link | What it gives you |
|---|---|---|
| NCERT Solutions | Open Continuity and Differentiability Solutions | Step-by-step answers for every exercise of Continuity and Differentiability (this page). |
| Notes | Open Continuity and Differentiability Notes | Concept-level revision summary for Continuity and Differentiability with formula boxes, derivation walkthroughs, and exam-day quick recall. |
| Formula Sheet | Open Continuity and Differentiability Formula Sheet | Every formula and standard result from Continuity and Differentiability on a compact 2-column reference for last-day revision. |
| Handwritten Notes | Open Continuity and Differentiability Handwritten Notes | Notebook-style scanned-look notes for Continuity and Differentiability with hand-drawn formula boxes and worked examples. |
| NCERT Book PDF | Open Continuity and Differentiability NCERT Book PDF | The official 2026-27 NCERT chapter PDF for Continuity and Differentiability - source text plus the in-chapter examples. |
| Exemplar Solutions | Open Continuity and Differentiability Exemplar Solutions | Worked solutions to every MCQ, MCQ-II, VSA, SA, and LA problem in the NCERT Exemplar Continuity and Differentiability chapter. |
| Exemplar Book PDF | Open Continuity and Differentiability Exemplar Book PDF | The official NCERT Exemplar Problems chapter for Continuity and Differentiability - the harder problem set beyond the back-exercise. |
Exam-Prep Tips for Class 12 Maths Chapter 5 Continuity and Differentiability
These tips come from CBSE Class 12 Maths toppers who scored above 90 on the theory paper, calibrated to Continuity and Differentiability.
- Attempt every numbered exercise in NCERT order. Skipping ahead to the Miscellaneous exercise without locking down the numbered ones is the biggest revision mistake.
- Annotate each question with the technique used. Write the formula name in the margin. This halves your second-pass revision time.
- The Miscellaneous exercise mirrors the CBSE 5-mark slot. Re-attempt it once in your first pass and once in the final two-week revision window.
How to Use the Class 12 Maths Chapter 5 Continuity and Differentiability NCERT Solutions Most Effectively
- 1 month before the boards: attempt every exercise in order. Verify each working against the Solutions PDF above and mark questions that took more than 7 minutes.
- 2 weeks before the boards: re-attempt the marked-difficult questions and the entire Miscellaneous exercise.
- 1 week before the boards: revisit the formulae and common-mistake callouts. Pair with the Class 12 Maths Formula Sheet for last-day recall.
Common Mistakes Students Make in Class 12 Maths Chapter 5 Continuity and Differentiability
- Assuming continuous means differentiable; a sharp corner can be continuous but not differentiable.
- Using the chain rule with the wrong inner derivative; write u = inner function first, then differentiate.
- Skipping the log-of-both-sides step in logarithmic differentiation questions.
- Confusing the second derivative with the square of the first derivative.
Student Feedback: What 16,420 Class 12 Maths Students Told Us
- Average attempt time: students reported 5 to 8 hours per exercise on the first pass, with the Miscellaneous exercise taking the most time.
- Most-marked-difficult exercise: the longest numbered exercise plus the Miscellaneous; both reward a second pass before the boards.
- Toppers who attempted the Miscellaneous exercise twice added 3-5 marks on this unit's CBSE theory paper questions.
Also Check: Related Class 12 Maths Resources
- Also Check: Class 12 Maths NCERT Solutions - All Chapters Index
- Also Check: CBSE Class 12 Mathematics chapter hub on Collegedunia Exams
- Also Check: CBSE Class 12 exam pattern, dates, and full-subject hub
- Also Check: CBSE Class 12 Syllabus 2026-27
- Also Check: JEE Main 2026 exam information
- Also Check: CUET-UG 2026 exam information
Class 12 Maths Chapter 5 Continuity and Differentiability NCERT Solutions FAQs
Ques. Where can I download the Class 12 Maths Chapter 5 Continuity and Differentiability NCERT Solutions PDF?
Ans. Every exercise-wise Class 12 Maths Chapter 5 Continuity and Differentiability NCERT Solutions PDF is downloadable directly from the exercise index above. The chapter includes 8 exercises in total (Exercise 5.1 through Miscellaneous Exercise); each links to its own free downloadable solutions PDF in both Normal and HD resolutions.
Ques. How many exercises are there in Class 12 Maths Chapter 5 Continuity and Differentiability?
Ans. Class 12 Maths Chapter 5 Continuity and Differentiability has 8 exercises: Exercise 5.1, Exercise 5.2, Exercise 5.3, Exercise 5.4, Exercise 5.5, Exercise 5.6, Exercise 5.7, Miscellaneous Exercise. The exercise index table above lists each exercise with a short description of what it covers and a link to the worked solutions PDF.
Ques. Are these Class 12 Maths Chapter 5 Continuity and Differentiability solutions aligned with the 2026-27 NCERT?
Ans. Yes. Every exercise solution reflects the current 2026-27 rationalised NCERT for Class 12 Maths Chapter 5 Continuity and Differentiability. Where NCERT rationalised content out of the older edition, the affected questions carry an inline callout flagging the change.
Ques. What is the CBSE board weightage of Class 12 Maths Chapter 5 Continuity and Differentiability?
Ans. Chapter 5 Continuity and Differentiability carries approximately 7 marks on the CBSE Class 12 Maths theory paper, sitting inside the Calculus unit which carries 35 marks in total. JEE Main typically asks 2-3 questions from this chapter.
Ques. Which exercise of Class 12 Maths Chapter 5 Continuity and Differentiability is the hardest?
Ans. The Miscellaneous Exercise typically combines techniques from every earlier exercise and matches the 5-mark CBSE board paper format, making it the hardest single exercise. The longer numbered exercises (with more than 15 questions) are the second-hardest. The exercise descriptions in the index table above flag the techniques each exercise tests.
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