# NCERT Solutions for Class 12 Maths Chapter 5 Continuity and Differentiability

## NCERT Solutions for Class 12 Maths Chapter 5 â€“ Free PDF Download

The NCERT Solutions for Class 12 Maths Chapter 5 Continuity and DifferentiabilityÂ provide solutions to all the questions under the chapter (All Exercises and Miscellaneous Exercise solutions). These NCERT Solutions for Class 12 Maths have been carefully compiled and developed, keeping into consideration the latest update on CBSE Syllabus 2023-24. Students can access these NCERT Solutions for Class 12 and strengthen their fundamentals.

Subject experts at BYJUâ€™S have created the NCERT Solutions for Class 12 Maths to help students while solving or practising problems. Further, all the solutions are in accordance with the latest CBSE Syllabus. Students can download the PDF of the NCERT Solutions for Class 12 Maths Chapter 5 from the link given below.

### NCERT Solutions for Class 12 Maths Chapter 5 Continuity and Differentiability

In this chapter of NCERT Solutions for Class 12 Maths, students will deal with continuity and differentiability problems solutions that contain questions based on proving an equation is continuous if given with different values of â€˜xâ€™.

Also, we will examine certain functions of continuity and generate conclusions. Students will come across explanations for the different types of questions, where they will be provided with the reasons if one quantity is replaced with different values. Students can utilise the NCERT Solutions for Class 12 Maths Chapter 5 for any quick references to comprehend complex topics.

#### Some of the important concepts from the Class 12 NCERT Maths Chapter5 are listed below

• The sum, difference, product and quotient of continuous functions are continuous.
• Every differentiable function is continuous, but the converse is not true.
• Rolleâ€™s Theorem: If f : [a, b] â†’ R is continuous on [a, b] and differentiable on (a, b) such that f(a) = f(b), then there exists some c in (a, b) such that f â€²(c) = 0
• Mean Value Theorem: If f : [a, b] â†’ R is continuous on [a, b] and differentiable on (a, b). Then there exists some c in (a, b) such that f'(c) = (f(b) â€“ f(a))/(b-a)

NCERT Solutions for Class 12 Maths Chapter 5 Exercises

Get detailed solutions for all the questions listed under the below exercises.

Exercise 5.1 Solutions: 34 Questions (Short Answers)

Exercise 5.2 Solutions: 10 Questions (Short Answers)

Exercise 5.3 Solutions: 15 Questions ( Short Answers)

Exercise 5.4 Solutions: 10 Questions (Short Answers)

Exercise 5.5 Solutions: 18 Questions ( Short Answers)

Exercise 5.6 Solutions: 11 Questions (Short Answers)

Exercise 5.7 Solutions: 17 Questions (Short Answers)

Exercise 5.8 Solutions: 6 Questions (Short Answers)

Miscellaneous Exercise Solutions: 23 Questions (6 Long, 17 Short)

### NCERT Solutions for Class 12 Maths Chapter 5 Continuity and Differentiability

The main topics covered in NCERT Solutions for Class 12 Chapter 5, Continuity and Differentiability, are

 Exercise Topic 5.1 Introduction 5.2 Continuity 5.3 Differentiability 5.4 Exponential and Logarithmic Functions 5.5 Logarithmic Differentiation 5.6 Derivatives of Functions in Parametric Forms 5.7 Second Order Derivative 5.8 Mean Value Theorem Others Miscellaneous Q&A

### Key Features of NCERT Solutions for Class 12 Maths Chapter 5 Continuity and Differentiability

1. NCERT Solutions are valuable material for the students to clear their doubts and score well.
2. Simple and easy language is used.
3. Each and every concept of the chapter is covered.
4. NCERT Solutions will help the students to strengthen their basics of Continuity and Differentiability.
5. NCERT Solutions will help in boosting studentsâ€™ confidence levels.

Students can also access the NCERT Solutions from BYJUâ€™S for other classes and subjects while studying or preparing for their examinations.

DisclaimerÂ Â

Dropped Topics â€“Â Examples 22 and 23, Example 27, 5.8 Mean Value Theorem, Exercise 5.8 and Miscellaneous Example 44 (ii), Ques. 19 (Miscellaneous Exercise) and Summary points 5 (derivatives of cot-1 x, sec-1 x, cosec-1 x), 7 and 8

## Frequently Asked Questions on NCERT Solutions for Class 12 Maths Chapter 5

Q1

### What are the topics covered in Chapter 5 of NCERT Solutions for Class 12 Maths?

Chapter 5 of Class 12 NCERT Maths deals with Continuity and Differentiability. It is one of the important chapters in Class 12 as the concepts are continued in higher classes also. Continuity, differentiability, exponential and logarithmic functions, logarithmic differentiation, derivatives of functions in parametric forms, second-order derivative and mean value theorem are some of the important concepts covered in the chapter.
Q2

### How many exercises are in Chapter 5 of NCERT Solutions for Class 12 Maths?

There are 8 exercises in the chapter, and the number of questions in each exercise is mentioned below.
Exercise 5.1 â€“ 34 questions
Exercise 5.2 â€“ 10 questions
Exercise 5.3 â€“ 15 questions
Exercise 5.4 â€“ 10 questions
Exercise 5.5 â€“ 18 questions
Exercise 5.6 â€“ 11 questions
Exercise 5.7 â€“ 17 questions
Exercise 5.8 â€“ 6 questions
Miscellaneous Exercise â€“ 23 questions
Q3

### Why should I choose NCERT Solutions for Class 12 Maths Chapter 5?

The NCERT Solutions designed by the experts at BYJUâ€™S offers several benefits for the students preparing for their board exams. Each and every topic provides an in-depth explanation to help students score well. The solutions are based on the latest syllabus of the CBSE 2023-24. Apart from the Class 12 board exams, these solutions also help students to prepare for various other competitive exams like JEE Main, JEE Advanced, etc.