CBSE Class 12 Mathematics NCERT Exemplar Solutions: Chapter Continuity and Differentiability
Rahul TomarThe NCERT Exemplar books are very important for engineering entrance exams like JEE Main, WBJEE and UPSEE as the level of the questions are very high. The questions given at the end of the chapter are very important for board exams also. Sometimes, students got confused while solving the questions given in NCERT Exemplar books. In this article, we providing you NCERT Exemplar Solutions Class 12 Mathematics Chapter 5 – Continuity and Differentiability Students can take help from these solutions if they stuck while solving any question. The solutions are presented in the most appropriate and simple way for easy understanding.
What topics will you read in chapter  Continuity and Differentiability?
Concept of continuity and differentiability 
Derivative of Composite functions 
Differentiation of Inverse trigonometric functions 
Derivative of Implicit functions 
Concept of exponential & logarithmic functions 
Derivative of functions expressed in parametric forms 
Second order derivatives 
Rolle's Theorem 
Lagrange's Mean Value Theorem 
Few problems along with their solutions from this chapter are given follows:
Question:
Examine the continuity of the function f (x) = x^{3} + 2x^{2}  1 at x = 1.
Solution:
Question:
An example of a function which is continuous everywhere but fails to be differentiable exactly at two points is ........ .
Solution:
An example of a function which is continuous everywhere but fails to be differentiable exactly at two points is x + x – 1. The functions is continuous everywhere but fails to be differentiable exactly at two points x = 0 and x = 1.
Question:
If f is continuous on its domain D, then  f  is also continuous on D.
Solution: True
If a function is continuous on its domain, then the modulus of the function is also continuous in the same domain.
Hence,  f is also continuous on D.
Question:
The composition of two continuous functions is a continuous function.
Solution: True
The composition of two continuous functions is also a continuous function
Question:
Trigonometric and inverse trigonometric functions are differentiable in their respective domain.
Solution: True
All the trigonometric and inverse trigonometric functions are differentiable in their respective domain.
Students can download the complete solutions in PDF form using the links given below:
Types 
Number of questions 
Link to download PDF 
Short answer type questions 
78 

Long answer type questions 
4 

Objective type questions 
14 

Fillers type 
5 

True/False type 
5 

Total 
106 

Why students should read Class 12 NCERT Exemplar Books?
 Offers indepth knowledge of each topic.
 Strictly follows the CBSE board curriculum.
 Questions are frequently asked in board exams.
 Important questions are given at the end of each chapter
 NCERT Exemplar books are written in an easy language by experienced teachers and professor having deep understanding of the subject.
 NCERT Exemplar books help students to understand the basics and fundamentals
 Contain standard questions plus some extra information for competitive exams.
 Many questions are asked in engineering entrance exams like JEEMain from NCERT Exemplar books.
In this chapter of the book, students will get the following things.
Brief summary of the complete chapter 
Short answer type questions 
Long answer types questions 
Objective type questions or MCQs 
Fill in the blanks 
True and False 
Students can download the complete NCERT Exemplar book from the link given below:
NCERT Exemplar Book Class 12 Maths: Continuity and Differentiability 