NCERT Solutions for Class 12 Maths Chapter 5 Miscellaneous Exercise: The NCERT Solutions for Class 12 Maths Chapter 5 miscellaneous exercise contains practice questions for all the topics explained in the chapter, which is Continuity and Differentiability. Students can benefit considerably from the miscellaneous exercise Chapter 5 Class 12 as they can practice the whole chapter in one go. It tests students’ basic understanding of the concepts explained throughout the chapter.

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• CBSE Class 12 Maths Exam Date – on 11th March 2023
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• List of Best Books for Maths CBSE Class 12

Chapter 5 Continuity and Differentiability Class 12 Maths is a continuation of the topic Differentiation of Functions studied in Class 11. Students will learn about essential concepts of continuity, differentiability and relations between them. Students are advised to practice all the in-text questions and the miscellaneous exercise Chapter 5 Class 12 to develop a strong foundation.

NCERT Solutions for Class 12 Maths Chapter 5 Miscellaneous Exercise: Chapter Overview

In the Chapter 5 Continuity and Differentiability Class 12 Maths, students get to learn about differentiation of inverse trigonometric functions and new topics like functions called exponential and logarithmic functions. These functions teach powerful techniques of differentiation. The concepts are illustrated with certain geometrically obvious conditions through differential calculus. Students will learn some fundamental theorems related to these concepts in the process.

The NCERT Solutions for Class 12 Maths Chapter 5 miscellaneous exercise has questions ranging from differentiation of functions, proving that a particular equation is a constant independent of two variables, justifying whether there is a continuous function everywhere but not differentiable at exactly two points, etc. In short, the Continuity and Differentiability Class 12 miscellaneous exercise prepares students to solve any question that can be asked in this chapter.

Before we move to the NCERT solutions for miscellaneous exercise Chapter 5 Class 12 Maths, students can check the overview of the topics and subtopics covered in the Continuity and Differentiability Class 12 Maths Chapter 5:

Sr no.	Topic no.	Topic name
1	5.1	Introduction
2	5.2	Continuity
3	5.2.1	Algebra of continuous functions
4	5.3	Differentiability
5	5.3.1	Derivatives of composite functions
6	5.3.2	Derivatives of implicit functions
7	5.3.3	Derivatives of inverse trigonometric functions
8	5.4	Exponential and Logarithmic Functions
9	5.5	Logarithmic Differentiation
10	5.6	Derivatives of Functions in Parametric Forms
11	5.7	Second Order Derivative
12	5.8	Mean Value Theorem

NCERT Solutions for Class 12 Maths Chapter 5 Miscellaneous Exercise PDF

Mathematics is a subject in which just understanding the concepts is insufficient. Students must solve plenty of practice questions to apply the concepts to solutions correctly. For this purpose, the Class 12 Maths NCERT Solutions PDF for Chapter 5 is the best way to ensure that students have questions to practice all the topics taught in Continuity and Differentiability. 

The easiest way to learn, practice and test the Continuity and Differentiability Class 12 is to solve the miscellaneous exercise Chapter 5 Class 12 and clarify doubts from teachers or Embibe. The Continuity and Differentiability NCERT Solutions Class 12 Maths exam preparation can be smooth and effective by practising the miscellaneous exercise Chapter 5 Class 12 Maths. It will help students gain basic knowledge of the topic and enable them to solve the questions accurately.

Sometimes questions are directly asked from the NCERT textbooks and Solutions. Here, students who have practised the NCERT Solutions for Class 12 Chapter 5 miscellaneous exercise can score full marks on those questions. This is where the Class 12 Maths NCERT Solutions PDF also comes in handy for offline practice.

Students can download and refer to Continuity and Differentiability Class 12 Maths NCERT Solutions PDF format from below and start practising:

Continuity and Differentiability Class 12: Chapter Concepts

While studying chapter 5, Continuity and Differentiability Solutions are required to learn a few key factors which will help them prepare for the exams well. The miscellaneous exercise Chapter 5 Class 12 Continuity and Differentiability can be effectively solved by following the specific rules which the students study in this chapter. 

Students must abide by these rules while solving the NCERT Solutions miscellaneous exercise and other intext questions. Below are the essential details are given below:

• A real-valued function is continuous at a point in its domain if the limit of the function at that point equals the value of the function at that point. A function is continuous if it is continuous on the whole of its domain.
• Every differentiable function is continuous, but the converse is not true.
• Logarithmic differentiation is a powerful technique to differentiate functions of the form f (x) = [u (x)]v (x). Both f(x) and u (x) need to be positive for this technique to make sense.
• Rolle’s Theorem: If f : [a, b] → 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 ′(c) = 0.
• Mean Value Theorem: If f : [a, b] → 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) – f(a))/(b-a).
• The differential function follows a continuous pattern which may not be the same for the converse. 
• The continuous function’s difference, sum, quotient, and product will always be constant.

Advantages of Solving NCERT Solutions for Class 12 Maths Chapter 5 Miscellaneous Exercise

There are several benefits of solving the NCERT solutions for Class 12 Maths Chapter 5 miscellaneous exercise. Some of the most considerable benefits are given below:

1. The NCERT Solutions for Class 12 Maths Chapter 5 have been created by Embibe’s subject matter experts.
2. The Continuity and Differentiability NCERT Solutions can be downloaded and practised at the convenience of students. Embibe has enabled easy and download so that students can study without any obstacles.
3. The miscellaneous exercise Chapter 5 Class 12 contains extensive questions written in comprehensive language to allow students to understand them clearly and apply relevant mathematical rules. 
4. The Continuity and Differentiability Class 12 Maths Chapter 5 NCERT Solutions have in-depth solutions and simplifications for every question. It enables students to check their answers and make improvements accordingly.
5. By referring to the NCERT Solutions for Class 12 Maths Chapter 5 pdf, students can understand the concept of differentiation of inverse trigonometric functions and new topics like functions called exponential and logarithmic functions.
6. Miscellaneous exercise Chapter 5 Class 12 are prepared as per CBSE and NCERT’s latest guidelines to keep the students updated with all the recent changes in the syllabus.
7. Practicing the Continuity and Differentiability NCERT solutions can help students gain efficiency in solving the questions and prevent making silly mistakes during the final Maths exam.
8. Students can independently solve the miscellaneous exercise Chapter 5 Class 12 at home and refer to the solutions to check their progress. This can be an excellent exercise to build self-confidence in Maths.
9. Students should study from the Class 12 Maths NCERT textbooks and NCERT solutions together to clear the basics and immediately solve related questions for all-around preparation.

CBSE Class 12 Maths NCERT Solutions All Chapters PDF

In this article, we have provided all the important information regarding the NCERT Solutions for Class 12 Maths Chapter 5 miscellaneous exercise. Students are advised to practice the intext questions as well as the miscellaneous exercise to build a strong foundation in the chapter. Students can also download the NCERT Solutions Class 12 Maths pdf for all chapters from the table below:

Chapter no.	NCERT Solutions Class 12 Maths	Download link
1	NCERT Solutions Class 12 Maths Chapter 1 Relations and Functions	Download Here
2	NCERT Solutions Class 12 Maths Chapter 2 Inverse Trigonometric Functions	Download Here
3	NCERT Solutions Class 12 Maths Chapter 3 Matrices	Download Here
4	NCERT Solutions Class 12 Maths Chapter 4 Determinants	Download Here
5	NCERT Solutions Class 12 Maths Chapter 5 Continuity and Differentiability	Download Here
6	NCERT Solutions Class 12 Maths Chapter 6 Application of Derivatives	Download Here
7	NCERT Solutions Class 12 Maths Chapter 7 Integrals	Download Here
8	NCERT Solutions Class 12 Maths Chapter 8 Application of Integrals	Download Here
9	NCERT Solutions Class 12 Maths Chapter 9 Differential Equations	Download Here
10	NCERT Solutions Class 12 Maths Chapter 10 Vector Algebra	Download Here
11	NCERT Solutions Class 12 Maths Chapter 11 Three Dimensional Geometry	Download Here
12	NCERT Solutions Class 12 Maths Chapter 12 Linear Programming	Download Here
13	NCERT Solutions Class 12 Maths Chapter 13 Probability	Download Here

FAQs on NCERT Solutions for Class 12 Maths Chapter 5 Miscellaneous Exercise

Q.1. Which topics are covered in Continuity and Differentiability Class 12 Chapter 5 Maths?
Ans. In Continuity and Differentiability Class 12 Chapter 5 Maths, students will learn with the following important topics:

1. Continuity
2. Algebra of Continuous Functions
3. Differentiability
4. Derivatives of Composite Functions
5. Derivatives of Implicit Functions
6. Inverse Trigonometric Functions Derivatives
7. Exponential and Logarithmic Functions
8. Logarithmic Differentiation
9. Derivatives of Functions in Parametric Forms
10. Second-Order Derivative
11. Mean Value Theorem

Q.2. Why should students practice the Embibe miscellaneous exercise Chapter 5 Class 12 Maths?
Ans. The Embibe Continuity and Differentiability NCERT Solutions Chapter 5 Class 12 Maths are curated designed by subject experts. Practising these questions will enable students to solve any kind of question in the actual board exam. Students will be able to know in which topic they need to do more practice or topics in which they need clearer conceptual understanding. 

Q.3. Where can I download the Class 12 Maths NCERT Solutions pdf?
Ans. Students can download the Class 12 Maths NCERT Solutions PDF from this page. We have also provided direct links to download NCERT Solutions Class 12 Maths all chapters in this article. All the pdfs can be easily downloaded on students’ computer on mobile phone for. 

Q.4. Is the Chapter 5 Continuity and Differentiability Class 12 Maths difficult?
Ans. Class 12 Maths follows a moderate difficulty level. Students preparing for the exam need to ensure that they follow the important textbooks and solutions that will help to make their preparation easy. CBSE Class 12 Maths is a continuation of most of the chapters from Class 11. Therefore, the students can easily solve the papers when their basics in Class 11 are clear. 

Q.5. Is solving the miscellaneous exercise chapter 5 Class 12 enough for board exam?
Ans. The NCERT Solutions for Class 12 Maths Chapter 5 miscellaneous exercise helps students to obtain proper understanding of each topic. With a proper strategic approach in learning the concepts, students can improve their speed and accuracy in solving the questions.