NCERT Books for Class 11

July 4, 202239 Insightful Publications

**NCERT Solutions for Class 11 Maths Chapter 4 Principle of Mathematical Induction:** The fourth chapter of Class 11 Maths explains about the Principle of Mathematical Induction. In this article, we have provided NCERT Solutions prepared by Embibe’s subject experts as per the latest guidelines to help students score good in this chapter.

The NCERT Solutions for Class 11 Maths Chapter 4 have been prepared in a detailed step-wise manner to help students understand concepts and practise the in-text questions. Students can download the NCERT Solutions for Class 11 Maths to revise the solutions in offline mode as well. For better practice, one must understand the various concepts in Class 11 Maths Chapter 4. Read on to find more.

This chapter explains what mathematical induction is and how it works. This is explained with the help of examples. The principle of mathematical Induction states that to prove a statement about every natural number n, there are two things to verify. If the statement is true for n = k, it will be correct for its successor, k + 1. Besides, the sum of first n odd numbers is equivalent to the natural number nth square.

This topic explains the assumption that was made, based on certain universal facts. In simple language, one can say that induction means the generalisation of particular cases or facts. Students can check the important topics covered in NCERT Class 11 Maths Chapter 4 from the table below:

Exercise No. | Important Topics |
---|---|

4.1 | Introduction |

4.2 | Motivation |

4.3 | The Principle of Mathematical Induction |

We have provided some important points that are covered in NCERT Class 11 Maths Chapter 4 to help students in their exam preparations. Refer to the list below:

- A sentence or description which can be judged to be true or false is called a statement. Statements involving mathematical relations are called mathematical statements.
- The proposition or statement P(n) can be proved by the principle of mathematical induction for n∈N as discussed in the following three steps:
- The first step is also termed as the basic step of induction in which we prove that the proposition P(n) is true for the smallest positive integer or the first natural number i.e, for n = 1. This is also called the verification step.
- The next step is the induction step in which the proposition is assumed to be true for some n = k ≥ 1 i.e, we assume P(k) to be true.
- The last step is the generalisation step. If P(k) is true, then the proposition is proved true for n = k + 1 i.e, for the next positive integer or the next natural number.
- Thus, P(n) is true for all n∈N.

Students can get more important points for NCERT Class 11 Maths Chapter 4 Principle of Mathematical Induction on Embibe for free!

The NCERT Solutions for Class 11 Maths are listed below to help students with their exam preparations:

**1st Chapter: Sets****2nd Chapter: Relations and Functions****3rd Chapter: Trigonometric Functions****4th Chapter: Principle of Mathematical Induction****5th Chapter: Complex Numbers and Quadratic Equations****6th Chapter: Linear Inequalities****7th Chapter: Permutations and Combinations****8th Chapter: Binomial Theorem****9th Chapter: Sequences and Series****10th Chapter: Straight Lines****11th Chapter: Conic Sections****12th Chapter: Introduction to Three Dimensional Geometry****13th Chapter: Limits and Derivatives****14th Chapter: Mathematical Reasoning****15th Chapter: Statistics****16th Chapter: Probability**

**Ans:** For the final exam of CBSE Class 11, the NCERT Maths is enough. Just make sure to solve previous year questions as well. However, for competitive engineering exams, like JEE (Main and Advanced, BITSAT, etc., you have to practice from some other advanced books as well.

**Ans:** Embibe provides free NCERT Solutions for 11th Maths all chapters for free.

** Ans:** Yes, all solutions provided by Embibe are available for free.

**Ans**: The principle of mathematical Induction states that to prove a statement about every natural number n, there are two things to verify. The process of proving a statement consists of two steps.

a. Base Step

b. Inductive step.

**Ans**: The NCERT Class 11 Chapter 4 have 3 topics and exercises, topics are as follows:

a. Introduction

b. Motivation

c. The Principle of Mathematical Induction

The free downloads of all the exercise solutions are provided in the article.