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Subject specialists have created NCERT Exemplar Solutions for Class 11 Maths Chapter 4:Principle of Mathematical Induction, which includes thorough solutions for reference. All unsolved questions from the textbook’s exercises are answered here. The NCERT Exemplar Solutions for Class 11 provide useful solutions for improving conceptual knowledge and help in entrance examinations like** JEE mains and advanced**.

The solutions are carefully solved using student-friendly terms while still adhering to the norms that must be followed when solving NCERT Exemplar Solutions for Class 11. Practicing these answers can be incredibly advantageous not only in terms of exams but also in terms of helping Class 11 pupils perform well in upcoming competitive exams.

The approaches for answering have been given special consideration to stay on target while not deviating from the intended answer. Because time is so important in exams, excellent time management when answering questions is essential for getting the best results.

This chapter consists of only one exercise and this will help students in learning the concepts based on the Principle of Mathematical Induction through the given solutions. The topic and subtopics that are discussed in Chapter 4 Principle of Mathematical Induction of NCERT Exemplar Solutions for Class 11 is listed below:

**4.1 Introduction: NCERT Exemplar Solutions for Class 11 Maths Chapter 4**

In this section, deductive reasoning with suitable examples and also the assumptions that are based on certain universal facts are explained.

**4.2 Motivation**

Here, the students learn about mathematical induction with the help of a real-life scenario which helps them to understand its basic working.

**4.3 The Principle of Mathematical Induction**

Here, the Principle of Mathematical Induction is explained by using the inductive steps and the inductive hypothesis.

Let us suppose the statement is P(n), where n is a natural number.

- If n = 1 then the statement is true, it means P(1) is true.
- If the statement n = k (where k is some positive integer) is true, then the statement n = k + 1 is also true, which means, the truth of P(k) implies the truth of P (k + 1).

**Key Features of NCERT Exemplar Solutions for Class 11 Maths Chapter 4- Principle of Mathematical Induction**

After learning the Principle of Mathematical Induction of Class 11 students are able to know about the Steps involved in the proof of induction. Students also learn about the applications and principles of mathematical induction from the given solutions of NCERT questions. The concepts explained and used in the solutions of this chapter are as follows:

- Deductive reasoning is one of the basic keys to mathematical thinking. Until we have observed each and every case it depends on working with different cases and developing a conjecture by observing incidences. Hence, in simple words ‘induction’ is the generalization from particular cases or facts.
- The principle of mathematical induction is a tool that is used to prove a large number of mathematical statements. Let us suppose each statement is P(n), where n is a positive integer in which n=1 examines that the case is correct. Therefore, if P(k) is true for some positive integer k, then P (k+1) is also true.

**Frequently Asked Questions**

##### Explain the first principle of Mathematical Induction in Chapter 4 of NCERT Exemplar Solutions for Class 11 Maths.

The first principle of Mathematical Induction states that both the base step and inductive step are true, for all natural numbers. Many kinds of problems that are based on this concept are available in the NCERT textbook of Class 11. Exercise-wise problems and their solutions are also available which helps students to score well in the annual exam.

##### Why is the NCERT Exemplar Solutions for Class 11 Maths Chapter 4 PDF important from the exam point of view?

The NCERT Exemplar Solutions for Class 11 Maths Chapter 4 gives better concepts about the induction and deduction techniques with the help of which equations and statements are proved. With the help of solutions students get clear knowledge about the principle and applications of Mathematical Induction. These solutions will increase the confidence level among students who are preparing for the Class 11 exams.

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