NCERT Solutions for Class 11 Maths Chapter 4: How is your preparation going for the Class 11 Annual Exam? Awesome, isn’t it? We know you are working really hard to secure a good position in he final exam and we are here to assist you with some useful information in relation to NCERT Solutions for Class 11 Maths Chapter 4 – Principle of Mathematical Induction.
In this blog you will get to see the various aspects of NCERT Chapter 4 Solutions for Class 11 Maths which will boost your level of confidence. The sections that we will be highlighting here are related to the overview of Chapter 4 NCERT Solutions along with the benefits of referring to those solutions. You will also get topic wise/ exercise wise explanations which will leave you with zero queries. Read all the sections of the blog slowly.
NCERT Solutions for Class 11 Maths Chapter 4 Principle of Mathematical Induction
Mathematical induction is a mathematical technique which is used to prove results or establishing statements incase of natural numbers. The technique is applied to verify whether a statement, theorem or formula is true for every natural number. In the Chapter 4 NCERT Solutions for Class 11 Maths the students will get to explore the process of the proof through Induction techniques. This chapter will be beneficial for the students who want to understand application of the method by considering the natural numbers as the least inductive subset of real numbers.
In the NCERT textbook all the concepts related to the principles of mathematical Induction have been handled with extra bit of care. When you focus on the various answers you will be ready to face any kind of problems from this chapter. You will also notice the new pattern which the experts have followed while shaping the NCERT solutions Chapter 4. You can ask for Class 11 Maths Chapter 4 NCERT Solutions PDF files from your friends to improve your methods of preparation.
You can download CBSE NCERT Solutions for Class 11 Maths Chapter 4 from below.
What will you learn in CBSE Class 11 Maths Chapter 4 Principle of Mathematical Induction?
You will come across the questions from the following sub topics in the NCERT solutions-
Here are the topics/ subtopics of the chapter:
- Principle of Mathematical Induction
- The Principle of Mathematical Induction
CBSE Class 11 Maths Chapter 4 Exercise-wise listing
There are a total of 4 exercises along with miscellaneous exercise. You can expect solutions from each exercise.
- Exercise 4.1 consists of questions with solutions
- Exercise 4.2 consists of questions with solutions
- Exercise 4.3 consists of questions with solutions
- Exercise 4.4 consists of questions with solutions
- The miscellaneous exercise consists of questions with solutions
NCERT Solutions For Class 11 Maths Chapter 4 Exercise 4.1
Class 11 Maths NCERT Solutions Chapter 4 Exercise 4.1 focuses on the problems which are associated deductive reasoning. For example, the students will be provided a logical question or an argument in three or more statements, and students are required find out if the statements are true or false. All the NCERT solutions Chapter 4 in connection with deductive reasoning have been presented in a way which will be easier to understand. Here the students need to prove a statement with the help of deductive steps.
CBSE Class 11 Maths NCERT Solutions Chapter 4 Exercise 4.2
In this exercise you will be asked to solve questions which are based on motivation. The experts have highlighted various solutions and you just need to understand the basics of motivation first to solve questions with confidence. For example, you will be given a set of square tiles and will be asked to derive a statement based on your understanding of the tiles and actions. When you push the first time ultimately all the tiles tend to fall. To derive the statement is sufficient for you to know that when the first tile falls, the successor tiles will also fall along with it. Your conception will be cleared after you examine the solutions in the NCERT textbook. You will have to face those kind of questions and you will be asked to check if the statements which have been made are true or false
CBSE Class 11 Maths NCERT Solutions Chapter 4 Exercise 4.3
In this exercise you will gain knowledge regarding the techniques which are required to prove a formula and you will also know about the ways an equation is derived. You will also be in a position to apply the right kind of logic by checking the statement. The other things which you will learn from the NCERT solutions Chapter 4 are proving a formula with positive integers and then looking for the solutions for the rest formulas in a given equation. The experts have taken care of each section in the NCERT textbook while providing the best possible explanations and all you need to do is observe.
NCERT Solutions For Class 11 Maths Chapter 4 Exercise 4.4
Class 11 Maths NCERT Solutions Chapter 4 Exercise 4.4 consists of the various questions along with the right kind of solutions. Here you will be able to test your understanding in relation to the principle of Mathematical induction, when you start solving different questions on this particular topic you will know how to make proper use of the formulas and you will also know about the ways to derive. You can always check the answers when you face any kind of problems.
NCERT Solutions For Class 11 Maths Chapter 4 Miscellaneous Exercise
In this part you will get all the answers of the complex questions. Here you will have to deal with all kinds of questions which are based on the concepts of Mathematical Induction. When you go through the NCERT textbook all your doubts or confusions will be cleared and you will be able to attempt more questions on this topic. You need to allocate a separate timeslot n order to practice sums on Induction. Consider Chapter 4 NCERT Solutions as your guide.
Theorems and formulas used in 11 Maths Chapter 4 Principle of Mathematical Induction
Consider a statement P(n), where n is a natural number. Then to determine the validity of P(n) for every n, use the following principle:
- Step 1: Check whether the given statement is true for n = 1.
- Step 2: Assume that given statement P(n) is also true for n = k, where k is any positive integer.
- Step 3: Prove that the result is true for P(k+1) for any positive integer k.
- If the above-mentioned conditions are satisfied, then it can be concluded that P(n) is true for all n natural numbers.
The first step of the principle is a factual statement and the second step is a conditional one. According to this if the given statement is true for some positive integer k only then it can be concluded that the statement P(n) is valid for n = k + 1.
This is also known as the inductive step and the assumption that P(n) is true for n=k is known as the inductive hypothesis.
The different principles of Mathematical Induction of Class 11 help the students to examine the process of the proof via induction, motivating the application of the method by looking at natural numbers as the least inductive subset of real numbers.
The concept used in the solutions of this chapter are:
- One key basis for mathematical thinking is deductive reasoning. In contrast to deduction, inductive reasoning depends on working with different cases and developing a conjecture by observing incidences until we have observed each and every case. Thus, in simple language we can say the word ‘induction’ means the generalization from particular cases or facts
- The principle of mathematical induction is one such tool which can be used to prove a wide variety of mathematical statements. Each such statement is assumed as P(n) associated with positive integer n, for which the correctness of the case n = 1 is examined. Then assuming the truth of P(k) for some positive integer k, the truth of P (k+1) is established.
Advantages of following NCERT Solutions for Class 11 Maths Chapter 4
There are different kinds of benefits for referring to the NCERT Solutions for Class 11 Maths Chapter 4 Principle of Mathematical Induction and now we will talk about those solutions. You must collect it after you finish your syllabus.
- The students will be able to prepare themselves in a better way when they go through the contents of the solutions.
- The students will be able to cross all the hurdles in connection with Principals of Mathematical Induction without any kind of fear.
- All the chapters have been explained with proper illustrations and if you examine the contents carefully you will be left with zero queries.
- You will get new ideas to improve your methods of preparation and that is the beauty of following solutions.
- Shaping study materials becomes easier for you when you are ready with solutions.
- You get to new inputs to prepare for your competitive exams.
We have covered the complete guide on CBSE NCERT Solutions For Class 11 Maths Chapter 4 Principle of Mathematical Induction. Feel free to ask us any questions in the comment section below.