# NCERT Exemplar Class 11 Maths Chapter 8 Solutions: Binomial Theorem

NCERT Exemplar Solutions for Class 11 Maths Chapter 8 deal with the process to find the squares and cubes of binomials like p + q and p – q. Using the process, you could easily solve the numerical values of numbers like (99)², (998)³, etc. These NCERT Exemplar Class 11 Maths are a detailed and step-by-step guide to all your queries. Also, the main benefit of these solutions is that you can prepare not only for your academic exams but also for the entrance exams.

Some of the main topics of Chapter 8 – Binomial Theorem include Binomial Theorem for Positive Integral Indices, Pascal’s Triangle, the p the term from the end, Binomial coefficient, and General and Middle Terms. Practising this chapter will make you understand about a binomial theorem in detail.

In the NCERT Exemplar Solutions for Class 11 Maths Chapter 8, there are a total of 3 exercises with 62 questions. The questions from every section are solved perfectly by the subject matter experts at Instasolv. All the exercises consist of different types of questions including the short answer type, long answer type, fill in the blanks, true or false statement, and objective type questions.

## Important Topics for NCERT Maths Exemplar Solutions Class 11 Chapter 8 – Binomial Theorem

**Binomial Expression**

An expression that consists of two terms that are connected by + or – sign is known as binomial expression.

**Binomial Theorem**

If p and q are real numbers and n is a positive integer, the general statement of (x + 1)^{th} term in the expression is denoted by T_{r+1} = ^{n}C_{r} p^{n}-r q^{r}

**Pascal’s Triangle**

The coefficients of the expansions are organized in an array. This array is known as Pascal’s triangle.

**Middle Term in the Expansion of (p + q) ^{n}**

In the expansion of (p + q)^{n}, if n is an even number then the middle term is (n/2 + 1)^{th} term.

In the expansion of (p + q)^{n}, if n is an odd number then the middle terms are (n+1/ 2)^{th} term and (n+1/ 2)^{th} term.

**Method to Prove Binomial Theorem**

In general, there are two methods to prove binomial theorem including:

- Principle of Mathematical Induction.
- Combinatorial Method.

**Factorial Notation**

- n! = 1 x 2 x 3 x 4 x … x n; 0! = 1
^{n}C_{r}=^{n}C_{n-r}^{n}C_{r}= n! / r! (n – r)!^{n}C_{r}+^{n}C_{r-1}=^{n+1}C_{r}

### Exercise-wise Discussion of NCERT Maths Exemplar Solutions Class 11 Chapter 8 – Binomial Theorem

Chapter 8 – Binomial Theorem has a total of 3 exercises with 62 questions. The solution of all these exercises is prepared to focus on learning different math tricks, shortcuts, and tips for quick and easy calculations. The detailed description of these exercises is provided below:

**Exercise 8.1 – Short Answer Type Questions**

Exercise 8.1 of Chapter 8 – Binomial Theorem consists of a total of 11 short answer type questions. These questions are based on the important topics including binomial theorem for positive integral indices, Pascal’s triangle, the pth term from the end, binomial coefficient, and general and middle terms.

**Exercise 8.2 – Long Answer Type Questions**

This exercise consists of a total of 6 questions based on the process to find the squares and cubes of binomials. They are long answer type questions where you will find detailed solutions to the problems. Practising these questions will help you clear your concepts on the binomial theorem.

**Exercise 8.3 – Objective Type Questions**

It is the last exercise of NCERT Exemplar Solutions Class 11 Chapter 8 and is considered a very important exercise from the entrance exam point of view. It contains a total of 24 questions including fill in the blanks, state true or false, or multiple-choice questions. Solving the questions of this exercise will help you understand how clear your concepts are.

## Why Use NCERT Maths Exemplar Solutions Class 11 Chapter 8 – Binomial Theorem by Instasolv?

- NCERT Exemplar Class 11 Maths Chapter 8 contains all the solutions to the maths problems provided in the exemplar textbook of NCERT.
- These solutions are the comprehensive solutions provided by Instasolv which covers the latest syllabus of NCERT.
- These solutions have been prepared by the team of expert teachers.
- The NCERT Exemplar Solutions help you revise the complete chapter in minutes.
- NCERT Exemplar Class 11 Maths Chapter 8 Solutions are available to you on our web page for free.
- Referring to these solutions you can easily prepare for your CBSE as well as entrance exams.