Binomial Theorem Class 11th Notes - Free NCERT Class 11 Maths Chapter 8 notes - Download PDF

Binomial Theorem belongs to the 8 chapter of NCERT. The NCERT Class 11 Maths chapter 8 notes entirely cover up the main portions of the chapter Binomial Theorem. In the introduction Binomial Theorem Class 11 notes we will learn about how we can find an expanded form of an expression with an index. Binomial Theorem Class 11 notes describe how we get pascal’s triangle from the expansion of where n=1, 2, 3. Class 11 Math chapter 8 notes cover the main topics that are a number of terms of an expansion, how to use combination formula to the expanded form, the middle term of when n is an even or odd.

A Class 11 Math chapter 6 notes help you to find the entire chapter in an easy way. NCERT Notes for Class 11 Maths chapter 6 not only covers the NCERT notes but covers CBSE Class 11 Maths chapter 8 notes also.

After going through Class 11 Binomial Theorem notes

Students can also refer to,

• NCERT Solutions for Class 11 Maths Chapter 8 Binomial Theorem
• NCERT Exemplar Class 11 Maths Chapter 8 Binomial Theorem

NCERT Class 11 Maths Chapter 8 Notes

We know,

If we observe each expansion,

• The total number of terms of each expansion is 1 more than the index of.

• In the expansion, the power of the first quantity is gradually decreasing that is by 1 and the power of the second quantity is gradually increased that is by 1.

• Suppose n is the index of , then the sum of indices of a and b of each term of the expansion is n.

Now arranging of the coefficients of expansion with respect to their index

Index Coefficients

If we observe the pattern we can get the coefficient of the next index.

The pattern is given below

Figure: 1

This diagram is known as Pascal’s triangle.

If we apply Pascal’s triangle rule, then the coefficients of will be

1 5 10 10 5 1

Similarly, the coefficient of will be

1 6 15 20 15 6 1

Now we can apply the combination formula to find the coefficients.

Binomial coefficient (for a Positive integral index n ) where n and r are a positive integer and .

Figure 2 can be rewritten as

Index Coefficients

Binomial Theorem:

Binomial theorem for any positive integer n

Proof:

We will proof the theorem by using principal induction.

Let

Putting

For it is true.

Assume that it is true for

We will prove that i.eis true by using.

Now,

Add like terms

Now apply the formula,, and

Hence proved.

Properties of Binomial coefficient

1.

2.

and

hence prove both are equal.

3. If only if and

4.

5. If n is a positive integer and x, y are two complex numbers, then

Here are binomial coefficients.

6. Total no. of terms of the given as (n + 1) in the expansion

To find the middle terms of using the binomial theorem

The general equation of the binomial is given as

There are two case

1. If n is odd

The number of terms of when is an odd number is. Here is an even number. So there will be two middle terms. That are and of the expansion.

2. If n is even

The number of terms of when is an eve number is. Here is an odd number. So there will be one middle term. That is of the expansion.

To find the sum of the coefficient of the binomial terms we have to put the value of x numerical is one.

For example

Q if the binomial express is then find the sum of the binomial coefficient is?

Solution:- Write the given expression now we have to put the value of and get The coefficient sum =

=

= 1

So Sum of the binomial coefficient is 1.

Some Properties of the Binomial coefficients

Put

Put

Some Particular expansions

Significance of NCERT Class 11 Math Chapter 8 Notes

Class 11 Binomial Theorem notes will be really helpful to revise the chapter and get a brief overview of the important topics. Also, notes for Class 11 Maths chapter 8 is useful for covering Class 11 CBSE Maths Syllabus and also for competitive exams like BITSAT, and JEE MAINS. Class 11 Maths chapter 8 notes pdf download can be used for preparing in offline mode.

Binomial Theorem Class 11 notes pdf download: link

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Subject Wise NCERT Exemplar Solutions

• NCERT Exemplar Class 11 Solutions
• NCERT Exemplar Class 11 Maths
• NCERT Exemplar Class 11 Physics
• NCERT Exemplar Class 11 Chemistry
• NCERT Exemplar Class 11 Biology

Subject Wise NCERT Solutions

• NCERT Solutions for Class 11 Mathematics
• NCERT Solutions for Class 11 Chemistry
• NCERT Solutions for Class 11 Physics

• NCERT Solutions for Class 11 Biology

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