NCERT Class 11 Maths Binomial Theorem

Read and download NCERT Class 11 Maths Binomial Theorem in NCERT book for Class 11 Mathematics. You can download latest NCERT eBooks chapter wise in PDF format free from Studiestoday.com. This Mathematics textbook for Class 11 is designed by NCERT and is very useful for students. Please also refer to the NCERT solutions for Class 11 Mathematics to understand the answers of the exercise questions given at the end of this chapter

NCERT Book for Class 11 Mathematics Chapter 8 Binomial Theorem

Class 11 Mathematics students should refer to the following NCERT Book Chapter 8 Binomial Theorem in Class 11. This NCERT Book for Class 11 Mathematics will be very useful for exams and help you to score good marks

Chapter 8 Binomial Theorem NCERT Book Class 11

 

8.1 Introduction
In earlier classes, we have learnt how to find the squares and cubes of binomials like a + b and a – b. Using them, we could evaluate the numerical values of numbers like (98)2 = (100 – 2)2, (999)3 = (1000 – 1)3, etc. However, for higher powers like (98)5, (101)6, etc., the calculations become difficult by using repeated multiplication. This difficulty was overcome by a theorem known as binomial theorem. It gives an easier way to expand (a + b)n, where n is an integer or a rational number. In this Chapter, we study binomial theorem for positive integral indices only.

8.2 Binomial Theorem for Positive Integral Indices

Let us have a look at the following identities done earlier:

(a+ b)0 = 1       a + b ≠ 0

(a+ b)1 = a + b

(a+ b)2 = a2 + 2ab + b2

(a+ b)3 = a3 + 3a2b + 3ab2 + b3

(a+ b)4 = (a + b)3 (a + b) = a4 + 4a3b + 6a2b2 + 4ab3 + b4

In these expansions, we observe that

(i) The total number of terms in the expansion is one more than the index. For example, in the expansion of (a + b)2 , number of terms is 3 whereas the index of (a + b)2 is 2.

(ii) Powers of the first quantity ‘a’ go on decreasing by 1 whereas the powers of the second quantity ‘b’ increase by 1, in the successive terms.

(iii) In each term of the expansion, the sum of the indices of a and b is the same and is equal to the index of a + b

 

Please refer to attached file for NCERT Class 11 Maths Binomial Theorem

z Appendix 1: Infinite Series
NCERT Class 11 Maths Infinite Series
z Appendix 2: Mathematical Modelling
NCERT Class 11 Maths Mathematical Modelling

NCERT Book Class 11 Mathematics Chapter 8 Binomial Theorem

The above NCERT Books for Class 11 Mathematics Chapter 8 Binomial Theorem have been published by NCERT for latest academic session. The textbook by NCERT for Chapter 8 Binomial Theorem Mathematics Class 11 is being used by various schools and almost all education boards in India. Teachers have always recommended students to refer to Chapter 8 Binomial Theorem NCERT etextbooks as the exams for Class 11 Mathematics are always asked as per the syllabus defined in these ebooks. These Class 11 Chapter 8 Binomial Theorem book for Mathematics also includes collection of question. Along with Mathematics Class 11 NCERT Book in Pdf for Chapter 8 Binomial Theorem we have provided all NCERT Books in English Medium for Class 11 which will be really helpful for students who have opted for english language as a medium. Class 11 students will need their books in English so we have provided them here for all subjects in Class 11.

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