Binomial Theorem Class 11 CBSE Maths Chapter 8

Class 11 CBSE Maths Syllabus
Chapter 1:Sets
Chapter 2: Relations and Functions
Chapter 3: Trigonometric Functions
Chapter 4: Principles of Mathematical Induction
Chapter 5: Complex Numbers and Quadratic Equations
Chapter 6: Linear Inequalities
Chapter 7: Permutations and Combinations
Chapter 8: Binomial Theorem
Chapter 9: Sequences and Series
Chapter 10: Straight lines
Chapter 11: Conic Sections
Chapter 12: Introduction to 3D
Chapter 13: Limits and Derivatives
Chapter 14: Mathematical Reasoning
Chapter 15: Stastics
Chapter 16: Probability

Introduction

Following are the concepts which will be covered in this chapter:

Factorial Notation.
Representation of Binomial Expression.
Binomial Expression.
Expansion of (x+a)n
Expansion of (x-a)n
Examples of Mixed surds
Definition of parameters in the binomial theorem
rth term of binomial expansion.
Examples of finding binomial coefficient
Middle term of binomial expansion
Greatest coefficient binomial theorem
Numerically greatest term
Binomial coefficients
Properties of Binomial coefficients
Summation of Binomial coefficients
Multiplication of Binomial coefficients of same series
Multiplication of Binomial coefficients of different series
Binomial theorem for negative and fractional index
Multinomial Theorem
Pascal’s Triangle
Referring to the important points of a specific exercise helps a student to get a gist of the entire exercise.
- An expression consisting of two terms, connected by ++ or −- sign is called binomial expression.
- If x and a are real numbers, then for all n∈N, we have (x+a)n=nC0xna0+nC1xn−1a1+nC2xn−2a2+…..+nCrxn−rar+….+nCnx0an i.e, (x+ a)n= ∑nr=0 nCr xn-r ar.
- A Binomial Theorem for a positive integer has (n+1)n+1 terms.
- The sum of the indices of x and a in each term is n.
- The coefficients of terms equidistant from the beginning and the end are equal.