# BINOMIAL THEOREM CLASS 11 MATHS

## Summary

*The expansion of a binomial for any positive *integral* n is given by Binomial Theorem, which is (a + b) ^{n}*

*=*ab

^{n}C_{0}a^{n}+^{n}C_{1}a^{n – 1}b +^{n}C_{2}a^{n – 2}b^{2}+ ... +^{n}C_{n - 1 }

^{n - 1}+^{n}C_{n}b^{n}*The coefficients of the expansions are arranged in an array. This array is called Pascal’s triangle.*

*The general term of an expansion (a + b) ^{n} is T_{r + 1} = ^{n}C_{r}a^{n – r}. b^{r} *

*In the expansion (a + b) ^{n}* ,

*if n is even, then the middle term is the (n/2 + 1)*

^{th}term. If n is odd, then the middle terms are (n + 1)/2 and (n + 1)/2 +1 terms.## Lecture - 1

- Introduction to Binomial Theorem
- Pascal Triangle and Derivation for Binomial Theorem
- NCERT Exercise 8.1 (Q1 to Q3)

## Lecture - 3

- Total number of terms in a Binomial Expansion, General Term of Binomial Expansion, Finding Term in a Binomial Expansion
- NCERT Exercise 8.2 (Q1 to Q6)
- NCERT Exercise 8.2 (Q9 & Q12)

## Lecture - 4

- Method to find Middle term in a Binomial Expansion
- NCERT Exercise 8.2 (Q7, Q8, Q10 & Q11)
- Miscellaneous Exercise (Q2, Q5, Q6 & Q7)

## Lecture - 6

- NCERT Example 4
- NCERT Example 6
- NCERT Example 10
- NCERT Example 11
- NCERT Example 12
- NCERT Example 14
- NCERT Example 15
- NCERT Example 16
- NCERT Example 17