# Binomial Theorem class 11 Notes Mathematics

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## Binomial Theorem class 11 Notes Mathematics

Download CBSE class 11th revision notes for Chapter 8 Binomial Theorem class 11 Notes Mathematics in PDF format for free. Download revision notes for Binomial Theorem class 11 Notes Mathematics and score high in exams. These are the Binomial Theorem class 11 Notes Mathematics prepared by team of expert teachers. The revision notes help you revise the whole chapter in minutes. Revising notes in exam days is on of the best tips recommended by teachers during exam days.

CBSE Class 11 Mathematics
Revision Notes
Chapter-8
Binomial Theorem class 11 Notes Mathematics

1.  Binomial Theorem for Positive Integral Indices

2.  General and Middle Terms

• Binomial Theorem: The expansion of a binomial for any positive integral n is given by Binomial Theorem, which is
${{\left( a+b \right)}^{n}}{{=}^{n}}{{C}_{0}}{{a}^{n}}{{+}^{n}}{{C}_{1}}{{a}^{n-1}}b{{+}^{n}}{{C}_{2}}{{a}^{n-2}}{{b}^{2}}$$+....+^{n}{{C}_{n-1}}a{{b}^{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 $~~{{\left( \text{a }+~\text{b} \right)}^{n}}\ \ is\ {{T}_{r+1}}\ \ {{=}^{n}}{{C}_{r}}{{a}^{n-r}}.{{b}^{r}}$
• The general term of an expansion ${\left( {a - b} \right)^n} = {\left( { - 1} \right)^r}{.^n}{{\rm{C}}_r}.{a^{n - r}}.{b^r}$
• The general term of ${\left( {1 + x} \right)^n}{ = ^n}{{\rm{C}}_r}.{x^r}$
• The general term of ${\left( {1 - x} \right)^n} = {\left( { - 1} \right)^r}{.^n}{{\rm{C}}_r}.{x^r}$
• In the expansion ${{\left( \text{a }+\text{ b} \right)}^{n}}$, if n is even, then the middle term is the  ${{\left( \frac{n}{2}+1 \right)}^{th}}$term. If n is odd, then the middle terms are ${{\left( \frac{n}{2}+1 \right)}^{th}}$and ${{\left( \frac{n+1}{2}+1 \right)}^{th}}$ terms.
• ${r^{th}}$ term from the end in ${\left( {a + b} \right)^n} = {\left( {n + 2 - r} \right)^{th}}$ term fromt he beginning.
• Method to prove Binomial Theorem:

(a) Principle of Mathematical Induction.

(b) Combinatorial Method.

• Factorial notation:
(i) $n! = 1 \times 2 \times 3 \times 4....... \times n;$ $0! = 1$
(ii) ${^n{{\rm{C}}_r} = {{n!} \over {r!\left( {n - r} \right)!}}}$
(iii) $^n{{\rm{C}}_r}{ = ^n}{{\rm{C}}_{n - r}}$
(iv) $^n{{\rm{C}}_r}{ + ^n}{{\rm{C}}_{r - 1}}{ = ^{n + 1}}{{\rm{C}}_r}$

## The Binomial Theorem class 11 Notes

• CBSE Revision notes for Class 11 Mathematics PDF
• CBSE Revision notes Class 11 Mathematics – CBSE
• CBSE Revisions notes and Key Points Class 11 Mathematics
• Summary of the NCERT books all chapters in Mathematics class 11
• Short notes for CBSE class 11th Mathematics
• Key notes and chapter summary of Mathematics class 11
• Quick revision notes for CBSE exams

## CBSE Class-11 Revision Notes and Key Points

Binomial Theorem class 11 Notes Mathematics. CBSE quick revision note for class-11 Mathematics, Physics, Chemistry, Biology and other subject are very helpful to revise the whole syllabus during exam days. The revision notes covers all important formulas and concepts given in the chapter. Even if you wish to have an overview of a chapter, quick revision notes are here to do if for you. These notes will certainly save your time during stressful exam days.

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