Mathematics · Class 11
Binomial Theorem
Learn Binomial Theorem with notes, examples, and practice questions.
2 sections15–25 min read6 MCQs · 2 examples
Chapter Overview
Expands (a+b)ⁿ into a sum of terms involving ⁿCᵣ. Connects combinatorics to algebra; middle term and greatest coefficient are exam favourites.
Theorem
Binomial
(a+b)ⁿ = Σ ⁿCᵣ aⁿ⁻ʳ bʳ (r=0 to n)
General term
Tᵣ₊₁ = ⁿCᵣ aⁿ⁻ʳ bʳ
Middle term
n even: (n/2+1)th; n odd: two middle terms
Solved Examples
Step-by-step solutions — read each step before checking the final answer.
(x+2)³
Expand.
- 1⁴C₀x³+3x²(2)+3x(4)+8
Answer
x³+6x²+12x+8
Term with x² in (2x+3)⁵
Find coefficient.
- 1Tᵣ₊₁ has x^(5−r)·2^(5−r)
- 25−r=2 → r=3
- 3⁵C₃·2²·3³
Answer
1080
Key Points to Remember
- ✓ Pascal's triangle for small n
- ✓ ⁿCᵣ coefficient in expansion
- ✓ Special: (1+x)ⁿ
Exam Tips
- • General term Tᵣ₊₁ — note index r starts at 0
- • Separate coefficient and power of x
Practice MCQs — Binomial Theorem
Test your understanding with topic-wise multiple choice questions. Explanations appear after each answer.
Question 1 of 6Score: 0/0
(a+b)⁰ equals: