Currently Empty: $0.00
7.Binomial Theorem & General Term
Class 11 • Mathematics • NCERT
Binomial Theorem & General Term
[ Embed Your Video Lecture Here ]
This lesson introduces the Binomial Theorem and the general term of a binomial expansion as per NCERT Class 11. Students learn how to expand (a + b)ⁿ using binomial coefficients and find specific terms safely for exams.
Lesson Objectives
- Understand the Binomial Theorem.
- Expand (a + b)ⁿ for natural numbers n.
- Use binomial coefficients correctly.
- Find the general term in a binomial expansion.
1. Binomial Theorem (NCERT)
According to the Binomial Theorem, for any natural number n:
(a + b)ⁿ = nC0 aⁿ + nC1 aⁿ⁻¹b + nC2 aⁿ⁻²b² + … + nCn bⁿ
2. Binomial Coefficients
The numbers nCr appearing in the expansion are called binomial coefficients.
nCr = n! / [r!(n − r)!]
Properties:
• nC0 = nCn = 1
• nCr = nC(n − r)
Properties:
• nC0 = nCn = 1
• nCr = nC(n − r)
3. General Term of Binomial Expansion
The general term of the expansion of (a + b)ⁿ is denoted by Tr+1.
Tr+1 = nCr aⁿ⁻ʳ bʳ
4. Simple NCERT Examples
• Expand (x + y)³
= x³ + 3x²y + 3xy² + y³
= x³ + 3x²y + 3xy² + y³
• General term of (a + b)⁵:
Tr+1 = 5Cr a⁵⁻ʳ bʳ
5. Important NCERT Notes
• Number of terms in (a + b)ⁿ = n + 1
• Powers of a decrease, powers of b increase
• Sum of indices = n in every term
• Powers of a decrease, powers of b increase
• Sum of indices = n in every term
Practice Questions (NCERT)
- State the Binomial Theorem.
- Write the expansion of (a + b)².
- Write the expansion of (x + y)³.
- How many terms are there in (a + b)⁷?
- Write the general term of (a + b)ⁿ.
- Find the general term of (x + y)⁵.
- What is the value of 6C0?
- What is the value of 6C6?
- What is the sum of powers of a and b in any term?
- Is this topic part of NCERT Class 11 syllabus?
✅ Show Answer Key
- (a + b)ⁿ expansion using binomial coefficients.
- a² + 2ab + b²
- x³ + 3x²y + 3xy² + y³
- 8
- Tr+1 = nCr aⁿ⁻ʳ bʳ
- Tr+1 = 5Cr x⁵⁻ʳ yʳ
- 1
- 1
- n
- Yes
© Aviate Learning – Binomial Theorem (NCERT Class 11)