NCERT Class 11 Mathematics Mathematics: Chapter 7 — MATHEMATICS
This chapter introduces the Binomial Theorem for positive integral indices, addressing the limitations of calculating higher powers of binomials through repeated multiplication. It revisits familiar identities for (a+b)^0, (a+b)^1, (a+b)^2, and (a+b)^3, and demonstrates the expansion of (a+b)^4. Key observations about binomial expansions are highlighted: the number of terms is one more than the index, powers of the first term decrease while powers of the second term increase, and the sum of indices in each term equals the binomial index. The chapter also introduces Pascal's Triangle, a pattern of coefficients that aids in binomial expansions, and illustrates its use with an example expansion of (2x + 3y)^5. This theorem provides an efficient method for expanding binomials with positive integer exponents, crucial for advanced mathematical studies in CBSE.
Quick info
| Board | CBSE / NCERT |
|---|---|
| Class | Class 11 |
| Subject | Mathematics |
| Book | Mathematics |
| Chapter | Chapter 7 — MATHEMATICS |
| Language | English |
| PDF type | NCERT Textbook |
| Session | CBSE 2026 |
| Reading time | 3 minutes |
| Word count | 564 |
Learning outcomes
- Understand the need for the Binomial Theorem for expanding binomials with positive integral indices.
- Identify patterns in binomial expansions, including the number of terms and the powers of variables.
- Recognize and utilize Pascal's Triangle for determining binomial coefficients.
- Apply the Binomial Theorem to expand binomial expressions like (a+b)^n.
- Calculate numerical values of higher powers of binomials using the theorem.
Vocabulary
| Word | Meaning |
|---|---|
| Binomial | An algebraic expression consisting of two terms. |
| Theorem | A general proposition that is proved with the help of certain premises. |
| Index | The power to which a number or expression is raised. |
| Expansion | The process of expressing a binomial raised to a power in its expanded form. |
| Coefficients | The numerical or constant quantity placed before and multiplying the variable in an algebraic expression. |
| Pascal's Triangle | A triangular array of the binomial coefficients. |
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Practice questions
- How many terms are there in the expansion of (a + b)^5? Answer: There are 6 terms in the expansion of (a + b)^5.
- What is the sum of the indices of 'a' and 'b' in each term of the expansion of (a + b)^n? Answer: The sum of the indices of 'a' and 'b' in each term is equal to n.
- Which mathematician's name is associated with Pascal's Triangle? Answer: Blaise Pascal.
Practice MCQs
Q1. The expansion of (a + b)^0 is equal to:
Explanation: For any non-zero a+b, (a+b)^0 is defined as 1.
Q2. In the expansion of (a + b)^n, the powers of 'a' in successive terms:
Explanation: The powers of the first quantity 'a' decrease by 1 in each successive term of the binomial expansion.
Q3. Pascal's Triangle is also known as:
Explanation: Pascal's Triangle is also known as Meru Prastara by Pingla.
Q4. The number of terms in the expansion of (a + b)^n is:
Explanation: The total number of terms in the expansion of (a + b)^n is always one more than the index n.
Q5. Which of the following is an identity for (a+b)^2?
Explanation: The expansion of (a+b)^2 is + 2ab + .
Frequently asked questions
What is the Binomial Theorem?
The Binomial Theorem provides a formula for the algebraic expansion of powers of a binomial (a+b)^n, where n is a positive integer.
Why is the Binomial Theorem useful?
It simplifies the calculation of higher powers of binomials, which would be difficult and time-consuming using repeated multiplication.
What is Pascal's Triangle?
Pascal's Triangle is a triangular array of numbers where each number is the sum of the two numbers directly above it. It provides the coefficients for binomial expansions.
How many terms are in the expansion of (a+b)^n?
There are n+1 terms in the expansion of (a+b)^n.
What is the sum of the powers of the variables in each term of a binomial expansion?
The sum of the powers of the variables in each term of the expansion of (a+b)^n is always equal to n.
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NCERT Class 11 Mathematics — Mathematics — Chapter 7 — MATHEMATICS. Verified by NCERT Help Editorial Team. Reviewed on 29 Jul 2026. Last updated 10 Aug 2026.