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Revision Notes

Binomial Theorem

CBSE · Class 11 · Mathematics

Quick revision notes for Binomial Theorem — CBSE Class 11 Mathematics. Key concepts, formulas, and definitions for last-minute revision.

135 questions60 flashcards5 concepts

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Key Topics to Revise

1

Core idea and pattern of expansion

  • The expansion of (a + b)^n has n + 1 terms.
  • In every term, the power of a decreases by 1 from term to term, while the power of b increases by 1.
  • In each term, the sum of the indices of a and b is always n.
2

Binomial coefficients and Pascal's triangle

  • The coefficients in the binomial expansion are called binomial coefficients.
  • {}^nC_0 = 1 and {}^nC_n = 1 always.
  • Pascal's triangle gives the coefficients row by row.
3

Special expansions and corollaries

  • (x - y)^n is obtained from (a + b)^n by taking a = x and b = -y.
  • Signs alternate in the expansion of (x - y)^n.
  • The last sign is determined by (-1)^n.
4

Proof idea and verification methods

  • The proof of the binomial theorem for positive integer n uses mathematical induction.
  • The base step checks the theorem for n = 1.
  • The induction step shows that if it is true for n = k, then it is true for n = k + 1.

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Full Notes

Key Concepts

(a + b)^n = ^nC_0 a^nThe numbers ^nC_r in the expansionThe expansion of (a + b)^nIn successive termsThe coefficients of binomial expansions can

Frequently Asked Questions

What are the important topics in Binomial Theorem for CBSE Class 11 Mathematics?
Binomial Theorem covers several key topics that are frequently asked in CBSE Class 11 board exams. Focus on the core concepts listed on this page and practise related questions to build confidence.
How to score full marks in Binomial Theorem — CBSE Class 11 Mathematics?
Understand the core concepts first, then work through the 135 practice questions available for this chapter. Revise formulas and definitions regularly, and use flashcards for quick recall before the exam.

Sources & Official References

Content is aligned to the official syllabus. Refer to the board website for the latest curriculum.

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