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Revision Notes

Binomial Theorem — Revision Notes

CBSE · Class 11 · Mathematics

Binomial Theorem revision notes for CBSE Class 11 Mathematics: 4 topics in quick points. Part of the CBSE Class 11 Mathematics syllabus.

135 questions60 flashcards15 formulas & key relations5 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?
Key topics in Binomial Theorem include Core idea and pattern of expansion, Binomial coefficients and Pascal's triangle, Special expansions and corollaries, Proof idea and verification methods. Study these first, then practise questions on each for Class 11 exams.
How should I revise Binomial Theorem for Class 11 exams?
Learn the core ideas first, then work through the 135 practice questions on Binomial Theorem. Revise 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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All CBSE Class 11 Mathematics Revision Notes

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