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Binomial Theorem — Syllabus

Telangana Open School (TOSS) · Class 12 · Mathematics

What Binomial Theorem covers in Telangana Open School (TOSS) Class 12 Mathematics: 4 topics, for the 2026-27 session.

53 questions24 flashcards7 formulas & key relations5 concepts

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4 Topics · Telangana Open School (TOSS) Class 12 Mathematics · 2026-27

Topics in Binomial Theorem

1

Binomial Theorem for Positive Integral Index

  • The binomial expansion of \((x + y)^n\) has \(n + 1\) terms.
  • The coefficients of the terms are binomial coefficients, denoted by \(^nC_r\).
  • The general term is \(T_{r+1} = ^nC_r x^{n-r} y^r\).
2

General Term and Middle Term

  • The general term in the expansion of \((x + y)^n\) is \(T_{r+1} = ^nC_r x^{n-r} y^r\).
  • When \(n\) is even, the middle term is the \(\left(\frac{n}{2} + 1\right)^{\text{th}}\) term.
  • When \(n\) is odd, there are two middle terms: \(\left(\frac{n+1}{2}\right)^{\text{th}}\) and \(\left(\frac{n+3}{2}\right)^{\text{th}}\) terms.
3

Binomial Theorem for Rational and Negative Indices

  • For rational or negative exponents, the binomial expansion has infinitely many terms.
  • The expansion \((1 + x)^r\) is valid only when \(|x| < 1\).
  • The general term is \(T_{r+1} = \frac{r(r-1)(r-2)\cdots(r-k+1)}{k!} x^k\).
4

Applications in Approximations

  • The binomial theorem can approximate values like \(\sqrt[3]{9}\), \(\sqrt{1.02}\), etc.
  • Neglect higher powers of small quantities (like \(x^2, x^3\)) when \(x\) is very small.
  • Used in physics and engineering for linear approximations.

Key Concepts

Central concept: Binomial Theorem

Binomial ExpansionPascal's TriangleMathematical InductionGeneral TermMiddle Term(s)Binomial Theorem for Rational IndexApproximationsCombinatorics

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Frequently Asked Questions

What are the important topics in Binomial Theorem for Telangana Open School (TOSS) Class 12 Mathematics?
Key topics in Binomial Theorem include Binomial Theorem for Positive Integral Index, General Term and Middle Term, Binomial Theorem for Rational and Negative Indices, Applications in Approximations. Study these first, then practise questions on each for the Telangana Open School (TOSS) Class 12 board exam.
How should I revise Binomial Theorem for the Telangana Open School (TOSS) Class 12 board exam?
Learn the core ideas first, then work through the 53 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 Telangana Open School (TOSS) Class 12 Mathematics Syllabus

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