Skip to main content
Super TutorResources
Chapter 15 of 31
Revision Notes

Binomial Theorem — Revision Notes

Telangana Open School (TOSS) · Class 12 · Mathematics

Binomial Theorem revision notes for Telangana Open School (TOSS) Class 12 Mathematics: 4 topics in quick points.

53 questions24 flashcards7 formulas & key relations5 concepts

Interactive on Super Tutor

Studying Binomial Theorem? Get the full interactive chapter.

Quizzes, flashcards, AI doubt-solver and a step-by-step study plan — built for revision notes and more.

Try Super Tutor — Free

Free trial, no card needed.

Key Topics to Revise

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.

Get complete notes with diagrams and examples

Full Notes

Key Concepts

For any positive integer \(n\)The \((r+1)^{\text{th}}\) term in the expansionWhen \(n\) is evenWhen the exponent \(r\) isFor small values of \(x\)

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.

More resources for Binomial Theorem

All Telangana Open School (TOSS) Class 12 Mathematics Revision Notes

For serious students

Get the full Binomial Theorem chapter — start free.

Quizzes, flashcards, an AI doubt solver and a study plan for Telangana Open School (TOSS) Class 12 Mathematics. Free to start, no card needed.

Try Super Tutor Free
Try this chapter free