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

Binomial Theorem

Telangana Board · Class 12 · Mathematics

Quick revision notes for Binomial Theorem — Telangana Board Class 12 Mathematics. Key concepts, formulas, and definitions for last-minute revision.

30 questions24 flashcards5 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

1,000+ Class 12 students started this chapter today

Key Topics to Revise

1

Basic Binomial Expansion for Positive Integer n

  • For positive integer n: (x + y)ⁿ = ⁿC₀xⁿ + ⁿC₁xⁿ⁻¹y + ⁿC₂xⁿ⁻²y² + ... + ⁿCₙyⁿ
  • Total number of terms in expansion = n + 1
  • Sum of powers of x and y in each term = n
2

Middle Terms in Binomial Expansion

  • When n is even: Middle term = (n/2 + 1)th term
  • When n is odd: Two middle terms = (n+1)/2 th and (n+3)/2 th terms
  • Middle terms have maximum binomial coefficients
3

Properties of Binomial Coefficients

  • ⁿC₀ = ⁿCₙ = 1 (first and last terms always have coefficient 1)
  • ⁿCᵣ = ⁿCₙ₋ᵣ (symmetry property)
  • ⁿCᵣ + ⁿCᵣ₋₁ = ⁿ⁺¹Cᵣ (Pascal's triangle property)
4

Binomial Theorem for Rational/Negative Exponents

  • For rational exponent r: (1 + x)ʳ = 1 + rx + r(r-1)x²/2! + r(r-1)(r-2)x³/3! + ... (|x| < 1)
  • Infinite series when r is not a positive integer
  • Convergence condition: |x| < 1 is essential

Get complete notes with diagrams and examples

Full Notes

Key Concepts

A proof technique where we prove(x + y)^n = ⁿC₀x^n +The (r+1)th term in expansionWhen n is evenFor rational r and |x| <

Frequently Asked Questions

What are the important topics in Binomial Theorem for Telangana Board Class 12 Mathematics?
Binomial Theorem covers several key topics that are frequently asked in Telangana Board Class 12 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 — Telangana Board Class 12 Mathematics?
Start by understanding all key concepts. Practise previous year questions from this chapter. Revise formulas and definitions regularly. Use flashcards for quick revision 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 31 chapters — Telangana Board Class 12 Mathematics Revision Notes

For serious students

Get the full Binomial Theorem chapter — for free.

Quizzes, flashcards, AI doubt-solver and a step-by-step study plan for Telangana Board Class 12 Mathematics.

Try Super Tutor Free
Try the full chapter — Free