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Binomial Theorem

NCERT Class 11 Mathematics Chapter 7

Binomial Theorem for Class 11 Maths and JEE: the expansion of (a + b)ⁿ for positive integers, Pascal’s triangle, special cases, general and middle terms.

2 topics Updated 8 Nov 2026

For: Class 11 and JEE, unless a topic says otherwise

In the syllabus: JEE Class 11 syllabus

With your textbook

NCERT Mathematics (Class 11), Chapter 7 “Binomial Theorem”, reprint 2026-27.

Open the official NCERT chapter (PDF, 1.3 MB, ncert.nic.in)

Checked on 19 Oct 2026.

Learn in this order

  1. Binomial theorem

    The (a + b) formula, Pascal’s triangle, binomial coefficients, special cases and their sums, with solved examples.

    NCERT Sections 7.1–7.2 18 min read 4 solved examples 16 practice questions

  2. General and middle terms

    General term of a binomial expansion for JEE Main: T = C a b, middle terms for even and odd n, the term independent of x, with solved examples.

    JEE only 12 min read 5 solved examples 11 practice questions

Key formulas in this chapter

Binomial theorem

  • (a + b) = Ca + Cab + Cab + … + Cb
  • (x − y) = Cx − Cxy + Cxy − … + (−1) Cy
  • (1 + x) = C + Cx + Cx + … + Cx
  • C + C + … + C = 2
  • C − C + C − … + (−1) C = 0
  • C + C = C, 1 ≤ r ≤ n

General and middle terms

  • T = C a b, r = 0, 1, …, n
  • (x − y): T = (−1) C x y
  • n even: one middle term, the (n/2 + 1)th
  • n odd: two middle terms, the ((n + 1)/2)th and ((n + 3)/2)th
  • kth term from the end = (n − k + 2)th term
  • T / T = (n − r + 1)/r × b/a, 1 ≤ r ≤ n, a ≠ 0, T ≠ 0
  • C / C = (n − r + 1)/r

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