Binomial Theorem for JEE

• General term Tᵣ₊₁ = ⁿCᵣ aⁿ⁻ʳ bʳ
• Middle term: one if n even, two if n odd
• Sum of coefficients: put x = 1
• Greatest coefficient is the middle binomial coefficient

• Σ ⁿCᵣ = 2ⁿ
• Sum of even-index coefficients = 2ⁿ⁻¹
• Term independent of x: set power of x to 0
• ⁿCᵣ + ⁿCᵣ₋₁ = ⁿ⁺¹Cᵣ

Printable Binomial Theorem formula sheet: formulas, key ideas and traps on one page. Save it as a PDF for offline revision.

• Indexing Tᵣ instead of Tᵣ₊₁
• Sign errors with (a − b)ⁿ
• Forgetting negative powers of x in the general term

Appears frequently. One question per shift is typical, often about a specific coefficient.

Prerequisites: Permutations and Combinations.

Chapter names follow the current rationalised NCERT textbooks. Read these sections before solving PYQs.

Question. Find the coefficient of x¹⁰ in the expansion of (1 + x + x²)¹⁰.

This example was solved twice independently and both solutions agree.

Full-chapter free lectures picked from YouTube search results by views, from established JEE channels (mostly in Hinglish). Use the subtopic list to jump straight to the part you need (timestamps come from each video's own chapter list). Watch one, then solve PYQs the same day.

• Binomial Theorem FULL CHAPTER | Class 11th Maths | Arjuna JEE — Arjuna JEE, 5:03:05
  Jump to a subtopic (12)

  • 00:00 Introduction
  • 05:43 Pascal's Triangle
  • 20:10 Binomial Theorem
  • 39:52 General Term
  • 01:03:49 Middle Term
  • 01:09:27 Term Independent of x
  • 01:28:36 Numerically Greatest Term
  • 01:48:05 Finding Remainder
  • 03:00:11 Binomial Series_Type-1
  • 03:58:52 Binomial Series_Type-3(A)
  • 04:21:39 PYQs
  • 05:01:30 Thank You Bachoo!!
• BINOMIAL THEOREM in One Shot: All Concepts & PYQs Covered | JEE Main & Advanced — JEE Wallah, 6:37:54
  Jump to a subtopic (30)

  • 00:00 Introduction
  • 01:15 Topics to be covered
  • 04:29 Binomial expansion and general term
  • 08:35 Important notes
  • 1:01:38 Trick for power of five
  • 1:15:34 Middle term
  • 2:10:24 Numerically greatest term
  • 2:30:18 Property 1 of binomial coefficient
  • 2:40:00 Property 2
  • 2:43:00 Property 3
  • 2:47:10 Pascal’s triangle
  • 2:53:14 Property 4
  • 2:55:39 Property 5
  • 2:57:30 Property 6
  • 3:20:36 Summary of properties
  • 3:24:38 Binomial series type 1
  • 3:43:56 Type 2
  • 3:51:50 Type 3
  • 4:01:49 Most important formula
  • 4:20:34 Type 4
  • 4:29:02 Type 5
  • 4:38:59 Type 6/Double sigma problem
  • 5:03:18 Multinomial theorem
  • 5:25:33 Application of binomial theorem
  • 5:26:10 Divisibility problem/Finding remainder
  • 5:54:52 Finding last digit
  • 5:59:05 Integral & Fractional part
  • 6:20:45 Binomial theorem for rational number
  • 6:34:56 Important topics
  • 6:37:30 Thankyou bachhon

• 9 JEE Main 2026 PYQs on Binomial Theorem, with solutions.
• Read the chapter in NCERT textbooks (official, free), then solve its NCERT Exemplar (official, free) questions.
• Chapter-wise past questions: JEE Main and Advanced PYQs and question bank.
• Timed practice tests: NTA Abhyas practice tests (official, free) and our free mock tests.
• See it move: interactive simulation.