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Formula Sheet

Binomial Theorem — Formula Sheet

OJEE · Mathematics

Free Binomial Theorem formula sheet for OJEE Mathematics 2026 — all important formulas, equations, and constants for quick reference.

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A labeled diagram illustrating the general formula for the binomial expansion of (a+b)^n, showing the summation notation, individual terms, and the role of binomial coefficients.
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Formula Sheet — Binomial Theorem

Important formulas and equations from Binomial Theorem for OJEE Mathematics.

Formulas — Binomial Theorem

Basic Binomial Theorem

(a+b)^n = Σ(k=0 to n) nCk × a^(n-k) × b^k
(a+b)^n = nC0×a^n + nC1×a^(n-1)×b + nC2×a^(n-2)×b^2 + ... + nCn×b^n
nCr = n!/(r!(n-r)!)

Special Cases and Deductions

(x-y)^n = Σ(k=0 to n) nCk × x^(n-k) × (-y)^k
nC0 + nC1 + nC2 + ... + nCn = 2^n
nC0 - nC1 + nC2 - nC3 + ... = 0 (if n>0)

General Term and Applications

T(r+1) = nCr × a^(n-r) × b^r
Term independent of x in (x + k/x)^n occurs when power of x = 0
pth term from end = (n-p+2)th term from beginning

Negative and Fractional Powers

(1+x)^(-n) = 1 - nx + n(n+1)x²/2! - n(n+1)(n+2)x³/3! + ...
(1-x)^(-n) = 1 + nx + n(n+1)x²/2! + n(n+1)(n+2)x³/3! + ...

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Frequently Asked Questions

What topics are covered in Binomial Theorem for OJEE?
Binomial Theorem is an important chapter in OJEE Mathematics. It covers key concepts and formulas that are frequently tested in the exam. Key topics include: Introduction and Basic Concepts, Key Properties and Observations, Special Cases and Important Deductions, General Term and Its Applications.
How important is Binomial Theorem for OJEE?
Binomial Theorem is a frequently tested chapter in OJEE Mathematics. Questions from this chapter appear regularly in previous year papers. There are 391 practice questions available for this chapter.
How to prepare Binomial Theorem for OJEE?
Start by understanding the core concepts, then solve practice questions. Focus on formulas and their applications. Use revision notes for quick review before the exam.

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