IITJEE Mains • Mathematics New Syllabus
Module 05: Binomial Theorem Hub
Master the expansion of algebraic expressions. Explore the binomial theorem, general and middle terms, properties of binomial coefficients, and the principle of mathematical induction.
Topic 1.1 • Expansions
Binomial Theorem for Positive Integral Index and Pascal’s Triangle
Topic 1.2 • Term Mechanics
General Term, Middle Term(s), and Term Independent of x
Topic 2.1 • Coefficient Algebra
Sum of Binomial Coefficients and Basic Standard Identities
Topic 2.2 • Advanced Series
Calculus and Complex Number Applications in Coefficient Series
Topic 3.1 • Advanced Binomial
Numerically Greatest Term, Finding Remainders, and Last Digits
Topic 3.2 • Rational Index
Binomial Theorem for any Rational Index and Approximations
Topic 4.1 • Proof Methods
Principle of Mathematical Induction and Step-by-Step Logical Proofs
Topic 4.2 • Induction Applications