Maths · Class 11 · Chapter 7
Binomial Theorem
10 lessons 83 min 2 simulations
This chapter expands a power of a binomial, (a + b)ⁿ, for a positive integer n without multiplying the brackets out. It starts from the patterns in small powers, builds Pascal's triangle and rewrites its entries as nCr, states the binomial theorem and proves it by induction, and then uses the special cases (x − y)ⁿ, (1 + x)ⁿ and (1 − x)ⁿ, the general term, and the theorem's uses in computing powers, estimating and finding remainders.
What the exam asks
For JEE Main the binomial theorem is a regular, scoring chapter. Questions ask for a particular term or coefficient, the term free of x, the middle term, the sum of the coefficients, a remainder or divisibility result, or a quick value of a large power. Marks are lost by dropping the number or sign carried by each part of the binomial, by miscounting terms (Tᵣ₊₁, not Tᵣ), and by mixing up a coefficient with a binomial coefficient.
Lessons
10 lessons · 83 min
1Why a binomial theoremNCERT §7.17 min2Patterns in small powersNCERT §7.26 min3Pascal's triangleNCERT §7.26 min4Coefficients as nCrNCERT §7.27 min5The binomial theoremNCERT §7.2.17 min6Proof by inductionNCERT §7.2.17 min7Special casesNCERT §7.2.26 min8The general termNCERT §7.2.111 min 1 sim9Numbers, estimates and remaindersNCERT §7.2.211 min 1 sim10Chapter reviewMust-know facts, traps and formulas15 min