Chapter 7 · Class XI Mathematics · NCERT Exercises

Binomial Theorem — Exercises

Expand Any Power — All 36 Binomial Theorem Exercises Solved

📂 2 Exercises 📝 20 Questions 🎓 Moderate-High

▶ Start Exercises 📖 Revise Notes

Exercise Index

①

Exercise 7.1

Expansion; general term Tᵣ₊₁; specific term

14 Q Moderate

★

Miscellaneous

Coefficient of xⁿ; approximation; sum of coefficients

6 Q Hard

2 exercise files · 20 total questions

Chapter at a Glance

JEE MainJEE AdvancedCBSE BoardsBITSAT

9Concepts

12Formulas

Moderate-HighDifficulty

5–7%Weightage

Before You Begin

Prerequisites

✓Ch 6 — Combinations ⁿCᵣ
✓Algebraic identities
✓Exponent/index laws

Have Ready

🔧General term formula card
🔧Pascal's triangle rows 0–10

Exercise Topic Map

Exercise 7.1Write expansion; find Tᵣ₊₁=ⁿCᵣxⁿ⁻ʳyʳ; extract specific terms

Exercise 7.2Middle term(s); numerically greatest term; Σ Cᵣ identities

MiscellaneousCoefficient of xᵏ by setting power=k; approximation; sum

Key Formulae

\(T_{r+1} = {}^nC_r \cdot x^{n-r} \cdot y^r\)

\(\text{Sum of coefficients: set }x=y=1 \Rightarrow 2^n\)

\(\text{Middle term (n even): }T_{n/2+1}\)

\(\text{Middle terms (n odd): }T_{(n+1)/2}\text{ and }T_{(n+3)/2}\)

NCERT Solving Method

Step 1 — Write Tᵣ₊₁=ⁿCᵣ·xⁿ⁻ʳ·yʳ for every problem. Step 2 — Constant term (independent of x): set power of x=0, solve for r. Step 3 — Coefficient of xᵏ: set total power of x=k, solve r, substitute back. Step 4 — Greatest term: Tᵣ₊₁/Tᵣ≥1, solve r, verify with adjacent terms.

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