Binomial Theorem Class 11 Maths Notes – Formulas & Quick Revision

Binomial Theorem mein (a+b)ⁿ ka expansion, general term aur middle term aate hain — formula-based scoring chapter. Yahan aapko is chapter ke sabse important formulas aur quick revision points free milte hain — NCERT/CBSE syllabus ke hisaab se, boards aur JEE/NEET dono ke liye.

Important Formulas & Concepts — Binomial Theorem

• (a+b)ⁿ = Σ nCr·aⁿ⁻ʳ·bʳ
• General term: T(r+1) = nCr·aⁿ⁻ʳ·bʳ
• Terms in expansion = n + 1
• Middle term: n even → (n/2 + 1)th; n odd → do middle terms
• Term independent of x: power of x = 0 set karo
• Sum of coefficients: x = 1 rakho
• nC0 + nC2 + … = nC1 + nC3 + … = 2ⁿ⁻¹
• (1+x)ⁿ ≈ 1 + nx (x chhota ho to)

Quick Revision Points

• General term formula se hi 90% questions solve hote hain
• Coefficient of xᵏ nikalna: general term mein x ki power = k set karo
• Greatest term aur greatest coefficient alag concepts hain
• Pascal triangle se chhote expansions verify karo
• Binomial coefficients ki symmetry yaad rakho

FAQ

Independent term kaise nikalu?

T(r+1) likho, x ki power zero set karo, r nikalo — PDF mein 3-step solved pattern hai.

Boards mein kya aata hai?

General term, middle term aur coefficient — 4-6 marks confirm.

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