Binomial Theorem ISC Class-11 Maths ML Aggarwal

Binomial Theorem ISC Class-11 Maths ML Aggarwal Solutions Chapter-9. Step by step Solutions of ML Aggarwal ISC Class-11 Mathematics with Exe-1,  Exe-2, Exe-3 and Chapter Test Questions. Visit official Website CISCE for detail information about ISC Board Class-11 Mathematics.

Binomial Theorem ISC Class-11 Maths ML Aggarwal Solutions Chapter-9

Board	ISC
Class	11
Subject	Mathematics
Chapter-9	Binomial Theorem
Session	2024-25
Topics	Solutions of ML Aggarwal

Binomial Theorem

The binomial theorem states a formula for the expression of the powers of sums

Expand (a + b)ⁿ = ⁿC₀ aⁿ + ⁿC₁ a^n-1 b + ⁿC₂ a^n-2 b² + … + ⁿC_n-1 a b^n-1 + ⁿC_n bⁿ

special cases from the binomial theorem

• (x + y)ⁿ = ⁿC₀ xⁿ + ⁿC₁ x^n-1 by+ ⁿC₂ x^n-2 y² + … + ⁿC_n-1 x y^n-1 + ⁿC_n xⁿ
• (x – y)ⁿ = ⁿC₀ xⁿ – ⁿC₁ x^n-1 by + ⁿC₂ x^n-2 y² + … + (-1)^n nC_n xⁿ
• (1 – x)ⁿ = ⁿC₀ – ⁿC₁ x + ⁿC₂ x² – …. (-1)^n nC_n xⁿ
• , ⁿC₀ = ⁿC_n = 1

General and Middle terms

Consider the binomial expansion, (a + b)ⁿ = ⁿC₀ aⁿ + ⁿC₁ a^n-1 b + ⁿC₂ a^n-2 b² + … + ⁿC_n-1 a b^n-1 + ⁿC_n bⁿ

Here,  First term = ⁿC₀ aⁿ

Second term = ⁿC₁ a^n-1 b

Third term = ⁿC₂ a^n-2 b²

Similarly, we can write the (r + 1)th term as:

ⁿC_r a^n-r b^r

This is the general term of the given expansion.

Thus, (r + 1)Th term, i.e. T_r+1 = ⁿC_r a^n-r b^r is called the middle term of the expansion (a + b)ⁿ.

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Exe-9.1

Binomial Theorem ISC Class-11 Maths ML Aggarwal Solutions Chapter-9

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Exe-9.2

Binomial Theorem Class-11 Maths

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Exe-9.3

Ch-9 Binomial Theorem ISC Class-11 Maths

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Chapter Test

Binomial Theorem ISC Class-11 Maths Solutions Chapter-9

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