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AP EAMCET2010MathematicsBinomial Theorem

If (1+2 x+3 x^2 )¹⁰=a₀+a₁ x+a₂ x^2+ +a₂₀ x²⁰ then a₂ a₁ is equal to

Options

  1. A10.5
  2. B21
  3. C10
  4. D5.5

Correct answer

A. 10.5

Step-by-step solution

(1+2 x+3 x^2 )¹⁰=a₀+a₁ x+a₂ x^2+ +a₂₀ x²⁰= 1+x(2+3 x) ¹⁰ Then by binomial expansion = ¹⁰ C₀+ ¹⁰ C₁ x(2+3 x)+ ¹⁰ C₂ x^2(2+3 x)^2+ Now, the coefficient of x in this expansion =2 ¹⁰ C₁ ie., a₁=2 10=20 and the coefficient of x^2 in this expansion =3 ¹⁰ C₁+4 ¹⁰ C₂ ie., a₂=3 10+4 45=30+180=210 So, a₂ a₁ = 210 20 =10.5

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