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99 Percentile Qs Bank for JEE MainMathematicsBinomial Theorem

If ( (1-x+x^2 )¹⁰=a₀+a₁ x+a₂ x^2+ +a₂₀ x²⁰ ), then (2 a₂+3 a₃+4 a₄+ +20 a₂₀= )

Options

  1. A0
  2. B10
  3. C20
  4. D-20

Correct answer

C. 20

Step-by-step solution

( (1-x+x^2 )¹⁰=a₀+a₁ x+a₂ x^2+ +a₂₀ x²⁰ ) On differentiating ( aligned & 10 (1-x+x^2 )^9 (-1+2 x)=a₁+2 a₂ x+3 a₃ x^2 & + +20 a₂₀ x¹⁹ aligned ) At (x=1 ) ( a₁+2 a₂+3 a₃+ +20 a₂₀=10 ) At (x=0 a₁=-10 ) So, (2 a₂+3 a₃+ +20 a₂₀=20 )

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