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NDA2020MathematicsBinomial TheoremActual

If (1+2 x-x^2 )^6=a₀+a₁ x+a₂ x^2+ .+a₁₂ x¹² , then what is a₀-a₁+a₂-a₃+a₄- .+a₁₂ equal to?

Options

  1. A32
  2. B64
  3. C2048
  4. D4096

Correct answer

B. 64

Step-by-step solution

aligned & (1+2 x-x^2 )^6=a₀+a₁ x+a₂ x^2+ .+a₁₂ x¹² & Putting x=-1 & a₀-a₁+a₂+ .+a₁₂ = (1+2(-1)-(-1)^2 )^6 & =(1-2-1)¹²=(-2)^6=64 aligned

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