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NDA2010MathematicsBinomial TheoremActual

What is the coefficient of x¹⁷ in the expansion of (3 x- x^3 6 )^9 ?

Options

  1. A189/8
  2. B567/2
  3. C21/16
  4. DNone of the above

Correct answer

A. 189/8

Step-by-step solution

Coefficient of x¹⁷ in (3 x- x^3 6 )^9 aligned & =9 C₄(3 x)⁹⁻⁴ (- x^3 6 )^4 & =9 C₄ 3^5 (- 1 6 )^4 & = 19 4 5 3^5 6^4 = 189 8 aligned

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