Q191 / 270 · NDA 2010 (Phase 2) · Mathematics

What is the coefficient of $x^{17}$ in the expansion of $\left(3 x-\frac{x^3}{6}\right)^9 ?$

  • Correct answer
    A
    189/8
  • B
    567/2
  • C
    21/16
  • D
    None of the above

Solution

Coefficient of $x^{17}$ in $\left(3 x-\frac{x^3}{6}\right)^9$ $\begin{aligned} & =9 C_4(3 x)^{9-4} \times\left(-\frac{x^3}{6}\right)^4 \\ & =9 C_4 \times 3^5 \times\left(-\frac{1}{6}\right)^4 \\ & =\frac{19}{4 \mid 5} \times \frac{3^5}{6^4}=\frac{189}{8} \end{aligned}$

Hence, the correct answer is option: 'A'.

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