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NDA 2010
Exam
NDA
Year
2010
Subject
Mathematics
Chapter
Binomial Theorem

NDA 2010 · Mathematics · Binomial Theorem

What is the coefficient of x^ 17 in the expansion of (3...

What is the coefficient of x17x^{17} in the expansion of (3x−x36)9?\left(3 x-\frac{x^3}{6}\right)^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 x^{17} in (3x−x36)9\left(3 x-\frac{x^3}{6}\right)^9=9C4(3x)9−4×(−x36)4=9C4×35×(−16)4=194∣5×3564=1898\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}$$
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