The coefficient of x4 in the expansion of ${(\frac{x}{2} - \frac{3}{x^{2}})}^{10}$ is

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Solution

The correct option is C

$r = \frac{10 \times 1 - 4}{1 + 2} = \frac{10 - 4}{3} = \frac{6}{2} = 2 T h e c o e f f i c i e n t x^{4} i s^{10} C_{2} {(\frac{1}{2})}^{10 - 2} (- 3)^{2} = \frac{10 \times 9}{2} . \frac{1}{2^{8}} {.3}^{2} = \frac{10 \times 81}{2 \times 2^{8}} = \frac{5 \times 81}{256} = \frac{405}{256}$

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