Find the coefficient of the middle term of the expansion ${(x - \frac{1}{2 y})}^{10}$ :

- \frac{63}{8}

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24

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- \frac{33}{4}

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- 33

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Solution

The correct option is A $- \frac{63}{8}$
We need to find middle term of ${(x - \frac{1}{2 y})}^{10}$
Total number of terms are $11$ .
So, middle term will be the $6^{t h}$ term.
$∴ t_{5 + 1} =^{10} C_{5} (- 1)^{5} x^{10 - 5} (\frac{1}{2 y})^{5} = - \frac{63 x^{5}}{8 y^{5}}$
Hence, option A is correct.

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