The coefficient of $x^{9}$ in the expansion of $(x - 1) (x - 4) (x - 9) . . . (x - 100)$ is

- 325

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365

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425

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- 385

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Solution

The correct option is D $- 385$
The coefficient of $x^{9}$ is given by
$- [1 + 4 + 9 + 16 + 25 + 36 + 49 + 64 + 81 + 100]$
$= - 385$

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