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Arithmetic Progression

If the coeffi...

Question

If the coefficients of $x^{9}, x^{10}, x^{11}$ in the expansion of $(1 + x)^{n}$ are in arithmetic progression then $n^{2} - 41 n$ =

398

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298

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- 398

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198

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Solution

The correct option is A $- 398$
$\Rightarrow 2 = \frac{n - 10}{n - 9} + \frac{n - 10}{11} \Rightarrow 2 = \frac{110 + n^{2} - 19 n + 90}{11 n - 99}$
$\Rightarrow n^{2} - 41 n = - 398$

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