If the expansion of ${(x^{2} + \frac{2}{x})}^{n}$ for positive integer n has $13^{t h}$ term independent of x, then n is

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Solution

The correct option is B 18
$T_{13} = T_{12 + 1} =^{n} C_{12} (x^{2})^{n - 12} {(\frac{2}{x})}^{12} =^{n} C_{12} 2^{12} x^{2 n - 36} T h i s t e r m i s i n d e p e n d e n t o f x . ∴ 2 n - 36 = 0 i . e, n = 18$

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