If the coefficient of the $(n + 1)^{t h}$ term and the $(n + 3)^{t h}$ termin the expansion of $(1 + x)^{20}$ are equal, then the value of n is

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None of these

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Solution

The correct option is C
9

coefficient of $(n + 1)^{t h}$ term =Coefficient of $(n + 3)^{t h}$

We have:

$^{20} C_{n} =^{20} C_{n + 2}$

$\Rightarrow 2 n + 2 = 20$

$[∵$ If $^{n} C_{x} =^{n} C_{y} \Rightarrow x = y$ or x+y =n]

$\Rightarrow n = 9$

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