In the expansion of ${(1 - 3 x)}^{- 1}$ , coefficient of $x^{4}$ is

81

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27

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- 27

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28

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Solution

The correct option is A $81$
Given, $(1 - 3 x)^{- 1}$
Hence, the coefficient of $x^{4}$ will be $(\frac{n (n - 1) (n - 2) (n - 3)}{4!} (- 3 x)^{4})$
$= \frac{- 1 (- 2) (- 3) (- 4)}{4!} (3 x)^{4}$
$= \frac{4!}{4!} 3^{4} x^{4}$
$= 81 x^{4}$
Hence, coefficient is $81$

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