Coefficient of $x^{2001}$ in the expansion of $(1 + x + x^{2} + x^{3} + x^{4})^{1001} (1 - x)^{1002}$ is

0

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4^{1001} C_{501}

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- 2009

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2 \times^{1001} C_{501}

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Solution

The correct option is A $0$
In binomial expansion of negative index,
$(1 - x)^{- 1} = (1 + x + x^{2} + . . . . . . x^{n})^{1001}$ is
$\Rightarrow (1 + x + x^{2} + x^{3} + . . . . x^{n})^{1001} (1 - x)^{1002}$
$= (1 - x)^{- 1001} (1 - x)^{1002}$
$= (1 - x)$
$\Rightarrow$ coefficient of $x^{2001}$ is $0.....$

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