The co-efficient of $x^{53}$ in the expansion $(x - 3)^{100}$ is?

-

^{100} C_{53}

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^{100} C_{53}

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^{65} C_{53}

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None of these

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Solution

The correct option is D None of these
$co efficient of x^{53} in (x - 3)^{100}$
$T_{r + 1} = 100 Cr x^{4} (- 3)^{100 - r}$
$T_{54} = 100 C_{53} x^{53} (- 3)^{47}$
$c o e f f i c i e n t i s (- 3)^{47}^{100} C_{53}$

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