A) \[\left( \begin{align} & 200 \\ & 100 \\ \end{align} \right)\]
B) \[\left( \begin{align} & 201 \\ & 102 \\ \end{align} \right)\]
C) \[\left( \begin{align} & 200 \\ & 101 \\ \end{align} \right)\]
D) \[\left( \begin{align} & 201 \\ & 100 \\ \end{align} \right)\]
Correct Answer: A
Solution :
\[{{T}_{r+1}}={{\,}^{200}}{{C}_{r}}{{(1)}^{200-r}}.{{(x)}^{r}}\] Hence coefficient of\[{{x}^{100}}={{\,}^{200}}{{C}_{100}}=\left( \begin{align} & 200 \\ & 100 \\ \end{align} \right)\].
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