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Given that, $\log_{x}y = 100$ and $\log_{2}x = 10$

$\implies \dfrac{\log_{2}y}{\log_{2}x} = 100$

$\implies \dfrac{\log_{2}y}{10} = 100$

$\implies \log_{2}y = 1000$

$\implies y = 2^{1000}.$

So, the correct answer is $(C).$
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