A set contains $4 n + 1$ elements.The number of subsets of this set containing more than $2 n$ elements

2^{2 n - 1}

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2^{2 n}

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2^{2 n + 1}

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2^{4 n}

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Solution

The correct option is D $2^{4 n}$
The number of sub sets containing $n$ elements $= 2^{n + 1}$
Given the set contains $4 n + 1$ elements
Number of subsets with element more than $2 n$
$= {(2)}^{4 n}$
Hence the correct answer is ${(2)}^{4 n}$

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