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Q.

Set A has m elements and set B has n elements. If the total number of subsets of A is 224 more than the total number of subsets of B then the value of mn is ______

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answer is 40.

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Detailed Solution

$2^{m} = 224 + 2^{n} 2^{m} - 2^{n} = 224 2^{n} (2^{m - n} - 1) = 2^{5} (2^{3} - 1)$
n = 5, m – n = 3
m = 8
mn = 5 (8) = 40

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