If the difference between the number of subsets of two sets A and B is 120 , then n A × B is equal to

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Question: Answered & Verified by Expert

If the difference between the number of subsets of two sets

A

and

B

is

120

, then

n (A \times B)

is equal to

MathematicsSets and RelationsJEE Main

Options:

A $21$
B $25$
C $18$
D $24$

Solution:

1218 Upvotes Verified Answer

The correct answer is:

21

Let,

n (A) = α & n (B) = β

Given,

|2^{α} - 2^{β}| = 120 \Rightarrow (α, β) \equiv (7,3), (3,7)

∴ n (A \times B) = 7 \times 3 = 21

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