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Grade: 12
        A set contains (2n+1) elements.If the number of subsets of this set which contains almost n elements is 4096,then the value of n is
11 months ago

Answers : (1)

Arun
16287 Points
							

Take the power set. It has 2^(2n+1) members.

Replace any member which has n+1 or more elements by its complements.

Now the power set has members, which has n or fewer elements, and each such such member appears twice.

Therefore, when multiplicity is removed, you get 2^(2n+1)/2 members, which is 2^(2n).

 

Hence

2^2n = 4096

2^2n = 2^12

2n = 12

n = 6

 

Regards

Arun (askIITians forum expert) 

11 months ago
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