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

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)