NDA2023MathematicsBinomial TheoremActual

A set S contains (2n +1) elements. There are 4096 subset of S which contain at most n elements. what is n equal to

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Correct answer

B. 6

Step-by-step solution

aligned & Since, n ( s )=2 n +1 & Now, ^ 2 n +1 C ₀+ ^ 2 n +1 C ₁+ ^ 2 n +1 C ₂+ .+ ^ 2 n +1 C _ n + & ^ 2 n +1 C _ n +1 + ^ 2 n +1 C _ n +2 + . .+ ^ 2 n +1 C _ 2 n +1 =2^ 2 n +1 & 2 ( ^ 2 n +1 C ₀+ ^ 2 n +1 C ₁+ .+ ^ 2 n +1 C _ n )=2^ 2 n +1 =4096 & 2^ 2 n =2¹² 2 n =12 n =6 aligned

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