JEE Main 2020 (Online) 6th September Evening ShiftQuestion 1
Consider the data on $x$ taking the values $0,2,4,8,\ldots,2^n$ with frequencies ${}^nC_0,{}^nC_1,{}^nC_2,\ldots,{}^nC_n$ respectively. If the mean of this data is $\frac{728}{2^n}$, then $n$ is equal to ________.
Statistics
Answer$6$
Solution
Mean $=\frac{\sum_{k\ge1}\binom nk2^k}{2^n}=\frac{3^n-1}{2^n}=\frac{728}{2^n}$, so $3^n=729$, $n=6$.