If the mean of the squares of first n natural numbers is 105, then the median of first n natural number is

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answer is B.

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Detailed Solution

We have,12+22+…+n2n=105⇒(n+1)(2n+1)6=105⇒2n2+3n−629=0⇒(2n+37)(n−17)=0⇒n=17Thus, given numbers are 1,2,3,4,…,16,17Clearly, 9 is their median.