If the mean of the squares of first n natural numbers is 105, then the median of first n natural number is
8
9
10
11
We have,
12+22+…+n2n=105⇒(n+1)(2n+1)6=105⇒2n2+3n−629=0⇒(2n+37)(n−17)=0⇒n=17
Thus, given numbers are 1,2,3,4,…,16,17
Clearly, 9 is their median.