NIMCET 2011 Question Paper with solutions

Question : 31 of 120

Marks: +1, -0

If the mean of the squares of first

n

natural numbers be 11, then

n

is equal to

Solution:

According to the given condition,

\;{1^{2}+2^{2}+. . .+n^{2}}/{n}=11

⇒ {n(n+1)(2 n+1)}/{6 n}=11

⇒ 2 n^{2}+3 n-65=0

⇒ n= {-3 ± √{9+8 × 65}}/{4}= {-3 ± √{529}}/{4}

= {-3 ± 23}/{4}=5,- {13}/{2}

∴ n=5

( ∵ n

cannot be negative)

Go to Question:

Prev Question

Next Question