NIMCET 2018 Question Paper with solutions

Given that,
Mean [First n natural number] = 11
⇒ $\frac{\mathit{n}\left(\mathit{n}+1\right)\left(2\mathit{n}+1\right)}{6\mathit{n}}$ = 11
⇒ (n + 1) (2n + 1) = 66
⇒ $2{\mathit{n}}^2$ + 3n + 1 = 66
⇒ $2{\mathit{n}}^2$ + 3n - 65 = 0
⇒ n = $\frac{-3\pm \sqrt{9+520}}{4}$
= $\frac{-3\pm \sqrt{529}}{4}$
= $\frac{-3\pm 23}{4}$ = $\frac{20}{4}$ = 5
As , n = $\frac{-3-23}{4}$ = $\frac{-26}{4}$
[Since n cannot be negative]
∴ n = 5