The value of \(\lim _{n \rightarrow \infty} \frac{[\mathrm{r}]+[2 \mathrm{r}]+\ldots .+[\mathrm{nr}]}{n^2}\), where \(r\…

The value of \(\lim _{n \rightarrow \infty} \frac{[\mathrm{r}]+[2 \mathrm{r}]+\ldots .+[\mathrm{nr}]}{n^2}\), where \(r\) is a non-zero real number and\([r]\) denotes the greatest integer less than equal to '\(r\) ', is equal to:

[JEE Main 2021, 17 Mar (Shift 2)]