Ans: (C)
Hint : Required limit \(=\operatorname{It}_{n \rightarrow \infty} \sum_{r=1}^{n} \frac{1}{n} \sec ^{2}\left(\frac{r \pi}{4 n}\right)=\int_{0}^{1} \sec ^{2}\left(\frac{\pi x}{4}\right) d x=\left.\frac{4}{\pi} \tan \left(\frac{\pi x}{4}\right)\right|_{0} ^{1}=\frac{4}{\pi}\)