List of top Questions asked in IIT JAM MA

Find the limit: \[ \lim_{n \to \infty} \sum_{k=1}^{n} \sin \left( \frac{\pi}{2} + \frac{5\pi}{2} \cdot \frac{k}{n} \right) = \]

Evaluate the integral: \[ \int_0^1 \int_x^1 \sin(y^2) \, dy \, dx \]