Two vibrating tuning forks produce progressive waves given by $Y_1 = 4 \sin(500 \pi t)$ and $Y_2 = 2 \sin(506 \pi t)$. The number of beats produced per minute is:

$A$ ball is thrown on a lawn in such a way that it initially slides with a speed $v_0$ without rolling. It gradually picks up rotational motion. Find the speed of the ball at which there will be rolling without slipping.

If the vectors $p\hat{i} + \hat{j} + \hat{k}$,$\hat{i} + q\hat{j} + \hat{k}$,and $\hat{i} + \hat{j} + r\hat{k}$ $(p \neq q \neq r \neq 1)$ are coplanar,then find the value of $pqr - (p + q + r)$.

The electron affinity of sulfur is........

The angle between the tangents drawn to the parabola $y^2=4x$ from the point $(1,4)$ is