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:

$A$ solid cylinder of mass $M$ and radius $R$ rolls without slipping down an inclined plane of length $L$ and height $h$. What is the velocity of its center of mass when the cylinder reaches the bottom of the incline?

If $|a| = 2$,$|b| = 3$ and $a, b$ are mutually perpendicular,then the area of the triangle whose vertices are $0, a + b, a - b$ is

The correct order of reactivity of hydrogen halides with ethyl alcohol is

The average degree of freedom per molecule of a gas is $6$. The gas performs $25 \ J$ of work while expanding at constant pressure. The heat absorbed by the gas is .... $J$.

For any integer $n \geq 1$,the sum $\sum_{k=1}^n k(k+2)$ is equal to