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:

If the direction ratios of two lines are given by $3lm - 4ln + mn = 0$ and $l + 2m + 3n = 0$, then the angle between the lines is:

$A$ certain quantity of water cools from $70\,^{\circ}C$ to $60\,^{\circ}C$ in the first $5\, \text{minutes}$ and to $54\,^{\circ}C$ in the next $5\, \text{minutes}$. The temperature of the surroundings is ......... $^{\circ}C$.

What is $Z$ in the following reaction? $CH_3-CH_2-CO_2^{\ominus} Na^{\oplus} \stackrel{NaOH / CaO}{\longrightarrow} Z$

$A$ committee of $11$ members is to be formed from $8$ males and $5$ females. If $m$ is the number of ways the committee is formed with at least $6$ males and $n$ is the number of ways the committee is formed with at least $3$ females,then:

The product of the given reaction is: