Two bodies of masses $m$ and $4m$ are placed at a distance $r$. The gravitational potential at a point on the line joining them,where the gravitational field is zero,is

Two tuning forks $A$ and $B$ produce $8\ Hz$ beats per second when sounded together. $A$ gas column $37.5\ cm$ long in a pipe closed at one end resonates in its fundamental mode with fork $A$,whereas a column of length $38.5\ cm$ of the same gas in a similar pipe is required for a similar resonance with fork $B$. The frequencies of these two tuning forks are:

An ideal gas is expanding such that $PT^2 = \text{constant}$. The coefficient of volume expansion of the gas is (in $/T$)

Which of the following carries glucose from the digestive tract to the liver?

Two capacitors $C_1$ and $C_2$ in a circuit are joined as shown in the figure. The potential of point $A$ is $V_1$ and that of $B$ is $V_2$. The potential of point $D$ will be

In the following sequence of reactions,the alkene affords the compound $B$:
$CH_3-CH=CH-CH_3$ $\xrightarrow{O_3} A$ $\xrightarrow{Zn, H_2O} B$
The compound $B$ is