The sum of two numbers is $20$. If the product of the square of one number and the cube of the other is maximum,then the numbers are:

At $T(K)$,$100 \ L$ of dry oxygen is present in a sealed container. It is subjected to silent electric discharge,till the volumes of oxygen and ozone become equal. What is the volume (in litres) of ozone formed at $T(K)$?

Acetone on addition to methyl magnesium bromide forms a complex,which on decomposition with acid gives $X$ and $Mg(OH)Br$. Which one of the following is $X$?

$A$ gas is filled in a cylinder. Its temperature is increased by $20\%$ on the Kelvin scale and its volume is reduced by $10\%$. How much percentage of the gas will leak out?

$A$ parallel plate capacitor of capacitance $C$ is connected to a battery and is charged to a potential difference $V$. Another capacitor of capacitance $2C$ is connected to another battery and is charged to potential difference $2V$. The charging batteries are now disconnected and the capacitors are connected in parallel to each other in such a way that the positive terminal of one is connected to the negative terminal of the other. The final energy of the configuration is

In the circuit shown,the heat produced in $5 \Omega$ resistance due to current $I_2$ is $50 \text{ J/s}$. Then,the heat generated per second in $2 \Omega$ resistance is (in $text{ J/s}$)