Heat energy is incident on the surface at the rate of $1000 ~J/min$. If the coefficient of absorption is $0.8$ and the coefficient of reflection is $0.1$,then the heat energy transmitted by the surface in $5 ~min$ is: (in $~J$)

Select the mismatched pair from the following.

The number of divisors of $7!$ is

The maximum velocity of electrons emitted from a metal surface is $V$ when the frequency of light falling on it is $f$. What is the maximum velocity when the frequency becomes $4f$?

Two metal plates each of area $A$ form a parallel plate capacitor with air in between the plates. The distance between the plates is $d$. $A$ metal plate of thickness $d/2$ and of same area $A$ is inserted between the plates to form two capacitors of capacitances $C_1$ and $C_2$ as shown in the figure. If the effective capacitance of the two capacitors is $C^{\prime}$ and the capacitance of the capacitor initially is $C$,then $C^{\prime}/C$ is

$a^{m \log_a n} = $