For any integer $n \geq 1$,the number of positive divisors of $n$ is denoted by $d(n)$. Then,for a prime $P$,$d(d(d(P^7)))$ is equal to

An auditorium has a volume of $10^5 \ m^3$ and a total absorption area of $2 \times 10^4 \ m^2$. Its average absorption coefficient is $0.2$. The reverberation time of the auditorium in seconds is:

What do you understand by isoelectronic species? Name a species that will be isoelectronic with each of the following atoms or ions.
$(i)$ $F^{-}$ $(ii)$ $Ar$ $(iii)$ $Mg^{2+}$ $(iv)$ $Rb^{+}$

In the circuit shown in the figure, what is the value of $I_1$ just after pressing the key $K$?

Which one of the following is mainly responsible for the depletion of the ozone layer?

$A$ flask of volume $10^3 \text{ cc}$ is completely filled with mercury at $0 \ ^\circ\text{C}$. The coefficient of cubical expansion of mercury is $180 \times 10^{-6} / ^\circ\text{C}$ and that of glass is $40 \times 10^{-6} / ^\circ\text{C}$. If the flask is now placed in boiling water at $100 \ ^\circ\text{C}$,how much mercury (in $\text{cc}$) will overflow?