$A$ physical quantity $P$ is given by $P = \epsilon_0 L \frac{\Delta V}{\Delta t}$,where $\epsilon_0$ is electric permittivity,$L$ is length,$\Delta V$ is potential difference,and $\Delta t$ is time interval. The dimensional formula of $P$ is the same as that of

$A$ ball of radius $r$ and density $\rho$ dropped through a viscous liquid of density $\sigma$ and viscosity $\eta$ attains its terminal velocity at time $t$, given by $t = A \rho^{a} r^{b} \eta^{c} \sigma^{d}$, where $A$ is a constant and $a, b, c, d$ are integers. The value of $\frac{b+c}{a+d}$ is . . . . . . .

If the time period $T \propto P^a d^b E^c$,where $P$ is pressure,$d$ is density,and $E$ is energy,then the value of $c$ is:

$A$ gas bubble from an explosion under water oscillates with a period proportional to $P^a d^b E^c$,where $P$ is the static pressure,$d$ is the density of water,and $E$ is the energy of the explosion. Then $a, b,$ and $c$ are:

If the gravitational constant $(G)$,Planck's constant $(h)$,and the velocity of light $(c)$ are chosen as fundamental units,the dimension of the radius of gyration is:

Which one of the following combinations of constants has the dimensions of time? $[G=$ gravitational constant,$h=$ Planck's constant,$c=$ velocity of light$]$