Find the dimensional formula of $\frac{a}{b}$ in the equation $F=a \sqrt{x}+b t^2$,where $F$ is force,$x$ is distance,and $t$ is time.

The time dependence of a physical quantity $P$ is given by $P = P_0 \exp(-\alpha t^2)$,where $\alpha$ is a constant and $t$ is time. The constant $\alpha$:

$A$ 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 . . . . . . .

$E, m, l$ and $G$ denote energy,mass,angular momentum,and gravitational constant respectively. Then the dimensions of $\frac{El^2}{m^5G^2}$ are:

The speed of a wave produced in water is given by $v = \lambda^a g^b \rho^c$. Where $\lambda$,$g$,and $\rho$ are the wavelength of the wave,acceleration due to gravity,and density of water,respectively. The values of $a$,$b$,and $c$ are,respectively:

If energy $(E)$,velocity $(V)$,and time $(T)$ are chosen as the fundamental quantities,the dimensional formula of surface tension will be