If $R , X _{ L }$. and $X _{ C }$ represent resistance, inductive reactance and capacitive reactance. Then which of the following is dimensionless:

A spherical body of mass $m$ and radius $r$ is allowed to fall in a medium of viscosity $\eta $. The time in which the velocity of the body increases from zero to $0.63$ times the terminal velocity $(v)$ is called time constant $(\tau )$. Dimensionally $\tau $ can be represented by

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

If $R$ and $L$ represent respectively resistance and self inductance, which of the following combinations has the dimensions of frequency

A force $F$ is given by $F = at + b{t^2}$, where $t$ is time. What are the dimensions of $a$ and $b$