If the dimensions of a physical quantity are given by $M^aL^bT^c$ ,then physical quantity will be 

A book with many printing errors contains four different formulas for the displacement $y$ of a particle undergoing a certain periodic motion:

$(a)\;y=a \sin \left(\frac{2 \pi t}{T}\right)$

$(b)\;y=a \sin v t$

$(c)\;y=\left(\frac{a}{T}\right) \sin \frac{t}{a}$

$(d)\;y=(a \sqrt{2})\left(\sin \frac{2 \pi t}{T}+\cos \frac{2 \pi t}{T}\right)$

$(a=$ maximum displacement of the particle, $v=$ speed of the particle. $T=$ time-period of motion). Rule out the wrong formulas on dimensional grounds.

Dimensions of time in power are

Dimensional formula for torque is

The quantities which have the same dimensions as those of solid angle are:

The dimensions of Stefan-Boltzmann's constant $\sigma$ can be written in terms of Planck's constant $h$, Boltzmann's constant $k_B$ and the speed of light $c$ as $\sigma=h^\alpha k_B^\beta c^\gamma$. Here,