Which quantity among the following has neither units nor dimensions?

$A$ new unit $(\alpha)$ of length is chosen such that it is equal to the speed of light in vacuum. What is the distance between Venus and Earth in terms of $\alpha$ units if light takes $6 \text{ min } 40 \text{ s}$ to cover this distance (in $\text{ } \alpha$)?

If the volume and surface area of a cube are numerically equal,what is its volume in cubic units?

Match the following physical quantities with their respective dimensional formulas:

$(A)$ Thermal conductivity	$(i)$ $MLT^{-3}K^{-1}$
$(B)$ Boltzmann constant	(ii) $M^0L^2T^{-2}K^{-1}$
$(C)$ Latent heat	(iii) $ML^2T^{-2}K^{-1}$
$(D)$ Specific heat	(iv) $M^0L^2T^{-2}$

$Pascal-Second$ has the dimension of:

Match List-$I$ with List-$II$.

List-$I$	List-$II$
$(A)$ Coefficient of viscosity	$(I)$ $[ML^0T^{-3}]$
$(B)$ Intensity of wave	$(II)$ $[ML^{-2}T^{-2}]$
$(C)$ Pressure gradient	$(III)$ $[M^{-1}LT^2]$
$(D)$ Compressibility	$(IV)$ $[ML^{-1}T^{-1}]$

Choose the correct answer from the options given below: