If the unit of force and length each be increased by four times,then the unit of energy is increased by $...$ times.

Choose the correct statement from the following.

Match the List-$I$ with List-$II$. The correct match in the following is:

List-$I$	List-$II$
$A$. Boltzmann constant	$I$. $[ML^0T^0]$
$B$. Coefficient of viscosity	$II$. $[ML^{-1}T^{-1}]$
$C$. Water equivalent	$III$. $[ML^2T^{-2}K^{-1}]$
$D$. Coefficient of thermal conductivity	$IV$. $[MLT^{-3}K^{-1}]$

Read each statement below carefully and state,with reasons and examples,if it is true or false:
$A$ scalar quantity is one that
$(a)$ is conserved in a process
$(b)$ can never take negative values
$(c)$ must be dimensionless
$(d)$ does not vary from one point to another in space
$(e)$ has the same value for observers with different orientations of axes.

Match the physical quantities given in List-$I$ with their dimensions in List-$II$.

List-$I$	List-$II$
$A$. Gravitational potential	$I$. $M^0 L^2 T^{-2} K^{-1}$
$B$. Stefan's constant	$II$. $M^0 L^2 T^{-2}$
$C$. Permittivity	$III$. $M L^0 T^{-3} K^{-4}$
$D$. Specific heat capacity	$IV$. $M^{-1} L^{-3} T^4 I^2$

$(The dimensions of mass, length, time, temperature and current are $M$, $L$, $T$, $K$ and $I$ respectively.)$

The speed of light in vacuum is taken as unity. If light takes $6 \text{ min } 40 \text{ s}$ to reach the Earth from the Sun,the distance between the Sun and the Earth in new units is: