The dimensional formula of $\sqrt{\mu_r K}$ is equal to:

Mumbai needs $1.4 \times 10^{12} \, L$ of water annually. Its effective surface area is $600 \, km^2$ and it receives an average rainfall of $2.4 \, m$ annually. If $10 \%$ of this rainwater is conserved,it will meet approximately:

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	$IV$. $[MLT^{-3}K^{-1}]$

Which of the following quantities has a unit but is dimensionless?

Match List-$I$ with List-$II$ and select the correct answer.

List-$I$	List-$II$
$A$. Spring constant	$1$. $M^1L^2T^{-2}$
$B$. Pascal	$2$. $M^0L^0T^{-1}$
$C$. Hertz	$3$. $M^1L^0T^{-2}$
$D$. Joule	$4$. $M^1L^{-1}T^{-2}$

Match the physical quantities in List-$I$ with their dimensional formulas in terms of mass $(M)$, length $(L)$, time $(T)$ and electric current $(A)$ given in List-$II$.

List-$I$	List-$II$
$(a)$ Torque	$(i)$ $[M^{-1}L^{-2}T^4A^2]$
$(b)$ Gravitational constant	(ii) $[M^1L^2T^{-1}]$
$(c)$ Capacitance	(iii) $[M^{-1}L^3T^{-2}]$
$(d)$ Planck's constant	(iv) $[M^1L^2T^{-2}]$