Which of the following groups has different dimensions?

Match the following (Take the relative strength of the strongest fundamental forces in nature as $1$):

$I$ (Fundamental forces in nature)	$II$ (Relative strength)
$(A)$ Strong nuclear force	$(e)$ $10^{-2}$
$(B)$ Weak nuclear force	$(f)$ $1$
$(C)$ Electromagnetic force	$(g)$ $10^{10}$
$(D)$ Gravitational force	$(h)$ $10^{-13}$
	$(i)$ $10^{-39}$

The correct match is:

The pair having the same dimensions is

State whether the following statements are true or false:
$(a)$ $A$ dimensionally incorrect equation can be correct.
$(b)$ $1 \ AU = 9.46 \times 10^{15} \ m$
$(c)$ The dimensional formula of force and stress are the same.
$(d)$ The dimensions of a physical quantity are different in different systems of units.

Match List-$I$ and List-$II$:

List-$I$	List-$II$
$A$. Young's Modulus $(Y)$	$I$. $[M L^{-1} T^{-1}]$
$B$. Co-efficient of Viscosity $(\eta)$	$II$. $[M L^2 T^{-1}]$
$C$. Planck's Constant $(h)$	$III$. $[M L^{-1} T^{-2}]$
$D$. Work Function $(\varphi)$	$IV$. $[M L^2 T^{-2}]$

Choose the correct answer from the options given below:

Which of the following statements is incorrect?