Step 1: SO\(_2\) (Sulfur Dioxide).
SO\(_2\) has 2 bond pairs and 1 lone pair on the sulfur atom, thus corresponding to option (III) with BP = 2 and LP = 1.
Step 2: ClF\(_3\) (Chlorine trifluoride).
ClF\(_3\) has 3 bond pairs and 2 lone pairs on the chlorine atom, corresponding to option (IV) with BP = 3 and LP = 2.
Step 3: BrF\(_5\) (Bromine pentafluoride).
BrF\(_5\) has 5 bond pairs and 1 lone pair on the bromine atom, corresponding to option (II) with BP = 5 and LP = 1.
Step 4: XeF\(_4\) (Xenon tetrafluoride).
XeF\(_4\) has 4 bond pairs and 2 lone pairs on the xenon atom, corresponding to option (I) with BP = 4 and LP = 2.
Step 5: Conclusion.
Thus, the correct matching is:
(A) - (III), (B) - (II), (C) - (I), (D) - (IV). The correct answer is option (1).

