The central atom Phosphorus has 5 valence electrons and forms 5 bonds with Chlorine atoms. Using VSEPR theory, the steric number is 5 ($sp^{3}d$ hybridization), which corresponds to a Trigonal bipyramidal geometry (A-III).
Bromine has 7 valence electrons. It forms 5 bonds with Fluorine and has 1 lone pair. The steric number is 6 ($sp^{3}d^{2}$ hybridization). With 5 bond pairs and 1 lone pair, the geometry is Square pyramidal (B-IV).
Boron has 3 valence electrons. In $BF_{4}^{-}$, it forms 4 bonds. The steric number is 4 ($sp^{3}$ hybridization), which corresponds to a Tetrahedral geometry (C-I).
Nickel is in the +2 oxidation state ($d^{8}$ configuration). $CN^{-}$ is a strong field ligand, causing pairing of electrons. This results in $dsp^{2}$ hybridization, which corresponds to a Square planar geometry (D-II).
Final Answer: A-III, B-IV, C-I, D-II
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