Analyzing each complex based on Valence Bond Theory (VBT):
A. [Co(NH3)6]3+:
Co3+ is 3d6. NH3 is a strong field ligand (SFL) for Co3+, causing pairing. This leaves two 3d orbitals vacant. Hybridization is d2sp3 (Inner orbital complex). Statement A is correct.
B. [MnCl6]3−:
Mn3+ is 3d4. Cl− is a weak field ligand (WFL). No pairing occurs. To accommodate 6 ligands, it uses 4s, 4p, and 4d orbitals. Hybridization is sp3d2 (Outer orbital complex). Statement B is correct.
C. [CoF6]3−:
Co3+ is 3d6. F− is a WFL. No pairing occurs. Hybridization is sp3d2 (Outer orbital complex). Statement C is incorrect because it mentions d2sp3.
D. [FeF6]3−:
Fe3+ is 3d5. F− is a WFL. No pairing occurs. Hybridization is sp3d2 (Outer orbital complex). Statement D is correct.
E. [Ni(CN)4]2−:
Ni2+ is 3d8. CN− is a SFL, causing pairing of the two unpaired electrons in 3d. This leaves one 3d orbital vacant. Hybridization is dsp2 (Square planar, Inner orbital complex). Statement E is incorrect because it mentions sp3.
Correct statements are A, B, and D.