Identify the CORRECT set of details from the following: A. [Co (NH_...

Analyzing each complex based on Valence Bond Theory (VBT):
A. $[Co(NH_3)_6]^{3+}$:
$Co^{3+}$ is $3d^6$. $NH_3$ is a strong field ligand (SFL) for $Co^{3+}$, causing pairing. This leaves two $3d$ orbitals vacant. Hybridization is $d^2sp^3$ (Inner orbital complex). Statement A is correct.

B. $[MnCl_6]^{3-}$:
$Mn^{3+}$ is $3d^4$. $Cl^-$ is a weak field ligand (WFL). No pairing occurs. To accommodate 6 ligands, it uses $4s$, $4p$, and $4d$ orbitals. Hybridization is $sp^3d^2$ (Outer orbital complex). Statement B is correct.

C. $[CoF_6]^{3-}$:
$Co^{3+}$ is $3d^6$. $F^-$ is a WFL. No pairing occurs. Hybridization is $sp^3d^2$ (Outer orbital complex). Statement C is incorrect because it mentions $d^2sp^3$.

D. $[FeF_6]^{3-}$:
$Fe^{3+}$ is $3d^5$. $F^-$ is a WFL. No pairing occurs. Hybridization is $sp^3d^2$ (Outer orbital complex). Statement D is correct.

E. $[Ni(CN)_4]^{2-}$:
$Ni^{2+}$ is $3d^8$. $CN^-$ is a SFL, causing pairing of the two unpaired electrons in $3d$. This leaves one $3d$ orbital vacant. Hybridization is $dsp^2$ (Square planar, Inner orbital complex). Statement E is incorrect because it mentions $sp^3$.

Correct statements are A, B, and D.