To determine the correctness of the given options based on the nature of the complexes and their hybridizations, we need to analyze each option individually:
- Complex: \([\text{Co}(\text{NH}_3)_6]^{3+}\)
- The central metal ion is Co(III) with an electronic configuration: \([Ar] 3d^6\).
- The ligand NH3 is a strong field ligand, causing pairing of 3d electrons.
- This results in the inner orbital complex with hybridization \(d^2sp^3\).
- Conclusion: Option A is correctly identified as an inner orbital complex with \(d^2sp^3\) hybridization.
- Complex: \([\text{MnCl}_4]^{2-}\)
- The central metal ion is Mn(II), with an electronic configuration: \([Ar] 3d^5\).
- Cl− is a weak field ligand, which leads to no electron pairing and uses outer \(4d\) orbitals.
- This results in an outer orbital complex with hybridization \(sp^3d^2\).
- Conclusion: Option B is correctly identified as an outer orbital complex with \(sp^3d^2\) hybridization.
- Complex: \([\text{CoF}_6]^{3-}\)
- Co(III) has an electronic configuration: \([Ar] 3d^6\).
- F− is a weak field ligand, leading to the use of outer \(d\) orbitals.
- This would ideally form an outer orbital complex with \(sp^3d^2\) hybridization, not \(d^2sp^3\) as stated.
- Conclusion: Option C is incorrectly identified in terms of hybridization.
- Complex: \([\text{FeF}_6]^{3-}\)
- Fe(III) has an electronic configuration: \([Ar] 3d^5\).
- F− is a weak field ligand, using outer \(d\) orbitals.
- This leads to an outer orbital complex with \(sp^3d^2\) hybridization.
- Conclusion: Option D is correctly identified as an outer orbital complex with \(sp^3d^2\) hybridization.
- Complex: \([\text{Ni}(\text{CN})_4]^{2-}\)
- Ni(II) has an electronic configuration: \([Ar] 3d^8\).
- CN− is a strong field ligand, causing pairing of 3d electrons and utilizing inner d orbitals.
- This results in an inner orbital complex with \(dsp^2\) hybridization instead of \(sp^3\).
- Conclusion: Option E is incorrectly identified in terms of hybridization.
Based on the above analysis, the correct complexes are identified as A, B, and D only.