In Statement I, for K3[Co(CO3)3], Cobalt is in +3 oxidation state (Co3+:3d6). Carbonate (CO32−) is a weak field ligand. Thus, no pairing occurs, resulting in 4 unpaired electrons. Hybridisation is sp3d2, shape is octahedral, and μ=4(4+2)=24≈4.9 BM. Statement I is true.
In Statement II:
For [Ni(CN)4]2−, Ni2+ is 3d8. CN− is a strong field ligand, causing pairing. Hybridisation is dsp2, geometry is square planar, and μ=0 BM.
For [MnBr4]2−, Mn2+ is 3d5. Br− is a weak field ligand. Hybridisation is sp3, geometry is tetrahedral, and μ=5(5+2)=35≈5.9 BM.
For [CoF6]3−, Co3+ is 3d6. F− is a weak field ligand. Hybridisation is sp3d2, geometry is octahedral, and μ=4(4+2)=24≈4.9 BM.
Statement II is true.
Both statements are true.