Statement a: CFSE of [Co(NH3)6]3, [Rh(NH3)6]3, [Ir(NH3)6]3
Statement b: CFSE of [Co(NH3)6]3, [Co(en)3]3
Statement c: The low-spin state of Co3+ is more stable
Statement d: [Ni(H2O)6]2 complex is yellow while [Ni(en)3]2 is violet

Explanation:

Statement a: CFSE of [Co(NH3)6]3, [Rh(NH3)6]3, [Ir(NH3)6]3
The complex [Co(NH3)6]3+ has a d6 electronic configuration. The presence of six ligands (NH3) leads to the splitting of the d-orbitals into two sets of different energy levels, known as the t2g (lower energy) and eg (higher energy) levels. The CFSE (Crystal Field Stabilization Energy) of this complex is determined by the energy difference between the t2g and eg levels.
The [Rh(NH3)6]3+ and [Ir(NH3)6]3+ complexes also have d6 electronic configurations and octahedral geometries. Therefore, their CFSE values will also be determined by the energy difference between the t2g and eg levels. Thus, statement a is correct.

Statement b: CFSE of [Co(NH3)6]3, [Co(en)3]3
The [Co(NH3)6]3+ complex has a d6 electronic configuration, while the [Co(en)3]3+ complex has a d5 electronic configuration. The CFSE of a complex is determined by the energy difference between the t2g and eg levels. In the case of [Co(NH3)6]3+, the t2g level is completely filled with electrons, resulting in a lower CFSE compared to [Co(en)3]3+, where the t2g level is partially filled. Therefore, [Co(NH3)6]3+ will have a lower CFSE than [Co(en)3]3+. Thus, statement b is correct.

Statement c: The low-spin state of Co3+ is more stable
The stability of a low-spin or high-spin state depends on the ligand field strength. In general, ligands that form strong bonds with the central metal ion favor the low-spin state, while ligands that form weak bonds favor the high-spin state. Therefore, the stability of the low-spin state of Co3+ will depend on the ligands present in the coordination complex. However, the given statement does not provide any specific information about the ligands. Therefore, statement c cannot be determined based on the given information.

Statement d: [Ni(H2O)6]2 complex is yellow while [Ni(en)3]2 is violet
The color of a coordination complex is determined by the absorption of light in the visible region of the electromagnetic spectrum. The presence of certain ligands can cause a complex to absorb specific wavelengths of light, resulting in a characteristic color. In the case of [Ni