Which of the following complex ions has geometrical isomers?

Options

A. (a) `[Co(en)_3]^(3+)`
B. (b) `[Ni(NH_3)_5Br]^(+)`
C. (c) `[Co(NH_3)(en)_2]^(3+)`
D. (d) `[Cr(NH_3)_4(en)]^(3+)`

Explanation

To determine which complex ions exhibit geometrical isomerism, we need to analyze the coordination number and the types of ligands present in each complex. Geometrical isomerism typically occurs in coordination compounds with certain geometries, particularly octahedral and square planar complexes.

### Step-by-Step Solution:

1. **Identify the Coordination Number**:
- The coordination number is the number of ligand donor atoms that are bonded to the central metal ion. Common coordination numbers are 4 and 6.

2. **Examine the Ligands**:
- Determine if the ligands are monodentate (bonding through one donor atom) or bidentate (bonding through two donor atoms). Bidentate ligands can lead to different arrangements, which may result in isomerism.

3. **Analyze Complexes**:
- **Complex A: MA3** (where A is a symmetrical bidentate ligand like ethylenediamine)
- This complex has a coordination number of 6 (3 bidentate ligands). Since all ligands are symmetrical and identical, it cannot form geometrical isomers.
- **Conclusion**: No geometrical isomers.

- **Complex B: MA5** (where A is a monodentate ligand)
- This complex also has a coordination number of 6 (5 monodentate ligands). There is no possibility of geometrical isomerism as all ligands are identical.
- **Conclusion**: No geometrical isomers.

- **Complex C: [M(A2)(B2)]** (where A and B are different bidentate ligands)
- This complex has a coordination number of 6 (2 bidentate ligands of type A and 2 of type B). Different arrangements of A and B can lead to distinct geometrical isomers.
- **Conclusion**: Yes, geometrical isomers are possible.

- **Complex D: MA4A** (where A is a monodentate ligand)
- This complex has a coordination number of 6 (4 monodentate ligands). Similar to the previous complexes with identical ligands, it cannot form geometrical isomers.
- **Conclusion**: No geometrical isomers.

4. **Final Determination**:
- Based on the analysis, only Complex C exhibits geometrical isomerism due to the presence of different types of bidentate ligands.

### Answer:
The complex ion that has geometrical isomers is **Complex C: [M(A2)(B2)]**.