Which of the following coordination compounds exhibits ionisation isomerism
(a) `[Cr(NH_(3))_(6)]CI_(3)`
(b) `[Cr(en)_(3)CI_(3)]`
(c ) `[Cr(en)_(3)]CI_(3)`
(d) `[Co(NH_(3))_(5)Br]SO_(4)` .

Explanation

To determine which of the given coordination compounds exhibits ionization isomerism, we need to analyze each compound based on the definition of ionization isomerism. Ionization isomerism occurs when two or more compounds have the same formula but yield different ions in solution due to the exchange of ligands and counter ions.

### Step-by-Step Solution:

1. **Understanding Ionization Isomerism**:
- Ionization isomers are compounds that produce different ions in solution despite having the same molecular formula. This typically occurs when a counter ion can act as a ligand and can exchange places with a ligand in the coordination sphere.

2. **Analyzing Each Compound**:
- **(a) \[Cr(NH_3)_6Cl_3\]**:
- Here, the counter ion is chloride (Cl⁻), which is a negatively charged ion. Ammonia (NH₃) is a neutral ligand. Since a neutral ligand cannot be exchanged with a counter ion, this compound does not exhibit ionization isomerism.

- **(b) \[Cr(en)_3Cl_3\]**:
- In this case, the counter ion is again chloride (Cl⁻), and ethylene diamine (en) is a neutral ligand. Similar to the previous case, there is no possibility of exchanging a neutral ligand with a counter ion, so this compound does not exhibit ionization isomerism.

- **(c) \[Cr(en)_3Cl_3\]**:
- This compound is the same as (b) and has the same reasoning. It does not exhibit ionization isomerism for the same reasons.

- **(d) \[Co(NH_3)_5Br]SO_4\]**:
- Here, we have bromide (Br⁻) as a counter ion and sulfate (SO₄²⁻) as another counter ion. Both bromide and sulfate are negatively charged ions. In this case, bromide can be exchanged with sulfate, leading to the formation of a different ionization isomer. Therefore, this compound can exhibit ionization isomerism.

3. **Conclusion**:
- The only compound that can exhibit ionization isomerism is option **(d) \[Co(NH_3)_5Br]SO_4\]**.

### Final Answer:
The coordination compound that exhibits ionization isomerism is **(d) \[Co(NH_3)_5Br]SO_4\]**.