`(a) CoCl_3.4NH_3, (b) CoCl_3.5NH_3, (c) COCl_3.6NH_3" and" (d) CoCl(NO_3)_2.5NH_3`
Number of complex(es) which will exist in cis-trans form is/are ____________ .

Explanation

To determine the number of complexes that can exist in cis-trans form among the given compounds, we need to analyze each complex based on its coordination geometry and the nature of its ligands.

### Step-by-Step Solution:

1. **Identify the Coordination Number and Geometry**:
- The complexes mentioned are all cobalt complexes. Cobalt typically exhibits a coordination number of 6 in octahedral complexes.

2. **Analyze Each Complex**:
- **(a) CoCl₃·4NH₃**:
- This complex has 3 chloride ions and 4 ammonia ligands. In an octahedral geometry, the 3 chloride ions can be arranged in a cis or trans configuration. Therefore, this complex can exist in both cis and trans forms.

- **(b) CoCl₃·5NH₃**:
- This complex has 3 chloride ions and 5 ammonia ligands. Similar to the previous case, the arrangement of the 3 chloride ions allows for cis and trans configurations. Thus, this complex can also exist in both cis and trans forms.

- **(c) CoCl₃·6NH₃**:
- This complex has 3 chloride ions and 6 ammonia ligands. In this case, all ligands are identical (NH₃), and the 3 chloride ions can be arranged in a way that allows for cis and trans forms. So, this complex can exist in both cis and trans forms as well.

- **(d) CoCl(NO₃)₂·5NH₃**:
- This complex has 1 chloride ion, 2 nitrate ions, and 5 ammonia ligands. The presence of different ligands (Cl and NO₃) means that the complex can have a cis or trans arrangement. However, since there is only 1 chloride ion, it cannot form a trans configuration with respect to the chloride. Therefore, this complex does not exist in cis-trans form.

3. **Count the Complexes that Can Exist in Cis-Trans Form**:
- From the analysis:
- (a) CoCl₃·4NH₃: Yes (cis-trans)
- (b) CoCl₃·5NH₃: Yes (cis-trans)
- (c) CoCl₃·6NH₃: Yes (cis-trans)
- (d) CoCl(NO₃)₂·5NH₃: No (only one Cl)

- Therefore, the total number of complexes that can exist in cis-trans form is 3.

### Final Answer:
The number of complex(es) which will exist in cis-trans form is **3**.