Among the following optical activity is possible in
(a) `[Co(H_(2)O)_(2)(NH_(3))_(3)CI]^(o+)`
(b) `[Co(H_(2)O))_(4)CI_(2)]^(o+)]`
(c ) `[Co(NH_(3))_(4)(NO_(2))CI]^(o+)`
(d) `[Co(CN)_(5)NC]^(Θ)` .

Explanation

To determine which of the given coordination compounds can exhibit optical activity, we need to analyze the symmetry of each complex. Optical activity is possible in a compound if it is chiral, meaning it lacks any symmetry elements such as a plane of symmetry, center of symmetry, or an axis of symmetry.

Let's analyze each option step by step:

### Step 1: Analyze the first complex `[Co(H₂O)₂(NH₃)₃Cl]⁺`

1. **Identify the ligands**: The complex has 2 water (H₂O) ligands, 3 ammonia (NH₃) ligands, and 1 chloride (Cl) ligand.
2. **Determine the geometry**: This complex is likely octahedral due to the coordination number of 6 (2 + 3 + 1).
3. **Check for symmetry**: In an octahedral arrangement, if we place the 2 water molecules in a cis position and the 3 ammonia ligands in a trans position to one of the water molecules, we can see that there is no plane of symmetry or center of symmetry. Thus, this complex is chiral.
4. **Conclusion**: This complex can exhibit optical activity.

### Step 2: Analyze the second complex `[Co(H₂O)₄Cl₂]⁺`

1. **Identify the ligands**: The complex has 4 water (H₂O) ligands and 2 chloride (Cl) ligands.
2. **Determine the geometry**: This complex is also octahedral.
3. **Check for symmetry**: With 4 identical water ligands and 2 identical chloride ligands, there is a plane of symmetry present. The arrangement of ligands leads to symmetry.
4. **Conclusion**: This complex cannot exhibit optical activity.

### Step 3: Analyze the third complex `[Co(NH₃)₄(NO₂)Cl]⁺`

1. **Identify the ligands**: The complex has 4 ammonia (NH₃) ligands, 1 nitrite (NO₂) ligand, and 1 chloride (Cl) ligand.
2. **Determine the geometry**: This complex is also octahedral.
3. **Check for symmetry**: The presence of 4 identical NH₃ ligands means that there is a plane of symmetry in the arrangement. Therefore, this complex is symmetric.
4. **Conclusion**: This complex cannot exhibit optical activity.

### Step 4: Analyze the fourth complex `[Co(CN)₅NC]⁰`

1. **Identify the ligands**: The complex has 5 cyanide (CN) ligands and 1 amine (NC) ligand.
2. **Determine the geometry**: This complex is likely octahedral.
3. **Check for symmetry**: With 5 identical cyanide ligands, there is a plane of symmetry present. The arrangement of ligands leads to symmetry.
4. **Conclusion**: This complex cannot exhibit optical activity.

### Final Conclusion

Among the given options, only the first complex `[Co(H₂O)₂(NH₃)₃Cl]⁺` is chiral and can exhibit optical activity.

### Summary of Results
- **(a)** `[Co(H₂O)₂(NH₃)₃Cl]⁺` - **Optically active**
- **(b)** `[Co(H₂O)₄Cl₂]⁺` - **Optically inactive**
- **(c)** `[Co(NH₃)₄(NO₂)Cl]⁺` - **Optically inactive**
- **(d)** `[Co(CN)₅NC]⁰` - **Optically inactive**

### Correct Answer: (a) `[Co(H₂O)₂(NH₃)₃Cl]⁺`

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