The compound which exhibits linkage isomerism is :

Options

A. `[Cr(NH_3)_6]^(3+)`
B. `[Co(NH_3)_6]^(3+)`
C. `[Co(NH_3)_5NO_2]Cl_2`
D. `[Pt(NH_3)_2 Cl_2]`

Explanation

To determine which compound exhibits linkage isomerism, we first need to understand what linkage isomerism is and identify the relevant ligands.

### Step 1: Understand Linkage Isomerism
Linkage isomerism occurs when a ligand can attach to the metal center through different atoms. This typically happens with ambidentate ligands, which have two different atoms that can coordinate to the metal ion. Common examples of ambidentate ligands include:

- **NO2-** (can bind through nitrogen or oxygen)
- **SCN-** (can bind through sulfur or nitrogen)

### Step 2: Identify the Compounds
Now, we need to look at the options provided in the question to identify which compound contains an ambidentate ligand. The question mentions four options, and we need to analyze them.

### Step 3: Analyze the Options
Let's consider the ligands in the options:

1. **Option A:** Contains ligands that do not exhibit linkage isomerism.
2. **Option B:** Contains ligands that do not exhibit linkage isomerism.
3. **Option C:** Contains **NO2-** as a ligand, which can bind through either nitrogen or oxygen, thus exhibiting linkage isomerism.
4. **Option D:** Contains ligands that do not exhibit linkage isomerism.

### Step 4: Conclusion
Based on the analysis, the compound that exhibits linkage isomerism is **Option C**, which contains the ligand **NO2-**.

### Final Answer
The compound which exhibits linkage isomerism is **Option C: [Co(NH3)5(NO2)]Cl2**.

---