To solve the question regarding how many plants have a gynoecium that is bicarpellary, obligately placed, syncarpous, and with a placenta swollen with many ovules, we can follow these steps:
### Step 1: Understand the Terminology
- **Gynoecium**: The female reproductive part of a flower.
- **Bicarpellary**: This means the gynoecium consists of two carpels.
- **Obligately placed**: This indicates that the carpels are positioned in a specific arrangement.
- **Syncarpous**: This means that the carpels are fused together.
- **Swollen placenta with many ovules**: This describes the structure where ovules are attached, which is swollen and contains multiple ovules.
### Step 2: Identify the Family
The characteristics described are typical of plants in the **Solanaceae** family. This family is known for having flowers with a syncarpous gynoecium.
### Step 3: Analyze the Given Plants
Now, we will check each plant mentioned in the question to see if they belong to the Solanaceae family:
1. **Brinjal**: Yes, it belongs to the Solanaceae family.
2. **Gram**: No, it is a legume.
3. **Tulip**: No, it belongs to the Liliaceae family.
4. **Asparagus**: No, it belongs to the Asparagaceae family.
5. **Arhar**: No, it is a legume.
6. **Petunia**: Yes, it belongs to the Solanaceae family.
7. **Chilli**: Yes, it belongs to the Solanaceae family.
8. **Colchicum autumnale**: No, it is not a Solanaceae plant.
9. **Mulethi**: No, it is not a Solanaceae plant.
10. **Aloe**: No, it is not a Solanaceae plant.
11. **Pea**: No, it is a legume.
12. **Tobacco**: Yes, it belongs to the Solanaceae family.
13. **Lupin**: No, it is a legume.
### Step 4: Count the Plants
From the analysis, the plants that have the specified gynoecium characteristics are:
- Brinjal
- Petunia
- Chilli
- Tobacco
Thus, there are **four plants** that meet the criteria.
### Conclusion
The answer to the question is that **4 plants** have a gynoecium that is bicarpellary, obligately placed, syncarpous, and with a placenta swollen with many ovules.
