Which of the following is a set?

Options

A. The collection of all beautiful girls in india
B. The collection of all intelligent students in class XI
C. The collectoin of all metropolitian cities in india
D. The collection of all goods books in mathematics.

Answer

To determine which of the following collections is a set, we need to analyze each option based on the definition of a set. A set is a well-defined collection of distinct objects, where the criteria for membership are clear and unambiguous.

### Step-by-Step Solution:

1. **Collection of all beautiful girls in India**:
- This collection is subjective. What one person considers beautiful may differ from another person's opinion. Therefore, it is not a well-defined collection.
- **Conclusion**: Not a set.

2. **Collection of all intelligent students in class 11**:
- Similar to the first collection, the definition of "intelligent" can vary from person to person. Different criteria may lead to different conclusions about who is considered intelligent.
- **Conclusion**: Not a set.

3. **Collection of all metropolitan cities in India**:
- This collection is objective and well-defined. The criteria for being a metropolitan city are established by population and urban characteristics, and these do not vary based on personal opinion.
- **Conclusion**: This is a set.

4. **Collection of all good books in mathematics**:
- The term "good" is subjective and can differ based on personal preferences or opinions. Therefore, this collection is not well-defined.
- **Conclusion**: Not a set.

### Final Conclusion:
The only collection that qualifies as a set is the **collection of all metropolitan cities in India**.

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