Which of the following collections represent a set :
(i) The collection of women prime ministers of India
(ii) The collection of first 5 natural numbers
(iii) The collection of intelligent girls of class XI.
(iv) The collection of best eleven batsman of the world.

Answer

To determine which of the following collections represent a set, we need to understand that a set is defined as a well-defined collection of distinct objects. This means that the elements of the set must be clearly defined and unambiguous.

Let's analyze each option step-by-step:

### Step 1: Analyze the collection of women prime ministers of India
- **Definition**: A collection of women who have served as prime ministers in India.
- **Evaluation**: This collection is well-defined because we can list the names of women who have served as prime ministers in India (e.g., Indira Gandhi, Sonia Gandhi). There is no ambiguity in identifying who qualifies as a woman prime minister.
- **Conclusion**: This represents a set.

### Step 2: Analyze the collection of the first 5 natural numbers
- **Definition**: The first five natural numbers are 1, 2, 3, 4, and 5.
- **Evaluation**: This collection is well-defined as it is universally accepted and can be explicitly listed without any ambiguity.
- **Conclusion**: This represents a set.

### Step 3: Analyze the collection of intelligent girls of class XI
- **Definition**: A collection of girls in class XI who are considered intelligent.
- **Evaluation**: This collection is not well-defined because the term "intelligent" is subjective. Different people may have different opinions on who is intelligent, leading to ambiguity.
- **Conclusion**: This does not represent a set.

### Step 4: Analyze the collection of best eleven batsmen of the world
- **Definition**: A collection of the best eleven batsmen in the world.
- **Evaluation**: Similar to the previous case, this collection is not well-defined because "best" is subjective and can vary based on personal opinions or criteria used for evaluation.
- **Conclusion**: This does not represent a set.

### Final Conclusion:
- The collections that represent a set are:
1. The collection of women prime ministers of India (Set)
2. The collection of the first 5 natural numbers (Set)

- The collections that do not represent a set are:
1. The collection of intelligent girls of class XI (Not a set)
2. The collection of best eleven batsmen of the world (Not a set)

### Summary:
- **Sets**: (i) and (ii)
- **Not Sets**: (iii) and (iv)

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