To determine which of the given collections are sets, we need to check if each collection is well-defined. A collection is considered a set if we can clearly identify its members without ambiguity. Let's analyze each collection step by step:
### Step-by-Step Solution:
**(i)** The collection of all whole numbers less than 10.
- **Justification:** The whole numbers less than 10 are clearly defined as {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}.
- **Conclusion:** This is a set.
**(ii)** The collection of good hockey players in India.
- **Justification:** The term "good" is subjective and varies from person to person; thus, it is not well-defined.
- **Conclusion:** This is not a set.
**(iii)** The collection of all questions in this chapter.
- **Justification:** All questions in the chapter can be clearly identified and listed.
- **Conclusion:** This is a set.
**(iv)** The collection of all difficult chapters in this book.
- **Justification:** The term "difficult" is subjective and can differ among students; hence it is not well-defined.
- **Conclusion:** This is not a set.
**(v)** A collection of Hindi novels written by Munshi Prem Chand.
- **Justification:** The novels written by Munshi Prem Chand can be clearly identified and listed.
- **Conclusion:** This is a set.
**(vi)** A team of 11 best cricket players of India.
- **Justification:** The term "best" is subjective and varies from person to person, making it not well-defined.
- **Conclusion:** This is not a set.
**(vii)** The collection of all the months of the year whose names begin with the letter M.
- **Justification:** The months that start with 'M' are clearly defined as {March, May}.
- **Conclusion:** This is a set.
**(viii)** The collection of all interesting books.
- **Justification:** The term "interesting" is subjective and varies among individuals, making it not well-defined.
- **Conclusion:** This is not a set.
**(ix)** The collection of all short boys of your class.
- **Justification:** The term "short" is not well-defined without a specific height measurement.
- **Conclusion:** This is not a set.
**(x)** The collection of all those students of your class whose ages exceed 15 years.
- **Justification:** The age criterion is clear and can be objectively measured.
- **Conclusion:** This is a set.
**(xi)** The collection of all rich persons of Kolkata.
- **Justification:** The term "rich" is subjective and lacks a clear definition, making it not well-defined.
- **Conclusion:** This is not a set.
**(xii)** The collection of all persons of Kolkata whose assessed annual incomes exceed ₹20 lakh in the financial year 2016-17.
- **Justification:** This collection can be clearly defined based on income data.
- **Conclusion:** This is a set.
**(xiii)** The collection of all interesting dramas written by Shakespeare.
- **Justification:** The term "interesting" is subjective and varies among individuals, making it not well-defined.
- **Conclusion:** This is not a set.
### Summary of Results:
- Sets: (i), (iii), (v), (vii), (x), (xii)
- Not Sets: (ii), (iv), (vi), (viii), (ix), (xi), (xiii)
