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Let's walk through the questions and solve them one by one:

### Section A

1. **What is the median of the following set of numbers: 3, 5, 7, 9, 11?**
   - The median is the middle value when the numbers are arranged in ascending order.
   - Arranged: 3, 5, 7, 9, 11.
   - The middle value is **7**.
   - **Answer: A) 7**

2. **In a data set, what does the first quartile \(Q_1\) represent?**
   - The first quartile \(Q_1\) represents the value below which 25% of the data falls.
   - **Answer: C) The 25th percentile**

3. **What is the 90th percentile in a data set?**
   - The 90th percentile is the value below which 90% of the data falls.
   - **Answer: A) The value below which 90% of the data falls**

4. **What is the 7th decile of a data set?**
   - The 7th decile corresponds to the 70th percentile.
   - **Answer: A) The value below which 70% of the data falls**

5. **Which of the following is a type of set that contains no elements?**
   - A set with no elements is called a **null set**.
   - **Answer: A) Null set**

6. **Which of the following is a property of an equivalence relation?**
   - An equivalence relation must satisfy three properties: **Symmetry**, **Reflexivity**, and **Transitivity**.
   - **Answer: D) All of the above**

7. **What is the intersection of the sets \( A = \{2, 4, 6\} \) and \( B = \{4, 6, 8\} \)?**
   - The intersection of sets is the common elements between them. Common elements between \( A \) and \( B \) are \( 4 \) and \( 6 \).
   - **Answer: B) \{4, 6\}**

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### Section B

1. **Cumulative Frequency Table for Study Hours**
   - Hours: \( 0-2 \), \( 3-5 \), \( 6-8 \), \( 9-11 \)
   - Frequencies: 4, 8, 12, 6.
   - Cumulative frequency is the running total of the frequencies as you move down the table.

   | Hours    | Frequency | Cumulative Frequency |
   |----------|-----------|----------------------|
   | 0-2      | 4         | 4                    |
   | 3-5      | 8         | 12                   |
   | 6-8      | 12        | 24                   |
   | 9-11     | 6         | 30                   |

2. **Calculate the 3rd decile (D3) of the given data set**:
   - Data set: \( 45, 55, 60, 65, 70, 75, 80, 85, 90, 95 \)
   - Decile \( D_3 \) corresponds to the 30th percentile.
   - First, arrange the data in order (already done). The position of the 30th percentile is \( P = \frac{30}{100} \times 10 = 3 \).
   - The 3rd value in the data set is **60**.
   - **Answer: 60**

3. **Find \( A \times B \) and \( B \times A \) for the sets \( A = \{1, 2\} \) and \( B = \{a, b\} \)**.
   - \( A \times B \) is the set of ordered pairs where the first element is from \( A \) and the second is from \( B \):
     - \( A \times B = \{(1, a), (1, b), (2, a), (2, b)\} \).
   - Similarly, \( B \times A \) is:
     - \( B \times A = \{(a, 1), (a, 2), (b, 1), (b, 2)\} \).

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Let me know if you'd like further details on any of these questions or any clarifications!

Here are 5 related questions to explore further:

1. What is the difference between a percentile and a quartile?
2. How do you find the median for an even-numbered data set?
3. What is the relationship between deciles, percentiles, and quartiles?
4. Can a set have an infinite number of elements, and if so, what would it be called?
5. What are the practical applications of equivalence relations in mathematics?

**Tip:** When working with percentiles and quartiles, it's important to understand that they are measures of position, indicating how data points compare to the rest of the data set.

What is the median of the following set of numbers: 3, 5, 7, 9, 11? What does the first quartile Q1 represent? What is the 90th percentile in a data set? What is the 7th decile of a data set? Which of the following is a type of set that contains no elements? What is the intersection of sets A = {2, 4, 6} and B = {4, 6, 8}?

This page covers key mathematical concepts including how to calculate the median, first quartile, and 90th percentile. It also explores the 7th decile and how to find the intersection of two sets. Ideal for Grade 11 students.

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