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The image contains a set of mathematical questions covering various topics, including set theory, functions, calculus, combinatorics, statistics, and algebra. Here's a brief breakdown of each question and how to approach them:

### Q.1 True or False with Reasons:
1. **a)** Collection of rich persons in India forms a set.
   - **Answer:** False. The term "rich" is subjective and not well-defined, so it doesn't form a set.
   
2. **b)** Given diagram: Determine if it's a function.
   - **Answer:** True. Each element in set A is mapped to exactly one element in set B.

3. **c)** Derivative problem: 
   \[
   \frac{d}{dx} (9 - 7x)^5 = 45(9 - 7x)^4
   \]
   - **Answer:** False. Applying the chain rule correctly:
   \[
   \frac{d}{dx} (9 - 7x)^5 = 5(9 - 7x)^4 \times (-7) = -35(9 - 7x)^4.
   \]
   
4. **d)** In exclusive method, upper limit of a class is included in the same class.
   - **Answer:** True. In the exclusive method, the upper limit is part of the class interval.

5. **e)** The order of the matrix 
   \[
   \begin{bmatrix} 2 & 5 & 6 \\ 4 & 3 & 1 \end{bmatrix}
   \]
   is \( 3 \times 2 \).
   - **Answer:** False. The matrix has 2 rows and 3 columns, so the order is \( 2 \times 3 \).

### Q.2 Combinatorics with Playing Cards:
1. **a)** All cards of the same suit.
   - Total ways = \( \binom{4}{1} \times \binom{13}{4} \).

2. **b)** All cards red.
   - Total ways = \( \binom{26}{4} \).

3. **c)** All face cards.
   - Total ways = \( \binom{12}{4} \).

4. **d)** All cards are kings.
   - Total ways = \( \binom{4}{4} = 1 \).

5. **e)** All cards of different suits.
   - Total ways = \( 13^4 \).

### Q.3 Stem-and-Leaf Plot:
   - Arrange the numbers with a stem of 5. Split numbers by the tens place as the stem and the units place as the leaf.

### Q.4 Set Theory Verification:
   - Verify De-Morgan's laws and the left distributive law using the given sets.

### Q.5 Integration:
1. **a)** \( \int x^2 e^{2x} \, dx \)
   - Use integration by parts.

2. **b)** \( \frac{dy}{dx} \) for \( y = (4x + 5)^4 (9x + 4)^5 \)
   - Use the product rule.

### Q.6 Matrix Proofs and Data:
1. **a)** Matrix identity proof involving the expression \( a^2 - b^2 - c^2 \).
2. **b)** Define primary and secondary data with examples.

### Q.7 Box Plot:
   - Draw a box plot for the given data, indicating quartiles, median, and outliers.

### Q.8 Continuity and Histogram:
1. **a)** Determine \( a \) and \( b \) so the function is continuous at \( x = 2 \).
2. **b)** Draw a histogram and frequency polygon for the provided data.

Would you like a detailed solution for any specific question, or do you need help understanding the concepts?

### Relative Questions:
1. What is the definition of a function in mathematics?
2. How do you use the chain rule in differentiation?
3. How is a stem-and-leaf plot constructed?
4. What are De-Morgan's laws in set theory?
5. What does it mean for a function to be continuous at a point?

### Tip:
When working with derivatives involving products or compositions of functions, remember to apply the product and chain rules correctly to avoid common mistakes.

The image contains various math problems related to set theory, functions, calculus, combinatorics, matrix operations, statistics, and algebra.

This set of mathematical questions covers key topics such as set theory, functions, calculus, combinatorics, matrix operations, and statistics. Learn how to approach each problem step by step, from verifying De-Morgan's laws to applying the chain rule in calculus and solving combinatoric problems with playing cards.

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