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I have opened the image containing the math questions. Let's go through the questions and solve them one by one from Section A:

1. **1 + \( \frac{1}{3} + \frac{1}{9} \) = ?**
   - Simplify the fractions:
     \[
     1 + \frac{1}{3} + \frac{1}{9} = \frac{9}{9} + \frac{3}{9} + \frac{1}{9} = \frac{9 + 3 + 1}{9} = \frac{13}{9}
     \]
     Answer: \( \frac{13}{9} \) (Option b).

2. **How many solutions does a linear equation in one variable have?**
   - A linear equation in one variable has exactly **one solution**.
     Answer: One (Option a).

3. **What is the digit at the unit's place in the square of 26387?**
   - Find the unit digit of \( 26387^2 \). The unit digit of 26387 is 7, and the square of 7 is 49. Therefore, the unit digit of the square is **9**.
     Answer: 9 (Option b).

4. **Which of the following expressions is a polynomial?**
   - The options contain polynomial and non-polynomial expressions. A polynomial must have non-negative integer exponents. The correct expression is **\( 3x^3 + 3x^2 + 3x + 3 \)**.
     Answer: \( 3x^3 + 3x^2 + 3x + 3 \) (Option b).

5. **What is the volume of a cube whose edge is 4 cm?**
   - The volume of a cube is given by \( \text{side}^3 \). For an edge of 4 cm:
     \[
     V = 4^3 = 64 \, \text{cm}^3
     \]
     Answer: 64 cm³ (Option c).

6. **The square of \( (5x + 2y) \) would be?**
   - Use the formula for the square of a binomial: \( (a + b)^2 = a^2 + 2ab + b^2 \).
     \[
     (5x + 2y)^2 = (5x)^2 + 2(5x)(2y) + (2y)^2 = 25x^2 + 20xy + 4y^2
     \]
     Answer: \( 25x^2 + 20xy + 4y^2 \) (Option d).

7. **If \( \sqrt{2} + \sqrt{x} = 3 \), then \( x = ? \)**
   - Rearrange and solve for \( x \):
     \[
     \sqrt{x} = 3 - \sqrt{2}
     \]
     Square both sides:
     \[
     x = (3 - \sqrt{2})^2
     \]
     This simplifies to approximately **7**.
     Answer: 7 (Option b).

8. **Rational number not between \( \frac{1}{4} \) and \( \frac{1}{2} \) is:**
   - Among the given options, \( \frac{17}{48} \approx 0.354 \), which is between 0.25 and 0.5. The number not in this range is \( \frac{3}{8} \approx 0.375 \).
     Answer: \( \frac{1}{5} \) (Option d).

9. **If \( \frac{a}{7} + \frac{8}{7} = 8 \), then \( a = ? \)**
   - Combine the terms:
     \[
     \frac{a + 8}{7} = 8
     \]
     Multiply by 7:
     \[
     a + 8 = 56 \implies a = 48
     \]
     Answer: 48 (Option d).

10. **Which of the following is a Pythagorean triplet whose smallest member is 10?**
    - A Pythagorean triplet follows \( a^2 + b^2 = c^2 \). For the triplet (10, 24, 26):
      \[
      10^2 + 24^2 = 100 + 576 = 676 = 26^2
      \]
      Answer: 10, 24, 26 (Option b).

11. **When a die is thrown, the probability of getting a number greater than 5 is:**
    - There are 6 possible outcomes (1 to 6). Only two numbers (6 and 5) are greater than 5. So, the probability is:
      \[
      P = \frac{1}{6}
      \]
      Answer: \( \frac{1}{6} \).

Would you like further explanations on any of the answers or the next set of questions?

### Related Questions:
1. How do you identify a polynomial?
2. What is the general form for the volume of 3D shapes like spheres or cones?
3. How do you solve equations involving square roots?
4. What are the properties of rational numbers and how do they differ from irrational numbers?
5. What methods can be used to determine the probability of multiple events?

### Tip:
When solving problems involving square roots, always check if you can simplify them further before proceeding with operations like squaring both sides.

Solve various math problems from a midterm examination for Class VIII students, including algebraic expressions, volume of a cube, polynomial identification, Pythagorean triplets, and probability.

Solve various math problems for Class VIII, including algebraic expressions, volume of cubes, identifying polynomials, Pythagorean triplets, and basic probability. This exam covers essential concepts like number systems, geometry, and algebra.

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