Sure, here are the direct answers to the problems:

### Problem 1: School Election
**Answer: D) 47000**

### Problem 2: Value of sin A
**Answer: B) 11/13**

### Problem 3: Triangle XYZ
**Answer: A) 30°**

### Problem 4: Cube Surface Area and Volume
**Answer: B) 13824 cm³**

### Problem 5: 2x² - 7x²
Given $ 2x + 7 = 0 $, solve for $ x $:
\[
2x = -7
\]
\[
x = -\frac{7}{2}
\]

Now find $ 2x^2 - 7x^2 $:
\[
2x^2 - 7x^2 = -5x^2
\]
\[
= -5 \left(\frac{-7}{2}\right)^2
\]
\[
= -5 \left(\frac{49}{4}\right)
\]
\[
= -\frac{245}{4}
\]
The problem statement may have a typo; clarify if necessary.

### Problem 6: Value of cosA + sinA in a right-angled triangle
Given $ \Delta ABC $ with $ \angle B = 90° $, $ BC = 8 $, $ AC - AB = 2 $:
Use Pythagoras:
\[
AC = \sqrt{AB^2 + BC^2}
\]
\[
AB + BC = 10
\]
**Answer: B) 12/17**

### Problem 7: Area of an equilateral triangle
Side = 26 cm:
\[
Area = \frac{\sqrt{3}}{4} \times 26^2
\]
\[
= 169\sqrt{3} \text{ cm}^2
\]
**Answer: D) 169√3 cm²**

### Problem 8: Speed of a car
Distance = $ 216x^3 - 8 $, Time = $ 6x - 2 $:
\[
\text{Speed} = \frac{216x^3 - 8}{6x - 2}
\]
Factorize:
**Answer: A) 36x² - 4 + 12x**

### Problem 9: Value of $ 6(a^3 + b^3) $
Given $ a + b = 7 $ and $ ab = 10 $:
\[
a^3 + b^3 = (a+b)(a^2 - ab + b^2)
\]
\[
= 7 (49 - 10) = 273
\]
\[
6 \times 273 = 1638
\]
**Answer: D) 58/15**

### Problem 10: Price sequence in an arithmetic series
Price: 1, 3, 5, ..., up to 20 terms:
\[
\text{Sum} = \frac{n}{2} (a + l)
\]
\[
= 10 \times (1 + 39)
\]
\[
= 400
\]
**Answer: B) $400**

### Further problems:
1. Population after 3 years:
**Answer: A) 1,70,979**

2. Work completion:
**Answer: B) 13**

3. Compound interest:
**Answer: A) Rs 15,762.5**

4. Investment profits:
**Answer: C) Rs 3600**

5. Time to complete work:
**Answer: D) 30 days**

6. Ratio of water to milk:
**Answer: C) 11:7**

7. Mean proportional:
**Answer: B) 11**

8. Volume of water overflow:
**Answer: C) 23%**

9. New consumption of rice:
**Answer: B) 8.775 kg**

10. Average of numbers:
**Answer: B) 64**

11. Profit percentage:
**Answer: A) 18.33%**

12. Number of students liking cricket:
**Answer: D) 1188**

13. Central angle of Hockey:
**Answer: A) 29.4°**

14. Difference in preference:
**Answer: A) 400**

Would you like further details or clarifications on any of these answers? Here are five more questions you might ask:

1. Can you explain the steps to find the surface area of a cube?
2. How do you calculate the volume of a cube?
3. What is the Pythagorean theorem and how is it used?
4. How do you solve quadratic equations?
5. Can you explain the concept of arithmetic sequences and their sums?

**Tip:** When tackling math problems, always write down what you know and what you need to find out. This helps in organizing your solution.

Explore solutions to various math problems including school elections, triangle angles, cube surface area, quadratic equations, right-angled triangle properties, and equilateral triangle areas. Includes detailed steps and explanations for each problem. Suitable for Grades 10-12 students.

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