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.