Here are the solutions for each of the multiple-choice questions (MCQs) in the image:

1. If $\frac{3^2}{3^4} = 3^x$, then $x$ is equal to:

   • Simplifying the expression: $\frac{3^2}{3^4} = 3^{2-4} = 3^{-2}$.
   • So, $x = -2$.
   • Answer: (B) -2

2. Ratio has ____ unit:

   • A ratio compares quantities of the same unit.
   • Answer: (C) Same

3. A Triangle having two sides congruent is called:

   • A triangle with two equal sides is called an isosceles triangle.
   • Answer: (A) Isosceles

4. The logarithm of unity to any base is:

   • The logarithm of 1 to any base is 0: $\log_b(1) = 0$.
   • Answer: (B) 0

5. $a^2 - ab = ?$:

   • This is a simplification based on the choices.
   • $a^2 - ab = a(a-b)$.
   • Answer: (D) $a(a-b)$

6. Find $x$ in $(2x + 5)^2 = 25$:

   • $(2x + 5) = \pm 5$, so $2x + 5 = 5$ or $2x + 5 = -5$.
   • Solving gives $x = 0$ or $x = -5$.
   • Answer: (A) 0 or -5

7. If $a = 4$, what is $x^2 = a$ a complete square:

   • This looks like an incomplete question. Based on the options, when $a = 4$, $x = 2$ makes $x^2 = 4$, a perfect square.
   • Answer: (B) 2

8. Simplify: $\frac{\frac{3}{4} - \frac{1}{2}}{\frac{1}{3} + \frac{1}{6}}$:

   • $\frac{3/4 - 1/2}{1/3 + 1/6} = \frac{1/4}{1/2} = \frac{1/4 \times 2/1}{1} = \frac{1}{2}$.
   • Answer: (A) $\frac{1}{2}$

9. $x$ is a solution of the inequality $2x + 5 > 9$:

   • Solve the inequality: $2x + 5 > 9$ gives $x > 2$.
   • Answer: (A) $x > 2$

10. The distance between points $(0, 0)$ and $(1,1)$ is:

    • Using the distance formula: $\sqrt{(1-0)^2 + (1-0)^2} = \sqrt{1 + 1} = \sqrt{2}$.
    • Answer: (A) $\sqrt{2}$

11. The median used for different purposes between two triangles is:

    • The Centroid Theorem is used.
    • Answer: (A) Centroid

12. Measure of straight $\angle B$:

    • This question lacks sufficient information, but based on options:
    • Answer: (A) 90°

13. The perpendicular bisector of a chord:

    • A perpendicular bisector of a chord in a circle passes through the center.
    • Answer: (A) Bisector

14. The area enclosed by a triangle having vertices at (0, 0), (1, 0), and (0, 1) is:

    • The area of the triangle is $\frac{1}{2} \times \text{base} \times \text{height} = \frac{1}{2} \times 1 \times 1 = \frac{1}{2}$.
    • Answer: (B) $\frac{1}{2}$

15. $3x^2 = 36$, then $x =$:

    • Solve: $3x^2 = 36$ gives $x^2 = 12$, so $x = \pm \sqrt{12}$.
    • Answer: (B) $6$

If you need any clarification on these solutions or have further questions, feel free to ask!

Related Questions:

1. What is the general formula for the distance between two points?
2. How do you determine if a number is a perfect square?
3. What is the relationship between logarithms and exponents?
4. How do you solve quadratic equations by factoring?
5. What are the properties of the centroid in a triangle?

Tip: When dealing with inequalities, always check if the inequality sign changes when multiplying or dividing by a negative number.