The derivative of a constant is .

Here are the solutions to the problems:

20. The derivative of a constant is _____.
The derivative of any constant is zero.
The correct option is (b) 0.

$$\boxed{0}$$

21. The distance round a circle is called _____.
The distance around a circle is called its circumference.
The correct option is (c) Circumference.

$$\boxed{\text{Circumference}}$$

22. What is the Sin $\theta$ of $30^\circ$?
The value of $\sin(30^\circ)$ is 0.5.
The correct option is (c) 0.500.

$$\boxed{0.500}$$

23. Solve $x^2 - 5x + 6 = 0$ by factorization.

Step 1: Factor the quadratic equation. We need two numbers that multiply to 6 and add to -5. These numbers are -2 and -3.

$$(x-2)(x-3) = 0$$

Step 2: Set each factor to zero and solve for $x$.

$$x-2 = 0 \implies x = 2$$ $$x-3 = 0 \implies x = 3$$

The solutions are $x=2$ and $x=3$.
The correct option is (a) $x=3, 2$.

$$\boxed{x=2, 3}$$

24. The Negation of "all birds can fly" is _____.
The negation of a universal statement "All A are B" is an existential statement "Some A are not B".
Therefore, the negation of "all birds can fly" is "Some birds cannot fly".
The correct option is (a) "Some birds cannot fly".

$$\boxed{\text{Some birds cannot fly}}$$

25. In a right angled triangle, if the hypotenuse is 13m and one leg is 5m, what is the Length of the other Leg?

Step 1: Use the Pythagorean theorem, $a^2 + b^2 = c^2$, where $c$ is the hypotenuse and $a, b$ are the legs.
Let $c = 13$m and $a = 5$m. We need to find $b$.

$$5^2 + b^2 = 13^2$$

Step 2: Calculate the squares.

$$25 + b^2 = 169$$

Step 3: Solve for $b^2$.

$$b^2 = 169 - 25$$ $$b^2 = 144$$

Step 4: Take the square root to find $b$.

$$b = \sqrt{144}$$ $$b = 12 \text{m}$$

The length of the other leg is 12m.
The correct option is (b) 12m.

$$\boxed{12 \text{m}}$$

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SECTION B: THEORY

1. Given $\tan A = \frac{3}{8}$. Find the value of (i) $\sin A$ (ii) $\cos A$ (iii) $\sec A$ (iv) $\csc A$ (v) $\cot A$ (In Surd form)

Step 1: Draw a right-angled triangle and label the sides. If $\tan A = \frac{\text{opposite}}{\text{adjacent}} = \frac{3}{8}$, then the opposite side is 3 and the adjacent side is 8.

Step 2: Use the Pythagorean theorem to find the hypotenuse ($h$).

$$h^2 = 3^2 + 8^2$$ $$h^2 = 9 + 64$$ $$h^2 = 73$$ $$h = \sqrt{73}$$

Step 3: Calculate the trigonometric ratios.

a) $\sin A$:

$$$$