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. $$\boxed{12 \text{m}}$$ --- 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) $\sin A$: $$\sin A = \frac{\text{opposite}}{\text{hypotenuse}} = \frac