1. **Problem 1:** Find the distance of the point $A(4a, 3a)$ from the x-axis. - The distance of any point $(x, y)$ from the x-axis is the absolute value of its $y$-coordinate. - Here, the $y$-coordinate is $3a$. - Therefore, distance $= |3a| = 3a$ (assuming $a$ is positive). **Answer:** (A) 3a 2. **Problem 2:** Determine the nature of the natural number 1. - A prime number has exactly two distinct positive divisors: 1 and itself. - A composite number has more than two positive divisors. - The number 1 has only one positive divisor (1 itself). - Therefore, 1 is neither prime nor composite. **Answer:** (D) neither prime nor composite 3. **Problem 3:** Given $\cot \theta = 3$, find $\cos \theta$. - Recall that $\cot \theta = \frac{\cos \theta}{\sin \theta} = 3$. - Let $\sin \theta = s$, then $\cos \theta = 3s$. - Using the Pythagorean identity: $\sin^2 \theta + \cos^2 \theta = 1$. - Substitute: $s^2 + (3s)^2 = 1 \Rightarrow s^2 + 9s^2 = 1 \Rightarrow 10s^2 = 1$. - Solve for $s$: $s^2 = \frac{1}{10} \Rightarrow s = \frac{1}{\sqrt{10}}$. - Then $\cos \theta = 3s = \frac{3}{\sqrt{10}}$. **Answer:** (C) $\frac{3}{\sqrt{10}}$