KCET 2026 Mathematics Solved Paper

Concept: The given parametric equations represent a circle whose radius is identified by comparing with the standard form.Explanation: The standard parametric form of a circle is $x = a \cos\theta$ and $y = a \sin\theta$, where $a$ is the radius.Here, $x = \sqrt{3} \cos\theta$ and $y = \sqrt{3} \sin\theta$, so the radius is $a = \sqrt{3}$.The area enclosed by a circle is given by the formula $\text{Area} = \pi r^{2}$.Substitute $r = \sqrt{3}$ into the formula:$$\text{Area} = \pi(\sqrt{3})^{2} = \pi \times 3 = 3\pi$$Thus, the area enclosed by the curve is $3\pi$ square units.Answer: $3\pi$ sq. units, which is Option D.