The List-II contains products obtained from the reaction of compounds in List-I with $O_3$/Zn-$H_2O$ followed by cyclization (via more stable enolate) in the presence of aqueous NaOH. Match each entry in List-I with appropriate entry in List-II and choose the correct option.

List-I	List-II
(P)	(1)
(Q)	(2)
(R)	(3)
(S)	(4)
	(5)

Match the major products obtained in the reactions given in List-I with the corresponding structures in List-II and choose the correct option.

List-I	List-II
(P)	(1)
(Q)	(2)
(R)	(3)
(S)	(4)
	(5)

Consider the function $f : (0, \infty) \to (-\infty, \infty)$ given by

$f(x) = \sqrt{x} \log_e(x) - x + 1$.

Then which one of the following statements is TRUE?

Let $P$ be the point on the parabola $y = x^2$ such that the slope of the tangent to the parabola at the point $P$ is $4$. Let $Q$ be the point in the first quadrant lying on the circle $x^2 + y^2 = 2$ such that the slope of the tangent to the circle at the point $Q$ is $-1$. Let $R$ be the point in the first quadrant lying on the ellipse $x^2 + 4y^2 = 8$ such that the slope of the tangent to the ellipse at the point $R$ is $-\frac{1}{2}$. Then the radius of the circle passing through the points $P, Q$ and $R$ is