In the List-$I$ below, four different paths of a particle are given as functions of time. In these functions, $\alpha$ and $\beta$ are positive constants of appropriate dimensions and $\alpha \neq \beta$. In each case, the force acting on the particle is either zero or conservative. In List-$II$, five physical quantities of the particle are mentioned: $\overrightarrow{p}$ is the linear momentum, $\overrightarrow{L}$ is the angular momentum about the origin, $K$ is the kinetic energy, $U$ is the potential energy and $E$ is the total energy. Match each path in List-$I$ with those quantities in List-$II$, which are conserved for that path.

List-$I$	List-$II$
$P$. $\vec{r}(t) = \alpha t \hat{i} + \beta t \hat{j}$	$1$. $\overrightarrow{p}$
$Q$. $\vec{r}(t) = \alpha \cos \omega t \hat{i} + \beta \sin \omega t \hat{j}$	$2$. $\overrightarrow{L}$
$R$. $\vec{r}(t) = \alpha(\cos \omega t \hat{i} + \sin \omega t \hat{j})$	$3$. $K$
$S$. $\vec{r}(t) = \alpha t \hat{i} + \frac{\beta}{2} t^2 \hat{j}$	$4$. $U$
	$5$. $E$

• A
  $P \rightarrow 1, 2, 3, 4, 5; \quad Q \rightarrow 2, 5; \quad R \rightarrow 2, 3, 4, 5; \quad S \rightarrow 5$
• B
  $P \rightarrow 1, 2, 3, 4, 5; \quad Q \rightarrow 3, 5; \quad R \rightarrow 2, 3, 4, 5; \quad S \rightarrow 2, 5$
• C
  $P \rightarrow 2, 3, 4; \quad Q \rightarrow 5; \quad R \rightarrow 1, 2, 4; \quad S \rightarrow 2, 5$
• D
  $P \rightarrow 1, 2, 3, 5; \quad Q \rightarrow 2, 5; \quad R \rightarrow 2, 3, 4, 5; \quad S \rightarrow 2, 5$