Let $\alpha, \beta$ and $\gamma$ be real numbers. consider the following system of linear equations

$x+2 y+z=7$

$x+\alpha z=11$

$2 x-3 y+\beta z=\gamma$

Match each entry in List - $I$ to the correct entries in List-$II$

List - $I$	List - $II$
($P$) If $\beta=\frac{1}{2}(7 \alpha-3)$ and $\gamma=28$, then the system has	($1$) a unique solution
($Q$) If $\beta=\frac{1}{2}(7 \alpha-3)$ and $\gamma \neq 28$, then the system has	($2$) no solution
($R$) If $\beta \neq \frac{1}{2}(7 \alpha-3)$ where $\alpha=1$ and $\gamma \neq 28$, then the system has	($3$) infinitely many solutions
($S$) If $\beta \neq \frac{1}{2}(7 \alpha-3)$ where $\alpha=1$ and $\gamma=28$, then the system has	($4$) $x=11, y=-2$ and $z=0$ as a solution
	($5$) $x=-15, y=4$ and $z=0$ as a solution

Then the system has

• A

  $(\mathrm{P}) \rightarrow(3)(\mathrm{Q}) \rightarrow(2)(\mathrm{R}) \rightarrow(1)(\mathrm{S}) \rightarrow(4)$

• B

  $(P) \rightarrow (3) (Q) \rightarrow (2) (R) \rightarrow (5) (S) \rightarrow (4)$

• C

  $(P) \rightarrow (2) (Q) \rightarrow (1) (R) \rightarrow (4) (S) \rightarrow (5)$

• D

  $(\mathrm{P}) \rightarrow(2)(\mathrm{Q}) \rightarrow(1)(\mathrm{R}) \rightarrow(1)(\mathrm{S}) \rightarrow(3)$