Unclassified (maths): JEE Advanced 2023 Mathematics question

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