jee-main 2024 Q70

jee-main · India · session1_31jan_shift1 3x3 Matrices Linear System with Parameter — Infinite Solutions
If the system of linear equations $$\begin{aligned} & x - 2 y + z = - 4 \\ & 2 x + \alpha y + 3 z = 5 \\ & 3 x - y + \beta z = 3 \end{aligned}$$ has infinitely many solutions, then $12 \alpha + 13 \beta$ is equal to
(1) 60
(2) 64
(3) 54
(4) 58
If the system of linear equations
$$\begin{aligned}
& x - 2 y + z = - 4 \\
& 2 x + \alpha y + 3 z = 5 \\
& 3 x - y + \beta z = 3
\end{aligned}$$
has infinitely many solutions, then $12 \alpha + 13 \beta$ is equal to\\
(1) 60\\
(2) 64\\
(3) 54\\
(4) 58