Q69. Let $\alpha \beta \neq 0$ and $A = \left[ \begin{array} { r r r } \beta & \alpha & 3 \\ \alpha & \alpha & \beta \\ - \beta & \alpha & 2 \alpha \end{array} \right]$. If $B = \left[ \begin{array} { r r r } 3 \alpha & - 9 & 3 \alpha \\ - \alpha & 7 & - 2 \alpha \\ - 2 \alpha & 5 & - 2 \beta \end{array} \right]$ is the matrix of cofactors of the elements of $A$, then $\operatorname { det } ( A B )$ is equal to : (1) 64 (2) 216 (3) 343 (4) 125 Q70. $x + y + z = 4$, The values of $m , n$, for which the system of equations $2 x + 5 y + 5 z = 17$, has infinitely many solutions, $x + 2 y + \mathrm { m } z = \mathrm { n }$ satisfy the equation: (1) $m ^ { 2 } + n ^ { 2 } - m n = 39$ (2) $m ^ { 2 } + n ^ { 2 } - m - n = 46$ (3) $m ^ { 2 } + n ^ { 2 } + m + n = 64$ (4) $m ^ { 2 } + n ^ { 2 } + m n = 68$
Q69. Let $\alpha \beta \neq 0$ and $A = \left[ \begin{array} { r r r } \beta & \alpha & 3 \\ \alpha & \alpha & \beta \\ - \beta & \alpha & 2 \alpha \end{array} \right]$. If $B = \left[ \begin{array} { r r r } 3 \alpha & - 9 & 3 \alpha \\ - \alpha & 7 & - 2 \alpha \\ - 2 \alpha & 5 & - 2 \beta \end{array} \right]$ is the matrix of cofactors of the elements of $A$, then $\operatorname { det } ( A B )$ is equal to :\\
(1) 64\\
(2) 216\\
(3) 343\\
(4) 125
Q70.\\
$x + y + z = 4$,\\
The values of $m , n$, for which the system of equations $2 x + 5 y + 5 z = 17$, has infinitely many solutions, $x + 2 y + \mathrm { m } z = \mathrm { n }$ satisfy the equation:\\
(1) $m ^ { 2 } + n ^ { 2 } - m n = 39$\\
(2) $m ^ { 2 } + n ^ { 2 } - m - n = 46$\\
(3) $m ^ { 2 } + n ^ { 2 } + m + n = 64$\\
(4) $m ^ { 2 } + n ^ { 2 } + m n = 68$