If the inverse of $\left[\begin{array}{ccc}-x & 14 x & 7 x \\ 0 & 1 & 0 \\ x & -4 x & -2 x\end{array}\right]$ is $\left[\begin{array}{ccc}2 & 0 & 7 \\ 0 & 1 & 0 \\ 1 & -2 & 1\end{array}\right]$, then $\left|\begin{array}{ccc}x & x+1 & x+2 \\ x+1 & x+2 & x+3 \\ x+2 & x+3 & x+4\end{array}\right|=$

If the system of equations $2 x+3 y-3 z=3, x+2 y+0 z=1 2 x-y+z=\beta$ has infinitely many solutions, then $\frac{\alpha}{\beta}-\frac{\beta}{\alpha}=$

A value of $\theta$ lying between 0 and $\pi / 2$ and satisfying $\left|\begin{array}{ccc}1+\sin ^2 \theta & \cos ^2 \theta & 4 \sin 4 \theta \\ \sin ^2 \theta & 1+\cos ^2 \theta & 4 \sin 4 \theta \\ \sin ^2 \theta & \cos ^2 \theta & 1+4 \sin 4 \theta\end{array}\right|=0$ is

If the system of equations $2 x+p y+6 z=8$, $x+2 y+q z=5$ and $x+y+3 z=4$ has infinitely many solutions, then $p=$