Evaluate $\left|\begin{array}{cc}x & x+1 \\ x-1 & x\end{array}\right|$

If $abc \neq 0$ and the system of equations $x+7ay+2az=0$,$x+6by+2bz=0$,$x+5cy+2cz=0$ has a non-trivial solution,then $a, b, c$ are in

If the system of equations
$(k+1)^3 x + (k+2)^3 y = (k+3)^3$
$(k+1) x + (k+2) y = k+3$
$x + y = 1$
is consistent,then the value of $k$ is

For real numbers $x, y$ and $z$,if $x \neq y \neq z$,$\left|\begin{array}{ccc}x & x^2 & 1+x^3 \\ y & y^2 & 1+y^3 \\ z & z^2 & 1+z^3\end{array}\right|=0$ and $\left|\begin{array}{ccc}1 & x & x^2 \\ 1 & y & y^2 \\ 1 & z & z^2\end{array}\right| \neq 0$,then $xyz = $ . . . . . . .

If $\left[\begin{array}{ccc}1 & -1 & x \\ 1 & x & 1 \\ x & -1 & 1\end{array}\right]$ has no inverse,then the real value of $x$ is

If $\left| \begin{array}{ccc} a & b & 0 \\ 0 & a & b \\ b & 0 & a \end{array} \right| = 0$,then