If the system of equations $x – ky – z = 0$, $kx – y – z = 0$ and $x + y – z = 0$ has a non zero solution, then the possible value of k are

If $a \ne b \ne c,$ the value of $x$ which satisfies the equation $\left| {\,\begin{array}{*{20}{c}}0&{x – a}&{x – b}\\{x + a}&0&{x – c}\\{x + b}&{x + c}&0\end{array}\,} \right| = 0$, is

If $A = \left| {\,\begin{array}{*{20}{c}}1&1&1\\a&b&c\\{{a^3}}&{{b^3}}&{{c^3}}\end{array}\,} \right|,B = \left| {\,\begin{array}{*{20}{c}}1&1&1\\{{a^2}}&{{b^2}}&{{c^2}}\\{{a^3}}&{{b^3}}&{{c^3}}\end{array}\,} \right|,C = \left| {\,\begin{array}{*{20}{c}}a&b&c\\{{a^2}}&{{b^2}}&{{c^2}}\\{{a^3}}&{{b^3}}&{{c^3}}\end{array}\,} \right|,$ then which relation is correct

$l,m,n$ are the ${p^{th}},{q^{th}}$and ${r^{th}}$term of a G.P., all positive, then $\left| {\,\begin{array}{*{20}{c}}{\log l}&{p\,\,\,\,\,\begin{array}{*{20}{c}}1\end{array}}\\{\log m}&{q\,\,\,\,\,\begin{array}{*{20}{c}}1\end{array}}\\{\log n}&{r\,\,\,\,\,\begin{array}{*{20}{c}}1\end{array}}\end{array}\,} \right|$ equals

The value of the determinant $\left| {\,\begin{array}{*{20}{c}}{10!}&{11!}&{12!}\\{11!}&{12!}&{13!}\\{12!}&{13!}&{14!}\end{array}\,} \right|$ is