$2x + 3y + 4z = 9$,$4x + 9y + 3z = 10,$$5x + 10y + 5z = 11$ then the value of $ x$ is

If the system of linear equations $x - 2y + kz = 1$ ; $2x + y + z = 2$ ;  $3x - y - kz = 3$ Has a solution $(x, y, z) \ne 0$, then $(x, y)$ lies on the straight line whose equation is

Evaluate the determinants

$\left|\begin{array}{ccc}
3 & -4 & 5 \\
1 & 1 & -2 \\
2 & 3 & 1
\end{array}\right|$

If the lines $x + 2ay + a = 0$, $x + 3by + b = 0$  and $x + 4cy + c = 0$ are concurrent, then $a$, $b$ and $c$ are in

If system of equations $kx + 2y - z = 2,$$\left( {k - 1} \right)x + ky + z = 1,x + \left( {k - 1} \right)y + kz = 3$ has only one solution, then number of possible real value$(s)$ of $k$ is -
 

For positive numbers $x,y$ and $z$  the numerical value of the determinant $\left| {\,\begin{array}{*{20}{c}}1&{{{\log }_x}y}&{{{\log }_x}z}\\{{{\log }_y}x}&1&{{{\log }_y}z}\\{{{\log }_z}x}&{{{\log }_z}y}&1\end{array}\,} \right|$is