The three lines $lx + my + n = 0$,$mx + ny + l = 0$,and $nx + ly + m = 0$ are concurrent if:

If the point of intersection of the lines $2ax + 4ay + c = 0$ and $7bx + 3by - d = 0$ lies in the $4^{th}$ quadrant and is equidistant from the two axes, where $a, b, c,$ and $d$ are non-zero numbers, then $ad : bc$ is equal to

If the straight lines $ax + amy + 1 = 0$,$bx + (m + 1)by + 1 = 0$,and $cx + (m + 2)cy + 1 = 0$ $(m \neq 0)$ are concurrent,then $a, b, c$ are in:

The point of intersection of the lines $(a^3 + 3)x + ay + a - 3 = 0$ and $(a^5 + 2)x + (a + 2)y + 2a + 3 = 0$ (where $a$ is a real number) lies on the $y$-axis for:

If three lines whose equations are $y=m_{1}x+c_{1}$,$y=m_{2}x+c_{2}$,and $y=m_{3}x+c_{3}$ are concurrent,then show that $m_{1}(c_{2}-c_{3})+m_{2}(c_{3}-c_{1})+m_{3}(c_{1}-c_{2})=0$.

The system of equations $2x + y - 5 = 0$,$x - 2y + 1 = 0$,and $2x - 14y - a = 0$ is consistent. Then,$a$ is equal to