If the three lines $2x + y = 4$,$3x + 2y = 3$,and $ax + 3y = 2$ are concurrent,find the value of $a$.

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 line passing through the intersection of the lines $ax + 2by + 3b = 0$ and $bx - 2ay - 3a = 0$ (where $(a, b) \neq (0, 0)$) and parallel to the $x$-axis is:

The equation of the straight line passing through the point of intersection of the straight lines $3x - y + 2 = 0$ and $5x - 2y + 7 = 0$ and having an infinite slope is:

The distance between the points of concurrency of the two families of straight lines given by $x+(5 \lambda+1) y+1-3 \lambda=0$ and $(5 \mu+2) x-3 y+3+6 \mu=0$ is

If lines represented by $x+3y-6=0$,$2x+y-4=0$ and $kx-3y+1=0$ are concurrent,then the value of $k$ is