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:

Statement $(A)$: If $3a - 2b + 5c = 0$,then the line $ax + by + c = 0$ is always concurrent at a point.
Reason $(R)$: If $L_1 = 0$ and $L_2 = 0$ are two lines,then the family of lines $L_1 + \lambda L_2 = 0$ is concurrent at the intersection of $L_1$ and $L_2$.

If the lines $ax + by + c = 0$,$bx + cy + a = 0$,and $cx + ay + b = 0$ are concurrent,then:

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

For $c \neq 0, c \neq 1$,if the straight lines $x+y=1$,$2x-y=c$,and $bx+2by=c$ have one common point,then: