If the straight lines $2x - y + 1 = 0$,$4x + y + 2 = 0$,and $x + y - k = 0$ are concurrent,then $k$ equals

If the lines $ax + 2y + 1 = 0$,$bx + 3y + 1 = 0$,and $cx + 4y + 1 = 0$ are concurrent,then $a, b, c$ are in:

Let $\alpha, \beta, \gamma$ be three non-zero real constants and $a, b, c$ be three arbitrary real numbers which satisfy $\alpha a + \beta b + \gamma c = 0$. Then the point of concurrence of the family of lines $ax + by + c = 0$ is

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

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

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: