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

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 least positive value of $t$, so that the lines $x=t+\alpha, y+16=0$ and $y=\alpha x$ are concurrent, is

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

The straight lines $x+2y-9=0$, $3x+5y-5=0$, and $ax+by-1=0$ are concurrent if the straight line $35x-22y+1=0$ passes through the point

If $\pi / 3$ is the angle between the straight lines $px + qy + r = 0$ and $x \sin \alpha + y \cos \alpha = r$ $(r \neq 0)$ which meet at a point $A$,and the straight line $x \cos \alpha - y \sin \alpha = 0$ also passes through the point $A$,then: