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

Find the equation of the line passing through the intersection of the lines $x + y - 3 = 0$ and $2x - y + 1 = 0$ and the point $(2, -3)$.

The points $(3a, 0)$,$(0, 3b)$,and $(a, 2b)$ are:

Let the line $L_1$ passing through the point of intersection of the lines $2x + 3y - 5 = 0$ and $4x - 5y + 7 = 0$ divide the line segment joining the points $(2, 3)$ and $(1, -1)$ in the ratio $2:1$. If the equation of $L_1$ is $ax + by = 1$,then $33(a - b) =$

The equation of the straight line perpendicular to the straight line $3x + 2y = 0$ and passing through the point of intersection of the lines $x + 3y - 1 = 0$ and $x - 2y + 4 = 0$ is

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: