Number of values of $m$ for which the lines $x + y - 1 = 0$,$(m - 1)x + (m^2 - 7)y - 5 = 0$ and $(m - 2)x + (2m - 5)y = 0$ are concurrent,are

If $(x_1, y_1)$ are the roots of $x^2 + 8x - 20 = 0$,$(x_2, y_2)$ are the roots of $4x^2 + 32x - 57 = 0$ and $(x_3, y_3)$ are the roots of $9x^2 + 72x - 112 = 0$,then the points $(x_1, y_1), (x_2, y_2)$ and $(x_3, y_3)$:

If the sum of squares of all real values of $\alpha$,for which the lines $2x - y + 3 = 0$,$6x + 3y + 1 = 0$,and $\alpha x + 2y - 2 = 0$ do not form a triangle is $p$,then the greatest integer less than or equal to $p$ is $.........$

Find the equation of the line passing through the intersection of the lines $4x - 3y - 1 = 0$ and $5x - 2y - 3 = 0$ and parallel to the line $2x - 3y + 2 = 0$.

The three lines $lx + my + n = 0$,$mx + ny + l = 0$,and $nx + ly + m = 0$ are concurrent if:

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