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

The equation of a line passing through the point of intersection of the lines $x - 2y + 8 = 0$ and $3x - y + 4 = 0$ and passing through the origin is

If the lines $x + 2ay + a = 0$,$x + 3by + b = 0$,and $x + 4cy + c = 0$ are concurrent,then $a, b,$ and $c$ are in which of the following?

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

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:

For the straight lines given by the equation $(2 + k)x + (1 + k)y = 5 + 7k$,for different values of $k$,which of the following statements is true?