The number of integral values of $\alpha$ for which the abscissa of the point of intersection of the lines $y = x + 9\alpha$ and $3\alpha x + 2y + 9 = 0$ is an integer,is

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

What is the nature of the points $(-a, -b)$,$(0, 0)$,$(a, b)$,and $(a^2, ab)$?

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

For all values of $a$ and $b$,the line $(a+2b)x + (a-b)y + (a+5b) = 0$ passes through a fixed point. Find that point.

Consider the lines given by $L_1: x+3y-5=0$,$L_2: 3x-ky-1=0$,and $L_3: 5x+2y-12=0$. Match the statements in Column $I$ with the statements in Column $II$.

Column $I$	Column $II$
$(A)$ $L_1, L_2, L_3$ are concurrent,if	$(p)$ $k=-9$
$(B)$ One of $L_1, L_2, L_3$ is parallel to at least one of the other two,if	$(q)$ $k=-\frac{6}{5}$
$(C)$ $L_1, L_2, L_3$ form a triangle,if	$(r)$ $k=\frac{5}{6}$
$(D)$ $L_1, L_2, L_3$ do not form a triangle,if	$(s)$ $k=5$