Find the coordinates of the point where the line $3x - 2y - 6 = 0$ intersects the $Y$-axis.

$A$ straight line parallel to the line $y=\sqrt{3}x$ passes through $Q(2,3)$ and cuts the line $2x+4y-27=0$ at $P$. Then the length of the line segment $PQ$ is

If a straight line passing through the point $P(3,4)$ makes an angle $\frac{\pi}{6}$ with the $X$-axis and meets the line $12x+5y+10=0$ at $Q$,then the length of $PQ$ is

Let $\alpha \in R$. If the line $(\alpha+1) x+\alpha y+\alpha=1$ passes through a fixed point $(h, k)$ for all $\alpha$,then $h^2+k^2=$

The equation of the line which cuts off an intercept $3$ units on $OX$ and an intercept $-2$ units on $OY$ is:

The number of straight lines which are equally inclined to both the axes is