If the coordinates of the points $A$ and $B$ are $(1, 0)$ and $(2, \sqrt{3})$,then the angle made by the line $AB$ with the $x$-axis is .....$^o$.

Two points $(a, 0)$ and $(0, b)$ are joined by a straight line. Another point on this line is:

The vertex $A$ of a triangle lies on the lines $x+y=1$ and $2x+3y=6$. If the orthocentre of the triangle is $O\left(\frac{3}{7}, \frac{22}{7}\right)$,then the equation of $OA$ in the normal form is

$\beta$ is the angle made by the perpendicular drawn from the origin to the line $L \equiv x+y-2=0$ with the positive $X$-axis in the anticlockwise direction. If '$a$' is the $X$-intercept of the line $L=0$ and $p$ is the perpendicular distance from the origin to the line $L=0$,then $a \tan \beta + p^2 =$

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

The equation of a straight line,where the length of the perpendicular from the origin is $4$ units and the line makes an angle of $120^{\circ}$ with the $x$-axis,is: