If the slope of the line $ax + (3 - a)y + 7 = 0$ is $7$,then the value of the integral part of '$a$' 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 $a \tan \beta + p^2 =$

Suppose a line makes an angle of $120^{\circ}$ with the positive direction of $X$-axis. If the length of the perpendicular from the origin to that line is $4$,then the equation of the line is

The equation of the line perpendicular to the line $\frac{x}{a} - \frac{y}{b} = 1$ and passing through the point at which it cuts the $x$-axis,is

The line passing through $(-1, \pi/2)$ and perpendicular to $\sqrt{3} \sin \theta + 2 \cos \theta = \frac{4}{r}$ is

$A$ line cuts off equal intercepts on the coordinate axes. The angle made by this line with the positive direction of the $X$-axis is: (in $^{\circ}$)