The oxidation states of $S$ atoms in Caro's and Marshall's acids are

The angle between a pair of tangents drawn from a point $P$ to the circle $x^{2}+y^{2}+4x-6y+9 \sin^{2} \alpha + 13 \cos^{2} \alpha = 0$ is $2 \alpha$. The equation of the locus of the point $P$ is

If the angles of a triangle are in the ratio $1: 1: 4$,then the ratio of the perimeter of the triangle to its largest side is

Which of the following substances imparts a green color to the burner flame?

The area (in sq unit) of the region bounded by the curves $2x = y^2 - 1$ and $x = 0$ is

$A$ straight line $L$ at a distance of $4$ units from the origin makes positive intercepts on the coordinate axes,and the perpendicular drawn from the origin to this line makes an angle of $60^{\circ}$ with the line $x+y=0$. Then the equation of the line $L$ is