If p and q are the lengths of the perpendiculars from the origin on the lines,

x cosec $$\alpha$$ $$-$$ y sec $$\alpha$$ = k cot 2$$\alpha$$ and

x sin$$\alpha$$ + y cos$$\alpha$$ = k sin2$$\alpha$$

respectively, then k² is equal to :

cosec18$$^\circ$$ is a root of the equation :

If the following system of linear equations

2x + y + z = 5

x $$-$$ y + z = 3

x + y + az = b

has no solution, then :

The length of the latus rectum of a parabola, whose vertex and focus are on the positive x-axis at a distance R and S (> R) respectively from the origin, is :