If $$0 < x < \pi $$ and $$\cos x + \sin x = {1 \over 2},$$ then $$\tan x$$ is :

$$\int\limits_0^\pi {xf\left( {\sin x} \right)dx} $$ is equal to

The locus of the vertices of the family of parabolas
$$y = {{{a^3}{x^2}} \over 3} + {{{a^2}x} \over 2} - 2a$$ is :

In the ellipse, the distance between its foci is $$6$$ and minor axis is $$8$$. Then its eccentricity is :