If $$y = \left( {{2 \over \pi }x - 1} \right) cosec\,x$$ is the solution of the differential equation,

$${{dy} \over {dx}} + p\left( x \right)y = {2 \over \pi } cosec\,x$$,

$$0 < x < {\pi \over 2}$$, then the function p(x) is equal to :

If the normal at an end of a latus rectum of an ellipse passes through an extremity of the minor axis, then the eccentricity e of the ellipse satisfies :

If $$\alpha $$ and $$\beta $$ are the roots of the equation
2x(2x + 1) = 1, then $$\beta $$ is equal to :

The centre of the circle passing through the point (0, 1) and touching the parabola
y = x² at the point (2, 4) is :