The integral $$\int {{{\left( {{x \over {x\sin x + \cos x}}} \right)}^2}dx} $$ is equal to
(where C is a constant of integration):

Let y = y(x) be the solution of the differential equation,
xy'- y = x²(xcosx + sinx), x > 0. if y ($$\pi $$) = $$\pi $$ then
$$y''\left( {{\pi \over 2}} \right) + y\left( {{\pi \over 2}} \right)$$ is equal to :

If $$\left( {a + \sqrt 2 b\cos x} \right)\left( {a - \sqrt 2 b\cos y} \right) = {a^2} - {b^2}$$

where a > b > 0, then $${{dx} \over {dy}}\,\,at\left( {{\pi \over 4},{\pi \over 4}} \right)$$ is :

A circular disc of mass M and radius R is rotating about its axis with angular speed $${\omega _1}$$ . If another stationary disc having radius $${R \over 2}$$ and same mass M is droped co-axially on to the rotating disc. Gradually both discs attain constant angular speed $${\omega _2}$$ the energy lost in the process is p% of the initial energy. Value of p is __________.