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 :

Let [t] denote the greatest integer $$ \le $$ t. Then the equation in x,
[x]² + 2[x+2] - 7 = 0 has :

A two point charges 4q and -q are fixed on the x-axis at x = $$ - {d \over 2}$$ and x = $${d \over 2}$$ respectively. If a third point charge 'q' is taken from the origin to x = d along the semicircle as shown in the figure, the energy of the charge will :

Dimensional formula for thermal conductivity is (here K denotes the temperature):