If $P(A') = 0.6$,$P(B) = 0.8$,and $P(B/A) = 0.3$,then $P(A/B) = $

$A$ cube having an edge of length $5 \ cm$ is painted on all faces and then it is cut into equal cubes of unit volume. $A$ small cube is selected at random and it is found that at least one of its faces is painted. What is the probability that $2$ more faces of it are also painted?

The general solution of the differential equation $(x^3-y^3) dx = (x^2y - xy^2) dy$ is

The solution of the equation $x\frac{dy}{dx} = y - x\tan \left( \frac{y}{x} \right)$ is

Find the particular solution satisfying the given condition: $\left[x \sin ^{2}\left(\frac{y}{x}\right)-y\right] d x+x d y=0$; $y=\frac{\pi}{4}$ when $x=1$.

The general solution of the differential equation $\left(1+e^{\frac{x}{y}}\right) dx + \left(1-\frac{x}{y}\right) e^{\frac{x}{y}} dy = 0$ is ($C$ is an arbitrary constant).