$A$ bag contains $5$ red balls and $3$ green balls. $A$ ball is selected at random and not replaced. $A$ second ball is then selected. The probability of selecting one red ball and one green ball is

The solution of the differential equation $x y^{\prime} = 2 x e^{-y / x} + y$ is

$A$ 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?

$A$ curve passes through the point $\left(1, \frac{\pi}{6}\right)$. Let the slope of the curve at each point $(x, y)$ be given by $\frac{dy}{dx} = \frac{y}{x} + \sec \left(\frac{y}{x}\right)$,where $x > 0$. Then the equation of the curve is:

Which of the following is a homogeneous differential equation?

Identify the statement$(s)$ which is/are True.