Three fair coins are tossed. If both heads and tails appear,then the probability that exactly one head appears is:

The solution of the differential equation $\frac{dy}{dx} = \frac{x + y}{x - y}$ is

Find the particular solution satisfying the given condition:
$\frac{dy}{dx} - \frac{y}{x} + \csc\left(\frac{y}{x}\right) = 0$; $y = 0$ when $x = 1$.

Show that the differential equation $\left(x^{2}+x y\right) d y=\left(x^{2}+y^{2}\right) d x$ is a homogeneous equation and find its solution.

When $3$ dice are thrown at a time, the sum of the numbers appeared on $3$ dice was found to be $15$. Then the probability that the number $5$ does not appear on any one of the dice is

The homogeneous differential equation of the form $\left(1+e^{\frac{x}{y}}\right) dx + e^{\frac{x}{y}}\left(1-\frac{x}{y}\right) dy = 0$ can be solved by making the substitution: