For two events $A$ and $B$,$P(B) \neq 0$ and $P(A \mid B) = 1$,then which of the following is true?

Rooms in a hotel are numbered from $1$ to $19$. Rooms are allocated at random as guests arrive. The first guest to arrive is given a room which is a prime number. The probability that the second guest to arrive is given a room which is a prime number is

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

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

The solution of the differential equation $\frac{dy}{dx} = \frac{x - y}{x + y}$, with the initial condition $x = 0$ and $y = 0$, represents which of the following curves?

The substitution required to reduce the differential equation $t^2 dx + (x^2 - tx + t^2) dt = 0$ to a differential equation which can be solved by the variables separable method is