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

If $X = x + h, Y = y + k$ transforms $\frac{dy}{dx} = \frac{2x + 3y - 7}{3x + 2y - 8}$ to a homogeneous differential equation,then $(h, k) =$

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

Prove that $x^{2}-y^{2}=c(x^{2}+y^{2})^{2}$ is the general solution of the differential equation $(x^{3}-3xy^{2})dx=(y^{3}-3x^{2}y)dy,$ where $c$ is a parameter.

Two cards are drawn from a pack of $52$ playing cards one after the other without replacement. If the first card drawn is a queen,then the probability of getting a face card from a black suit in the second draw is

$A$ bag contains $3$ red,$6$ white,and $7$ blue balls. Two balls are drawn one after another. What is the probability that the first ball is white and the second ball is blue,if the first ball drawn is not replaced in the bag?