The probability that exactly $3$ heads appear in six tosses of an unbiased coin, given that the first three tosses resulted in $2$ or more heads is

For the differential equation $(x^2 + y^2) dy = xy dx$, it is given that $y(1) = 1$ and $y(x_0) = e$. Find the value of $x_0$.

$I: y^{\prime}=\frac{y+x}{x} ; \quad II: y^{\prime}=\frac{x^2+y}{x^3} ; \quad III: y^{\prime}=\frac{2xy}{y^2-x^2}$
$S1$: Differential equations given by $I$ and $II$ are homogeneous differential equations.
$S2$: Differential equations given by $II$ and $III$ are homogeneous differential equations.
$S3$: Differential equations given by $I$ and $III$ are homogeneous differential equations.

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

An unbiased coin is tossed $3$ times. If the third toss results in a head,what is the probability of getting at least one more head in the first two tosses?

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