The total change in the oxidation state of manganese involved in the reaction of $\mathrm{KMnO}_{4}$ and potassium iodide in the acidic medium is ____________.

The homoleptic and octahedral complex of $\mathrm{Co}^{2+}$ and $\mathrm{H}_{2} \mathrm{O}$ has ___________ unpaired electron(s) in the $t_{2\mathrm{g}}$ set of orbitals.

The total number of isoelectronic species from the given set is ___________.

$\mathrm{O}^{2-}, \mathrm{F}^{-}, \mathrm{Al}, \mathrm{Mg}^{2+}, \mathrm{Na}^{+}, \mathrm{O}^{+}, \mathrm{Mg}, \mathrm{Al}^{3+}, \mathrm{F}$

Let $x=x(y)$ be the solution of the differential equation

$2(y+2) \log _{e}(y+2) d x+\left(x+4-2 \log _{e}(y+2)\right) d y=0, y>-1$

with $x\left(e^{4}-2\right)=1$. Then $x\left(e^{9}-2\right)$ is equal to :