A compound contains atoms of $\mathrm{x}, \mathrm{y}$ and z elements. Oxidation numbers of $x, y$ and $z$ are $+3,+5$ and -2 respectively. Identify the possible formula of this compound?

For a neutral compound, the sum of oxidation numbers must be zero. Given: oxidation number of $x = +3$, $y = +5$, and $z = -2$.

For $\mathrm{XYZ}_2$, total charge is $+3 + (+5) + 2(-2) = 4$, which is non-zero.

For $\mathrm{Y}_2(\mathrm{XZ}_3)_2$, the polyatomic ion $\mathrm{XZ}_3$ has charge $+3 + 3(-2) = -3$. Total charge: $2(+5) + 2(-3) = 4$, non-zero.

For $\mathrm{X}_3(\mathrm{YZ}_4)_3$, the polyatomic ion $\mathrm{YZ}_4$ has charge $+5 + 4(-2) = -3$. Total charge: $3(+3) + 3(-3) = 0$, confirming neutrality.

For $\mathrm{X}_3(\mathrm{Y}_4\mathrm{Z})_2$, the polyatomic ion $\mathrm{Y}_4\mathrm{Z}$ has charge $4(+5) + (-2) = +18$. Total charge: $3(+3) + 2(+18) = 45$, non-zero.

Only option C yields a neutral compound.