Redox Reactions · JEE Advanced previous year questions

At room temperature, disproportionation of an aqueous solution of \textit{in situ} generated nitrous acid ($\mathrm{HN}{\mathrm{O}}_2$) gives the species

1. A.${\mathrm{H}}_3{\mathrm{O}}^{+}$, $\mathrm{N}{\mathrm{O}}_3^{-}$ and $\mathrm{NO}$
2. B.${\mathrm{H}}_3{\mathrm{O}}^{+}$, $\mathrm{N}{\mathrm{O}}_3^{-}$ and $\mathrm{N}{\mathrm{O}}_2$
3. C.${\mathrm{H}}_3{\mathrm{O}}^{+}$, $\mathrm{N}{\mathrm{O}}^{-}$ and $\mathrm{N}{\mathrm{O}}_2$
4. D.${\mathrm{H}}_3{\mathrm{O}}^{+}$, $\mathrm{N}{\mathrm{O}}_3^{-}$ and ${\mathrm{N}}_2\mathrm{O}$

In a metal deficient oxide sample, ${\mathrm{M}}_{\mathrm{X}}{\mathrm{Y}}_2{\mathrm{O}}_4$ ($\mathbf{M}$ and $\mathbf{Y}$ are metals), $\mathbf{M}$ is present in both +2 and +3 oxidation states and $\mathbf{Y}$ is in +3 oxidation state. If the fraction of ${\mathrm{M}}^{2+}$ ions present in $\mathbf{M}$ is $\frac{1}{3}$, the value of $\mathbf{X}$ is ____.

1. A.0.25
2. B.0.33
3. C.0.67
4. D.0.75

Consider the following molecules: $\mathrm{B}{\mathrm{r}}_3{\mathrm{O}}_8$, ${\mathrm{F}}_2\mathrm{O}$, ${\mathrm{H}}_2{\mathrm{S}}_4{\mathrm{O}}_6$, ${\mathrm{H}}_2{\mathrm{S}}_5{\mathrm{O}}_6$, and ${\mathrm{C}}_3{\mathrm{O}}_2$. Count the number of atoms existing in their zero oxidation state in each molecule. Their sum is _____.