In a metal deficient oxide sample, $\mathbf{M}_{\mathbf{x}} \mathbf{Y}_2 \mathbf{O}_4$ ( $\mathbf{M}$ 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 $\mathbf{M}^{2+}$ ions present in $\mathbf{M}$ is $\frac{1}{3}$, the value of $\mathbf{X}$ is _______ .

Atom $\mathrm{X}$ occupies the fcc lattice sites as well as alternate tetrahedral voids of the same lattice. The packing efficiency (in %) of the resultant solid is closest to

For the given close packed structure of a salt made of cation X and anion Y shown below (ions of only one face are shown for clarity), the packing fraction is approximately (packing fraction = $${{packing\,efficiency} \over {100}}$$)

The arrangement of X^$$-$$ ions around A⁺ ion in solid AX is given in the figure (not drawn to scale). If the radius of X^$$-$$ is 250 pm, the radius of A⁺ is