$CCP$ lattice of a solid made up of $B^{-}$ ions has an edge length of $3 \ \mathring{A}$ and a density of $5 \ g/cm^3$. If in this lattice $A^{+}$ ions are placed at alternate tetrahedral voids,then the percentage increase in density will be $............. \ \%$. [Molar mass of $A^{+} = 30 \ g/mol$,$N_A = 6 \times 10^{23}$]

$A$ mixture of $KCl$ and $KF$ is added to sodium chloride.

Calculate the volume of the unit cell of an element with a density of $7.2 \ g \ cm^{-3}$ that forms a $bcc$ structure. ($288 \ g$ of this element contains $3.35 \times 10^{24}$ atoms).

What is the percent by mass of titanium in rutile,a mineral that contains titanium and oxygen,if the structure can be described as a closest-packed array of oxide ions,with titanium in one half of the octahedral holes? What is the oxidation number of titanium? $(Ti = 48, O = 16)$

The cubic unit cell structure of a compound containing cation $M$ and anion $X$ is shown below. When compared to the anion,the cation has a smaller ionic radius. Choose the correct statement$(s)$:
$(A)$ The empirical formula of the compound is $MX$.
$(B)$ The cation $M$ and anion $X$ have different coordination geometries.
$(C)$ The ratio of $M-X$ bond length to the cubic unit cell edge length is $0.866$.
$(D)$ The ratio of the ionic radii of cation $M$ to anion $X$ is $0.414$.

Which one of the following statements is not correct?