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 $0.414$.

$CCP$ 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 $A^{+} = 30 \ g/mol$,$N_A = 6 \times 10^{23}$]

The halide of a metal $MX$ crystallizes in a $ccp$ structure ($NaCl$ type). If all the atoms situated at one of the tetrad axes are removed,what will be the simplest molecular formula of the halide?

Give the correct order of initials $T$ (true) or $F$ (false) for the following statements:
$I.$ In an anti-fluorite structure,anions form $FCC$ lattice and cations occupy all tetrahedral voids.
$II.$ If the radius of cations and anions are $0.2 \ \mathring{A}$ and $0.95 \ \mathring{A}$,then the coordination number of the cation in the crystal is $4$.
$III.$ An atom/ion is transferred from a lattice site to an interstitial position in a Frenkel defect.
$IV.$ The density of a crystal always increases due to a substitutional impurity defect.

Silver has an atomic radius of $144 \ pm$ and the density of silver is $10.6 \ g \ cm^{-3}$. Based on this information, identify the correct statement.

Which one of the following statements is not correct?