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 $0.414$.

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?

Which of the following statements is correct regarding the packing efficiency or void size?

Which of the following is the correct cooling curve for an amorphous solid?

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.

Which of the following statements is correct?