Match the following:

List-$I$	List-$II$
$A$. $ABCABC...$ layers	$I$. $F$-centres
$B$. Thermodynamics defects	$II$. $X$-ray diffraction
$C$. $Farbenzenter$	$III$. Vacancy defects
$D$. $Debye-Scherrer$ method	$IV$. Semiconductors
	$V$. Silver

Atoms of metals $x$,$y$,and $z$ form face-centred cubic $(fcc)$ unit cell of edge length $L_x$,body-centred cubic $(bcc)$ unit cell of edge length $L_y$,and simple cubic unit cell of edge length $L_z$,respectively. If $r_z = \frac{\sqrt{3}}{2} r_y$; $r_y = \frac{8}{\sqrt{3}} r_x$; $M_z = \frac{3}{2} M_y$ and $M_z = 3 M_x$,then the correct statement$(s)$ is (are) [Given: $M_x$,$M_y$,and $M_z$ are molar masses of metals $x$,$y$,and $z$,respectively. $r_x$,$r_y$,and $r_z$ are atomic radii of metals $x$,$y$,and $z$,respectively.]
$(A)$ Packing efficiency of unit cell of $x >$ Packing efficiency of unit cell of $y >$ Packing efficiency of unit cell of $z$
$(B)$ $L_y > L_z$
$(C)$ $L_x > L_y$
$(D)$ Density of $x >$ Density of $y$

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? $(Ti = 48, O = 16)$

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.

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 $0.414$.

Calculate the number of atoms present in $1.58 \ g$ of a metal that forms a $bcc$ structure,given that $\varrho \times a^3 = 1.58 \times 10^{-22} \ g$.