In a mixed oxide of $A$ and $B$,$A$ occupies all the octahedral voids while $B$ occupies $(2/3)$rd of the tetrahedral voids. The molecular formula of this oxide is

In hexagonal systems of crystals,a frequently encountered arrangement of atoms is described as a hexagonal prism. Here,the top and bottom of the cell are regular hexagons and three atoms are sandwiched in between them. $A$ space-filling model of this structure,called hexagonal close-packed $(HCP)$,is constituted of a sphere on a flat surface surrounded in the same plane by six identical spheres as closely as possible. Three spheres are then placed over the first layer so that they touch each other and represent the second layer. Each one of these three spheres touches three spheres of the bottom layer. Finally,the second layer is covered with a third layer that is identical to the bottom layer in relative position. Assume radius of every sphere to be $r$.
$1.$ The number of atoms on this $HCP$ unit cell is
$(A)$ $4$ $(B)$ $6$ $(C)$ $12$ $(D)$ $17$
$2.$ The volume of this $HCP$ unit cell is
$(A)$ $24 \sqrt{2} r^3$ $(B)$ $16 \sqrt{2} r^3$
$(C)$ $12 \sqrt{2} r^3$ $(D)$ $\frac{64 r^3}{3 \sqrt{3}}$
$3.$ The empty space in this $HCP$ unit cell is
$(A)$ $74 \%$ $(B)$ $47.6 \%$ $(C)$ $32 \%$ $(D)$ $26 \%$
Give the answer for questions $1, 2$ and $3.$

Which of the following statements is not correct?

How will you distinguish between the following pairs of terms:
$(i)$ Hexagonal close-packing $(hcp)$ and cubic close-packing $(ccp)$?

$A$ solid is made of two elements $X$ and $Z$. The atoms $Z$ are in $CCP$ arrangement while the atoms $X$ occupy all the tetrahedral sites. What is the formula of the compound?

The number of tetrahedral voids in the unit cell of a face-centered cubic $(fcc)$ lattice of similar atoms is: