$A$ compound is formed by two elements $X$ and $Y$. The element $Y$ forms a cubic close-packed $(CCP)$ arrangement and the atoms of element $X$ occupy one-third of the tetrahedral voids. What is the formula of the compound?

$A$ metal crystallises in an $FCC$ lattice with $ABCABC...$ packing. If the distance between the nearest neighbours is '$a$',then the distance between the centres of the nearest triangular voids of two consecutive layers is:

The ratio of densities if the same element undergoes $FCC$ and $HCP$ close packing is:

$A$ compound made up of elements $A$ and $B$ (with a general formula $A_x B_y$), where $B$ forms an $hcp$ lattice and $A$ occupies $2/3$ of the tetrahedral voids. The formula of the compound is

$A$ two-dimensional solid is made by alternating circles with radius $a$ and $b$ such that the sides of the circles touch. The packing fraction is defined as the ratio of the area under the circles to the area under the rectangle with sides of length $x$ and $y$. The ratio $r=b/a$ for which the packing fraction is minimised is closest to $.....$

$A$ compound is formed by $X$ and $Y$ elements. Atoms of $Y$ (anions) form $hcp$ lattice. Atoms of $X$ (cations) are in some octahedral holes. The formula of the compound is $XY_3$. What is the fraction of octahedral holes unoccupied by $X$?