Which of the following is the strongest Lewis acid?

Boron halides behave as Lewis acids because of their

Hydrolysis of $BCl_3$ gives $X$,which on treatment with sodium carbonate produces $Y$. $X$ and $Y$,respectively,are

Boron trifluoride on reaction with lithium aluminium hydride in ether gives $LiF$, $AlF_3$ and $X$. $X$ on reaction with $NH_3$ gives $Y$. $Y$ on further heating gives a compound $Z$. The number of $\sigma$-bonds and $\pi$-bonds in $Z$ are $x$ and $y$ respectively. $(x+y)$ is equal to

$Na_2B_4O_7 \cdot 10H_2O \xrightarrow{\text{Heat}} X + NaBO_2 + H_2O$,$X + Cr_2O_3 \xrightarrow{\text{Heat}} \underset{(\text{Green coloured})}{Y}$. $X$ and $Y$ are

The correct order of atomic radii of group $13$ elements is