(A) : B–F bond length in BF₃ is less than in ${\mathrm{BF}}_4^{-}$.
(R) : Back bonding is present in BF₃ but not in ${\mathrm{BF}}_4^{-}$.

The B−F bond length in BF₃ is shorter than the B−F bond length in BF4-. In BF₃ bond length is 130pm, whereas in BF4- bond length is 143pm.

Explanation:

BF₃ is an electron-deficient species. With a vacant p-orbital on boron, the fluorine and boron atoms undergo pπ−pπ back-bonding to remove this deficiency. Due to this a double-bond character developed to the B−F bond. This double-bond character decreases the bond length in BF₃ (130pm). 

However, when BF₃ coordinates with the fluoride ion, a change in hybridization took place from sp² (in BF₃) to sp³ (in BF4-) occurs. Boron now forms 4 sigma bonds, and the double-bond character is lost. It doesn't empty 2p - orbital, so there is no back bonding. This accounts for a B−F bond length of 143pm in BF4- ion.