1. Find the covalency of boron in $[\mathrm{BF}_4]^-$

   Covalency means the number of covalent bonds formed by the atom.

   In $[\mathrm{BF}_4]^-$, boron is bonded to four fluorine atoms.

   Therefore, the covalency of boron is: $4$

2. Find the oxidation state of boron in $[\mathrm{BF}_4]^-$

   Let the oxidation state of boron be $x$.

   Each fluorine has oxidation state $-1$.

   Total oxidation state of the ion is $-1$, so: $x + 4(-1) = -1$ $x - 4 = -1$ $x = +3$

   Therefore, the oxidation state of boron is: $+3$

3. Match with the options

   • A: $3$ and $4$ $\to$ incorrect
   • B: $4$ and $3$ $\to$ correct
   • C: $4$ and $4$ $\to$ incorrect
   • D: $3$ and $5$ $\to$ incorrect

Hence, the correct answer is B.