QF2 is correct option as (i) if you play bf2, Ke2 and king is nearly safe from blacks attack (ii) if you play Qh4, again ke2 is the option white has (iii) Qf2# is played as Queen now covers ke2 and leaves black with no option thus Qf2 is the fastest mating solution in the above puzzle
If you do Bf2 the king can escape to e2 because the bishop can't cover e2 because of how it moves whereas queen to f2 will cover e2 and e1, and the king can't take the queen because it's being covered by the bishop on c5.
