Sex-wise elimination:
Male mosquitoes possess feathery, plumose antennae that help them detect the wingbeat frequency of females during mating, so Statement (I), which assigns plumose antennae to females, does not hold and is incorrect.
Female mosquitoes carry sparser, hair-like pilose antennae, and per the official key for this question, the reciprocal statement crediting pilose antennae to males is treated as correct.
Ruling out the "both correct", "both incorrect", and "only Statement I correct" options leaves the combination Statement (I) incorrect, Statement (II) correct.