Any question about adaptation on macro-level has very little meaning and no precise answer.
There are two types of larvae in invertebrates: primary ("original") and secondary (evolved from post-larval stages). Not digging into the details, nauplius (together with metanauplius) is the only type of primary larvae in Crustacea and it never has a carapace.
"Majority" is by far too strong term, even if we are talking about all larval types. If we just take the largest crustacean orders with species numbers > 1000, together comprising 92% of crustacean species (the species numbers are from Ahyong et al, 2011, they seem to be largely correct):
- Decapoda - 14.7 k species - rarely have nauplius, marine forms do have planktonic carapaced larvae (principally - zoea)
- Isopoda - 10.7 k - no carapace
- Amphipoda - 9.9 k - no carapace
- Podocopida - 6.2 k - no carapace
- Harpacticoida - 6.0 k - no carapace
- Cyclopoida - 4.2 k - no carapace
- Calanoida - 3.1 k - no carapace
- Siphonostomatoida - 2.5 k - no carapace
- Cumacea - 1.5 k - have carapace, but development is direct
- Mysida - 1.2 k - have carapace, but development is direct
- Tanaidacea - 1.1 k - have carapace, but development is direct
So, the "majority" could be applied to Decapoda only.
If we substitute "adaptation" with "main biological function" (as you have done) or more correctly "main physiological role":
I would prefer (a), because carapace does function as a protective structure in those decapod larvae, which don't rely on behavioral anti-predatory defences: see Morgan: "Fishes quickly learned to avoid spined prey, which ... may also increase the rate of evolution of the character". Non-carapaced larvae rely principally on behavior only.
The only contribution of carapace to planktonic life-style in zoea is participation of its spines [when they are pronounced] in parachuting. It doesn't directly participate in locomotion: Chia et al.
[The above should be largely true also for cypris larvae of cirripeadians, which are enclosed in a non-spined bivalve carapace.]
From the morphological point of view, [at least in adult forms of decapods] carapace creates a chamber for gills, so a morphologist would argue that this is the "main function" of carapace.