False. The caching system means that the roots don't pay per query;
they pay per cache miss--and the number of cache misses is going to be
roughly proportional to the number of TLDs.
The number of cache misses will be in relation to the frequency at which
queries arrive versus the TTL for the TLD's authoritative servers. The
number of TLDs is completely irrelevant.
the latter statement is false, because the more TLDs there are, the more
potential cache misses for some TLD (thus requiring a query to a root server)
at any resolver.