For example, ADABTC, LTCBTC, are there any which do not trade with BTC.
If so, are there any that do not trade with BTC, LTC and ETH?
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There might be some out there in some minor exchanges, but it is very very unlikely to be this case. BTC is the dominant liquid currency in the cryptocurrency economy. Most altcoins will trade against it. Perhaps you could find some coins that do not trade against BTC here https://www.coingecko.com/en/exchanges majority does.
BTC is more dominant than ETH at the moment for liquidity