1. On the train going to Calcutta, she speaks for the first time.

2. On the train which goes to Calcutta, she speaks for the first time.

3. On the train which is going to Calcutta, she speaks for the first time.
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Does #1 mean #2 or #3?

They all mean the same thing. #1 is a more graceful sentence. 2 and 3 are a little clumsy, but mean the same thing.