A Company from the United States of America filed an application at USPTO on 02/05/2001 and another…

Under section 154 of the Trade Marks Act, 1999, an applicant who files in India within six months of an application in a convention country is entitled to registration with priority, and the date of the convention application is "deemed for the purposes of this Act to be the date of registration". The Indian application of 02/10/2001 is within six months of the US filing of 02/05/2001 on which priority is claimed, so the date of registration is 02/05/2001.

The later EUIPO filing does not matter because priority is claimed from the US application, and the Indian filing and actual registration dates are displaced by the priority date.