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'The' is never used before any proper nouns. 'India' and 'America' are the proper nouns. In 'The United States Of America', 'the' is used before the adjective 'united'.

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We use 'the' in front of United States of America because United is a common noun. So we use 'the' in front of countries if the name contains a common noun. But India has its own name and does not share its name with any other country, so we do not use 'the' in front of India.