Why we say the US and not say the India?

Answer 1

We say "the US" or "the USA", because US stands for United States, and USA stands for United States of America. We would (and do) say "the United States" and "the United States of America", so we say "the US" and "the USA".

For some reasons, Americans used to say "the Ukraine", and I cannot explain that. When Ukraine became a separate country, we had to learn to refer to it as simply Ukraine and not the Ukraine.