@Abid you are right, Hindustan does feel good to ears, but in my opinion Bharat is more beautiful because it reflects the history of our country which dates back to the days when King Bharat ruled over. I don't remember much of it but he belonged to the Raghvanshi dynasty, descendents of God Rama and was so brave that as a child he used to count the number teeth in a lion's mouth!
"India' sounds sweeter. The Indian constitution recognizes 'India' as well as 'Bharat'. 'Hindustan' is neither recognized not a sweet sounding name.
India is also more appropriate for historic reasons. India derives er name from 'Indus valley civilization. India is derived from 'Indus'.