Bharat vs Hindustan
Why does Duolingo refer to India as Bharat?
I see people (at least in serials) refer to India as Hindustan.
India was referred to as Hindustan for the most part of the Mughal rule. It is a misconception that Hindustan means the land of Hindus. It comes from the Indian name of the Indus river, which is called Sindhu in Sanskrit (and most other Indian languages). S and H were often interchanged between Sanskrit and Old Avestan (and thus Persian), so the people who came from Persia, called it Hindu. Hindu would literally mean people who live on the other side of the Indus, and Hindustan is the land of Indus. As you could guess, Indus is where the country gets its English name "India" from. However, Hindustan is not an official name of the country anymore. The Indian constituion mentions two names for the country, India and Bharat.
Bharat is a word in hindi and urdu for India, it's a more appropriate way because it's just a name of a country, while Hindustan means "The land of the Hindus", this name totally excludes Muslims and Sikhs in India. That's probably why Bharat is used over Hindustan
Both are interchangeable in most casual contexts. The official name of the country in Hindi is भारत (more specifically भारत गणराज्य- Republic of India) and as Ertugrul_Ghazi mentioned, it may be insensitive to use हिंदुस्तान when you are talking about religion. But other than that, you can use both names.