Democratic Socialist Republic of Bharat

Is it possible that democracy and socialism work together in a country? A Socialist Central government and the democratic state level government with powers strictly limited region wise to state affairs, education, development, PWD etc. There's more on my mind but let get the answers to the basics first.

It depends on what you call "democracy". Everything is possible but having a "bourgeois" democracy with bourgeois political parties in a socialist system is quite unlikely.