Well yes following are the exchanges that are right now run by a company registered under Companies Act, 2013.
Bitcoin Exchange site :
www.bitxoxo.comName: BITXOXO BITCOINS ONLINE PRIVATE LIMITED
CIN : U74900TG2016PTC102589
Registered on : 05/01/2016
Bitcoin Exchange site :
www.btcxindia.comName: S CAPITAL SOLUTIONS PRIVATE LIMITED
CIN : U67190TG2013PTC091266
Registered on : 25/11/2013
Bitcoin Exchange site :
www.coinsecure.inName: SECURE BITCOIN TRADERS PRIVATE LIMITED
CIN : U74999DL2014PTC269373
Registered on : 24/07/2014
Bitcoin Exchange site :
www.unocoin.comName: UNOCOIN TECHNOLOGIES PRIVATE LIMITED
CIN : U72200KA2015PTC080145
Registered on : 06/05/2015
Bitcoin Exchange site :
www.zebpay.comName: ZEB IT SERVICE PRIVATE LIMITED
CIN : U72900GJ2015PTC083609
Registered on : 19/06/2015
I was surprised to realize how people just giveaway money, without knowing whom they are giving it too :3