The Sensex gained 78 points at 40,440 and the Nifty also rose 20 points at 11,859.
The most active stocks on the NSE are IRCTC, SBI, Reliance and Indiabulls Housing.
Among sectors, Bank Nifty, pharma and auto indices were trading in the red, while realty index rose 1%, followed by FMCG, IT and media.
The Indian rupee opened 7 paise higher at 71.85 per dollar against the previous day's close at 71.92/$.
Meanwhile, RBI Governor Shaktikanta Das said on Monday that there is space for further rate cuts despite upside risks to the inflation outlook.
Asian markets were trading on a mixed note with the Nikkei 225 index dropping 3% in Tuesday morning trade. The Topix index declined 2.8% and the Shanghai Composite also fell 1%, however, South Korea’s Kospi index recovered from Monday’s loss and is trading higher.