Domestic stock markets started Tuesday's session on a positive note but soon turned negative. The S&P BSE Sensex plunged as much as 96.21 points to touch 35,753.95, while the Nifty50 barometer of the National Stock Exchange lost 38.85 points to 10,733.25. The losses on Dalal Street were led by banking and auto stocks. Heavyweights HDFC Bank, HDFC, Reliance and Axis Bank contributed the most to the losses on the Sensex.