The Sensex at the Bombay Stock Exchange rallied a solid 350 points, or 2.2 percent, to close above the 16,000 mark, at 16,165, on fresh buying by funds, amid hopes of rate cuts by the Reserve Bank, and rising global markets, on Tuesday. The Nifty at the National Stock Exchange gained 107 points, or 2.3 percent, to 4,850. Stock markets in Japan, China, Hong Kong, South Korea and Singapore rose between 0.4 percent and 2.7 percent.