The strong start came in the face of sharp jump in inflation numbers, which were released on Monday.
The 30-share barometer, which had gained 235.44 points in the previous session on Monday, was trading higher by 153.61 points, or 0.48 per cent, at 31,602.64, with FMCG, auto, power, consumer durables, IT, metal and realty stocks leading the gains. Markets remained closed yesterday on account of Independence Day.
On similar lines, the NSE Nifty was up by 36.60 points, or 0.37 per cent, at 9,830.75 points.
Wholesale inflation too rose sharply to 1.88 per cent in July -- first rise in five months -- as some food articles turned dearer even as the industry pitched for cut in interest rates citing weak industrial activity.
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Brokers also said a mixed trend at other Asian markets as fears receded over a potential clash between the US and North Korea and overnight gains at Wall Street also influenced sentiments here.
Globally, Hong Kong's Hang Seng was up 0.45 per cent, while Japan's Nikkei gained 0.02 per cent in their early trade. Shanghai's Composite index, however, down 0.10 per cent.