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Buying in IT counters and Reliance Industries added to the momentum.
In a volatile session, the 30-share BSE benchmark ended 214.17 points or 0.37 percent higher at 58,350.53. During the day, it hit a high of 58,415.63 and a low of 57,788.78.
The broader NSE Nifty went up by 42.70 points or 0.25 percent to 17,388.15.
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On the other hand, Maruti Suzuki, Sun Pharma, Kotak Mahindra Bank, IndusInd Bank, and Bajaj Finance were among the laggards.
In Asia, markets in Seoul, Tokyo, and Hong Kong ended higher, while Shanghai settled lower.
European stocks were trading in the green during mid-session deals. The US markets had ended lower on Tuesday.
Meanwhile, international oil benchmark Brent crude declined 0.91 percent to USD 99.63 per barrel.
Foreign institutional investors remained net buyers in the capital markets as they bought shares worth Rs 825.18 crore on Tuesday, as per exchange data.