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At 9:38 am, the Sensex traded 303.06 points - or 0.74 per cent - higher at 41,197.44 while the Nifty was up 84.40 points - or 0.70 per cent - at 12,076.90.
Forty five stocks on the 50-scrip benchmark index traded higher at the time. Bharti Infratel, Coal India, NTPC, Nestle, JSW Steel and Reliance Industries - trading between 1.35 per cent and 6.60 per cent higher - were the top percentage gainers in the Nifty. On the other hand, Yes Bank, Tata Motors and Britannia - down between 0.70 per cent and 1.71 per cent - were the top losers.
Reliance Industries, HDFC and Axis Bank were the top contributors to the surge in Sensex, together accounting for a gain of more than 140 points in the index.
Equities in other Asian markets edged up as investors tried to shake off worries about the coronavirus epidemic after a slight decline in the number of new cases.
MSCI's broadest index of Asia-Pacific shares outside Japan eked out a minor 0.03 per cent gain but spent much of the morning session bouncing between gains and losses. Chinese shares erased early declines to trade 0.15 per cent higher while Japan's Nikkei stock index rose 0.5 per cent.
Finance Minister Nirmala Sitharaman met a group of industry representatives on Tuesday to take stock of the coronavirus outbreak and its impact on the economy. "We wanted to know how Indian industries would be impacted by coronavirus," Ms Sitharaman said after the meeting.
Her meeting with industries comes at a time when the coronavirus epidemic has threatened to affect world trade and economic growth, while the Indian economy stares at its worst annual rate of expansion recorded since the 2008-09 global financial crisis.
The death count from China's new coronavirus epidemic jumped to 2,000 on Wednesday after 132 more people died in Hubei province, the hard-hit epicentre of the outbreak. That brought the total number of cases in mainland China past 74,000.
China, the world's second-largest economy, is still struggling to get its manufacturing sector back online after imposing severe travel restrictions to contain a virus that emerged in the central Chinese province of Hubei late last year. Many investors view Chinese data on the coronavirus with a great deal of scepticism, but there are hopes that officials will roll out more stimulus to support the world's second-largest economy.
On Tuesday, the Sensex had declined 161.31 points - or 0.39 per cent - to end at 40,894.38 and the Nifty settled at 11,992.50, down 53.30 points - or 0.44 per cent - from the previous close - both lowest closing levels recorded since February 4.