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After hitting a high of 29,316.80, the 30-share BSE barometer was trading 505.20 points or 1.78 per cent higher at 28,945.52.
Similarly, the NSE Nifty rose 199.85 points, or 2.41 per cent, to 8,480.95.
Tata Steel, HDFC, Axis Bank, M&M, Reliance Industries, ONGC, ITC, HCL Tech and Titan rallied up to 3 per cent.
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In the previous session, the 30-share BSE barometer ended 1,375.27 points or 4.61 per cent lower at 28,440.32, and the broader Nifty fell 379.15 points, or 4.38 per cent, to close at 8,281.10.
Foreign institutional investors (FIIs) turned net sellers in the capital market, as they offloaded equity shares worth Rs 4,363.61 crore on Monday, according to provisional exchange data.
According to traders, despite concerns over the rising number of COVID-19 cases in the country and the economic fallout of the nationwide lockdown, investors are value-buying during each dip.
On the global front, bourses in Shanghai were trading on a positive note after China’s manufacturing sector steadily resumed production after the COVID-19 shutdown, with 98.6 per cent of the major industrial firms nationwide having restarted work.
Stocks in Hong Kong, Tokyo and Seoul were also trading significantly higher. Benchmark exchanges on Wall Street rallied over 3 per cent in overnight trade.
Meanwhile, the Indian rupee appreciated 10 paise to 75.48 against the US dollar in morning trade.
Brent crude futures, the global oil benchmark, rose 2.16 per cent to USD 26.99 per barrel.
The number of COVID-19 cases in India has surged past 1,200, according to health ministry log. While there are more than 1,100 active cases, nearly 100 have been cured.
Deaths around the world linked to the pandemic crossed have 37,000.