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Among the 30 Sensex firms, NTPC, HCL Technologies, Bharti Airtel, Tech Mahindra, Power Grid, Axis Bank, Tata Consultancy Services and Adani Ports were the biggest gainers.
Bajaj Finserv, Bajaj Finance, Hindustan Unilever, Mahindra & Mahindra, Tata Motors and State Bank of India were among the laggards.
In Asian markets, Shanghai and Hong Kong settled higher while Seoul and Tokyo ended lower.
European markets were trading on a mixed note. The US markets ended significantly higher on Monday.
Foreign Institutional Investors (FIIs) bought equities worth Rs 1,176.55 crore on Monday, according to exchange data. Domestic Institutional Investors (DIIs) also bought equities worth Rs 1,757.02 crore.
Global oil benchmark Brent crude declined 1.39 per cent to USD 70.84 a barrel.
"With an overnight rebound on Wall Street, strong net buying from both FIIs and DIIs, and sluggish oil prices, bullish traders are expected to pursue bargains," Prashanth Tapse, Senior VP (Research), Mehta Equities Ltd, said.
The BSE benchmark Sensex rebounded 375.61 points or 0.46 per cent to settle at 81,559.54 on Monday. The NSE Nifty went up by 84.25 points or 0.34 per cent to finish at 24,936.40 after three days of fall.
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