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The 30-share BSE Sensex jumped 379.68 points to hit a record peak of 79,855.87 in early trade. The Nifty climbed 94.4 points to hit a lifetime high of 24,236.35.
Among the Sensex pack, HCL Technologies, Tata Consultancy Services, Infosys, Bharti Airtel, HDFC Bank and Power Grid were the biggest gainers.
Tata Motors, Bajaj Finance, Kotak Mahindra Bank and ICICI Bank were among the laggards.
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The BSE Sensex was trading down 77.93 points, or 0.10 per cent, to 79,398.26 points. The broader NSE Nifty fell 25.65 points, or 0.11 per cent, to 24,116.30 points.
On Monday, the BSE benchmark settled higher by 443.46 points or 0.56 per cent at an all-time high of 79,476.19. The Nifty climbed 131.35 points or 0.55 per cent to settle at a fresh lifetime high of 24,141.95.
In Asian markets, Tokyo, Shanghai and Hong Kong were trading in the positive territory on Tuesday, while Seoul quoted lower.
US markets ended in the green on Monday.
India’s gross GST collection increased 8 per cent to Rs 1.74 lakh crore in June, sources said on Monday.
Global oil benchmark Brent crude climbed 0.23 per cent to USD 86.80 a barrel.
Foreign Institutional Investors (FIIs) offloaded equities worth Rs 426.03 crore on Monday, according to exchange data.