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The 30-share BSE Sensex climbed 134.64 points to hit a new all-time high of 78,188.16 in early trade. The Nifty went up by 28.2 points to 23,749.50.
However, later both the benchmark indices encountered volatile trends and were trading between highs and lows.
Among the 30 Sensex companies, UltraTech Cement, ICICI Bank, Larsen & Toubro, Kotak Mahindra Bank, NTPC, Bajaj Finance and Tata Motors were the biggest gainers.
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In Asian markets, Seoul and Tokyo quoted with gains while Shanghai and Hong Kong traded lower. US markets ended mostly higher on Tuesday. Global oil benchmark Brent crude climbed 0.41 per cent to USD 85.36 a barrel.
Foreign Institutional Investors (FIIs) bought equities worth Rs 1,175.91 crore on Tuesday, according to exchange data.
The BSE benchmark jumped 712.44 points or 0.92 per cent to settle at a new closing peak of 78,053.52 on Tuesday. The Nifty went up by 183.45 points or 0.78 per cent to settle at a record closing peak of 23,721.30.