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In a volatile trade, profit booking in consumer durables, capital goods and energy shares negated strong gains in banking and financial stocks.
Rallying for the fifth straight session, the 30-share BSE Sensex climbed 36.45 points or 0.05 per cent to settle at a new closing high of 77,337.59. During the day, it soared 550.49 points or 0.71 per cent to hit the fresh lifetime peak of 77,851.63.
The NSE Nifty ended at 23,516, down 41.90 points or 0.18 per cent. Intra-day, it rose 106.1 points or 0.45 per cent to hit a new record of 23,664.
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On the other hand, Titan, Maruti, Bharti Airtel, Larsen & Toubro, NTPC, Reliance Industries, Bajaj Finance and Power Grid were among the laggards.
In Asian markets, Seoul, Tokyo and Hong Kong settled higher, while Shanghai ended lower.
European markets were trading lower in mid-session deals. US markets ended in positive territory on Tuesday.
Foreign Institutional Investors (FIIs) bought equities worth Rs 2,569.40 crore on Tuesday, according to exchange data.
Global oil benchmark Brent crude declined 0.22 per cent to USD 85.14 a barrel.
The BSE benchmark Sensex climbed 308.37 points or 0.40 per cent to settle at 77,301.14 on Tuesday. The Nifty went up by 92.30 points or 0.39 per cent to hit a record closing high of 23,557.90.