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The 30-share BSE Sensex climbed 51.69 points or 0.06 per cent to settle at a new lifetime high of 80,716.55. During the day, it advanced 233.44 points or 0.28 per cent to hit a fresh record high of 80,898.30.
The NSE Nifty went up by 26.30 points or 0.11 per cent to settle at an all-time closing high of 24,613. Intra-day, it rallied 74.55 points or 0.30 to hit a new record peak of 24,661.25.
Sensex and Nifty have been on a record-breaking run since Friday as foreign investors have turned buyers in the Indian equities ahead of the presentation of the Union budget for 2024-25. Encouraging quarterly results by blue-chips have also supported the rally despite high valuation concerns, according to analysts.
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On the other hand, Kotak Mahindra Bank, Reliance Industries, NTPC, UltraTech Cement and Power Grid were among the laggards.
Foreign Institutional Investors (FIIs) bought equities worth Rs 2,684.78 crore on Monday, according to exchange data.
In Asian markets, Seoul, Tokyo and Shanghai settled higher, while Hong Kong ended lower amid dovish comments from the US Fed Chair Jerome Powell bolstering hopes of a rate cut by September.
European markets were trading lower. US markets ended in positive territory on Monday.
Global oil benchmark Brent crude dipped 0.80 per cent to USD 84.13 a barrel.
On Monday, the BSE benchmark climbed 145.52 points or 0.18 per cent to settle at a new record high of 80,664.86. The NSE Nifty rallied 84.55 points or 0.35 per cent to settle at an all-time closing high of 24,586.70.
Markets will remain closed on Wednesday for Muharram.