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A strengthening rupee also boosted market sentiments, traders said.
After scaling a record intra-day high of 44,601.63, the 30-share BSE Sensex ended 445.87 points or 1.01 per cent higher at a record 44,523.02.
Similarly, the broader NSE Nifty rose 128.70 points or 1 per cent to close above the 13,000-mark for the first time at 13,055.15.
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On the other hand, HDFC, Titan, Nestle India, Bharti Airtel, ONGC and Infosys were among the laggards.
Sector-wise, BSE bankex, auto and finance indices rose up to 2.37 per cent.
Foreign institutional investors remained net buyers in the capital market as they purchased shares worth Rs 4,738.44 crore on Monday, according to provisional exchange data.
The rupee appreciated 10 paise to close at 74.01 against the US dollar.
Elsewhere in Asia, bourses in Hong Kong, Tokyo and Seoul ended with significant gains, while Shanghai closed in the red.
Stock exchanges in Europe were trading on a mixed note in early deals.
Meanwhile, Brent crude futures, the global oil benchmark, rose 0.85 per cent to USD 46.45 per barrel.