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The broader NSE Nifty was down by 15.30 points or 0.12 per cent at 13,093.75 in opening trade.
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Besides, positive developments on COVID-19 vaccine front, improved domestic macro-economic data and weakness of the American currency against key rivals also supported the rupee.
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The dollar index, which gauges the greenback's strength against a basket of six currencies, was down 0.04 per cent to 91.95.
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Meanwhile, the dollar index, which gauges the greenback's strength against a basket of six currencies, was down 0.07 per cent to 91.93.
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Meanwhile, the dollar index, which gauges the greenback's strength against a basket of six currencies, was down 0.16 per cent to 92.08.
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The dollar index, which gauges the greenback's strength against a basket of six currencies, was down 0.13 per cent to 92.26.
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IndusInd Bank was the top gainer in the Sensex pack, surging around 5 per cent, followed by Bajaj Finserv, Bajaj Finance, Reliance Industries, ONGC, NTPC and Tata Steel.
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The dollar index, which gauges the greenback's strength against a basket of six currencies, rose 0.16 per cent to 92.46.
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PowerGrid was the top laggard in the Sensex pack, shedding over 2 per cent, followed by Axis Bank, ICICI Bank, HDFC duo, Asian Paints and Bharti Airtel.
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After touching its lifetime intra-day high of 44,215.49, the 30-share BSE benchmark ended 227.34 points or 0.52 per cent higher at its record closing of 44,180.05
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The rupee on Tuesday appreciated 16 paise to settle at 74.46 against the US dollar.
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PowerGrid was the top gainer in the Sensex pack, rising over 1 per cent, followed by SBI, M&M, L&T, IndusInd Bank, ICICI Bank, Bajaj Finance and ONGC.
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The rupee was trading in a narrow range on Friday considering the weak demand for riskier assets on the occasion of Dhanteras.
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Surging crude oil prices in the overseas market added pressure to the domestic unit, dealers said.
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At the interbank forex market, the domestic currency opened up at 74.04 against the US dollar, then edged slightly lower to 74.05 in early deals, a rise of 10 paise over its last close.
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Reliance Securities in a report said that the uptick in the rupee was supported by foreign portfolio flows.
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IndusInd Bank was the top laggard in the Sensex pack, shedding around 3 per cent, followed by ICICI Bank, ONGC, SBI, HDFC, Infosys and Reliance Industries.
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Tata Steel was the top gainer in the Sensex pack, shedding around 2 per cent, followed by Maruti, ICICI Bank, Bharti Airtel, Bajaj Finance, HDFC twins and TCS.
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PowerGrid topped the Sensex gainers' chart, climbing 4.13 per cent, followed by Bharti Airtel, Tata Steel, NTPC, HDFC Bank, Kotak Bank, UltraTech Cement and HDFC. HDFC twins accounted
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The dollar index, which gauges the greenback's strength against a basket of six currencies, was trading 0.17 per cent lower at 93.52.
