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Traders said the weakness of the American currency in the overseas market also supported the domestic unit.
At the interbank forex market, the domestic unit opened at 73.52 against the US dollar, then inched higher to 73.51 against the greenback, registering a rise of 4 paise over its previous close.
On Thursday, the rupee had settled at 73.55 against the US dollar. Forex and equity market were closed on Friday on account of Christmas.
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On the domestic equity market front, the 30-share BSE benchmark Sensex was trading 227.35 points higher at 47,200.89, and the broader NSE Nifty advanced 75.60 points to 13,824.85.
Foreign institutional investors were net buyers in the capital market as they purchased shares worth Rs 1,225.69 crore on a net basis on Thursday, according to provisional exchange data.
Brent crude futures, the global oil benchmark, fell 0.43 per cent to USD 51.07 per barrel.