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At the interbank foreign exchange market, the Indian unit traded in a small range of 73.35-73.39 in early deals.
The rupee had closed 20 paise lower at 73.31 a dollar on Thursday.
The dollar index, which gauges the greenback’s strength against a basket of six currencies, rose 0.03 per cent to 89.85.
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On the domestic equity market front, the BSE Sensex surged 362.16 points or 0.75 per cent to 48,455.48 in morning trade, and the broader NSE Nifty climbed 104.50 points or 0.74 per cent to 14,241.85.
Foreign investors bought shares worth Rs 382.30 crore on a net basis on Thursday January 7, according to exchange data.