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On Thursday, the rupee had settled at 83.50 against the US dollar.
Meanwhile, the dollar index, which gauges the greenback's strength against a basket of six currencies, was at 104.61, higher by 0.15 per cent.
Brent crude futures, the global oil benchmark, rose 0.26 per cent to USD 83.49 per barrel.
"Indian rupee was again sold off despite gains in other Asian currencies on Thursday and closed at RBI-controlled level of 83.50," said Anil Kumar Bhansali, Head of Treasury and Executive Director Finrex Treasury Advisors LLP.
Bhansali further noted that the rupee is likely to trade in a narrow range of 83.45 to 83.55 during the day.
On the domestic equity market, the 30-share BSE Sensex was trading 196.15 points, or 0.27 per cent lower at 73,467.57 points. The broader NSE Nifty was down 44.00 points, or 0.2 per cent, to 22,359.85 points.
Foreign Institutional Investors (FIIs) were net sellers in the capital markets on Thursday, as they offloaded shares worth Rs 776.49 crore, according to exchange data.