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The rupee is trading at 60.46/47 versus Thursday's close of 60.4950/5050.
Financial markets were closed on Friday for a local holiday.
Traders said demand was matching supply but volumes were low on either side due to US Labour Day holiday.
Gains in the domestic share market are aiding the rupee, but sentiment remains cautious.
Traders are awaiting the Supreme Court's hearing on Monday on whether it will cancel the coal blocks. Cancellations could spark more coal imports and widen trade deficit, warn some analysts.
