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The rupee is trading at 61.75 vs Monday's close of 61.73/74.
Custodian banks are seen selling dollars.
The Indian unit earlier hit one-month low of 61.8750 on dollar buying by oil firms.
Index of the dollar versus six majors is down 0.25%.
Investors are awaiting this week minutes of US Fed's policy meeting.
The 50-share Nifty is almost flat, after earlier gaining as much as 0.28% to touch a record high.
