The rupee opened almost flat at 63.80 as against last closing level of 63.82 at the Interbank Foreign Exchange (Forex) market and later rose to 63.59 before quoting at 63.61 at 1100 hours.
The rupee hovered in a range of 63.80 and 63.59 during the morning deals.
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Oil prices fell in early trade in Asia following healthy gains at the end of last week while there are still concerns about a global supply glut as OPEC prepares for meeting where it's expected to maintain output.
Meanwhile, the BSE Sensex was trading higher 80.32 points, or 0.29%, at 27,908.76 at 1110 hours.
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