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The rupee reversed direction to trade at 60.48/49 versus its previous close of 60.45/46.
Traders say good dollar buying from state-run banks is seen, likely on behalf of oil importers to meet month-end demand.
Shares are trading up 0.15% in cautious trade ahead of the long weekend. Flows remain in focus.
Financial markets will remain closed on Friday for a local holiday.
Most Asian currencies are trading stronger against the dollar.
