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At 10.50 a.m, the rupee was at 56.04/05 to a dollar, a level last seen on June 1. The next target for the rupee is seen as 56.28, the session high on that day.
The rupee is now close to the record low level of 56.52 hit on May 31.
Traders said that dollar selling by a US-based bank had prevented a further fall in the local unit.