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The currency hit 170.60 per dollar, the fourth straight session of record lows, going below the previous nadir of 170.40 hit on Friday.
It closed at 170.25/30 per dollar on Friday.
The rupee has weakened 0.9 percent against the dollar so far this month, building on the 4.7 percent loss in September. It has declined 11.15 percent so far this year.