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The rupee had appreciated by 5 paise to close at Rs 45.13/14 per dollar in the previous session on Friday on the back of dollar-selling dollar by exporters.
Forex dealers said dollar weakness against the euro and a higher opening in the stock market kept the rupee sentiment firm as well.
Meanwhile, the Bombay Stock Exchange Sensex was up by 128.92 points, or 0.72 per cent, at 18,007.73 in opening trade on Monday.