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The 30-share index hit an all-time intra-day high of 38,989.65 at the outset but the market lost steam as investors prefered to book profits after three straight days of gains.
The BSE barometer dropped to a low of 38,679.57 points towards the fag-end before settling at 38,722.93 points, down by 173.70 points, or 0.45 per cent over the last close.
Also, the NSE Nifty index in choppy movements finished lower by 46.60 points, or 0.40 per cent, at 11,691.90.
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The rupee plunged to a record low of 70.57 (intra-day) to the dollar, largely on strong month-end demand from importers and banks amid weakness in other Asian currencies.