The 30-share BSE Sensex was trading 102.51 points or 0.25 per cent higher at 41,776.43 in opening session.
Forex traders said the rupee ended on a weak note as importers rushed for hedging amid expectations of intervention by the RBI.
Silver prices declined by Rs 65 to Rs 45,485 per kg against the previous close of Rs 45,550, HDFC Securities said.
The 30-share BSE Sensex settled 115.35 points, or 0.28 per cent, higher at its fresh closing record of 41,673.92.
At the Interbank Foreign Exchange, the rupee opened weak at 71.01 then fell to 71.02 against the US dollar
The 30-share BSE index was trading 24.89 points or 0.06 per cent lower at 41,533.68.
The 30-share BSE Sensex settled 206.40 points, or 0.50 per cent, higher at its all-time closing high of 41,558.57.
Silver moved up by Rs 14 to Rs 45,649 per kg against previous close of Rs 45,635 per kg.
Analysts said the fall in crude oil futures was mostly due to trimming of positions by traders amid weak global cues.
On the Sensex, metal stocks drove the rally riding on US-China trade deal optimism.