The Indian rupee jumped as much as 10 paise against the US dollar on Tuesday following the record-breaking run in the Indian stock markets with Sensex and Nifty\u00a0making new lifetime highs respectively. The rupee gained 10 paise at 63.77 apiece US dollar at the interbank foreign exchange market\u00a0on Tuesday. However, in the opening session, the domestic currency started 3 paise down at 63.90. The\u00a0Reserve Bank of India fixed the reference rate of the rupee at 63.8895 against the US dollar on Monday. Earlier yesterday,\u00a0The\u00a0rupee\u00a0reversed its position from the intraday low value to settle down 2 paise against the US dollar. During the day, the rupee\u00a0neared 64 level after falling as much as 14 paise vs the US dollar. In the meantime on Friday last week, India\u2019s foreign exchange reserves jumped by $2.7 billion to a new lifetime high of $413.825 billion due to increase in foreign currency assets, according to Reserve Bank of India. In the reporting week, foreign currency assets, a major component of the overall reserves, rose by $2.685 billion to $389.834 billion. Meanwhile,\u00a0India's stock market opened higher on Tuesday with the key equity indices Sensex and Nifty\u00a0hitting their respective all-time highs led by the rally in the shares of heavyweight companies such as Reliance Industries, Infosys, and HDFC. The domestic markets started the day at record highs with Sensex and Nifty\u00a0shying off from the round figure levels of 36,000 and 11,000 respectively. Within seconds of opening up of the market, Nifty extended the gains very quickly surpassing the 11,000-mark for the first time ever. Following this,\u00a0in the wee minutes of morning trades, Sensex surged heavily to breach the psychological level of 36,000, and that too just after three sessions when the benchmark index crossed 35,000-mark. The domestic markets are on a continuous rising spree since about last 13 months with the benchmark indices Sensex and Nifty making and breaking newer highs day after day. The 30-share barometer Sensex jumped 262.7 points to hit an all-time high of 36,060.71 on Tuesday while the wider share indicator Nifty 50 surged as much as 86.85 points to hit a\u00a0lifetime peak of 11,053.05.