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Rising for the seventh straight session, the 30-share index spurted 104.05 points, or 0.29 per cent, to 36,451.13.
The barometer had rallied over 1,387 points in the previous six sessions.
Led by FMCG, oil and gas, PSU and realty, sectoral indices advanced up to 0.99 per cent.
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Brokers said sustained buying by investors and foreign fund inflows, coupled with strengthening rupee against the US dollar and falling global crude oil prices, influenced trading sentiment here.
Negative Asian cues on a likely Federal Reserve interest rate hike, limited the gains here, traders said.
The rupee breached the 70 mark by surging 50 paise to trade at 69.94 against the dollar in early trade at the interbank forex market.
Prominent gainers were Asian Paint, Axis Bank, ITC, Maruti Suzuki, SBI, HDFC, Yes Bank, Bharti Airtel, HUL, Tata Steel, Bajaj Auto, L&T, RIL and HDFC Bank, rising up to 1.70 per cent.
However, Infosys emerged worst Sensex performer, falling 1.20 per cent, followed by Vedanta, TCS, Tata Motors and Sun Pharma.
Shares of aviation companies rose after crude prices hit a 14-month low. InterGlobe Aviation, SpiceJet and Jet Airways rallied up to 5 per cent.
Stocks of oil marketing companies like IOC, HPCL, BPCL and OIL too gained up to 1.43 per cent.
Brent crude, an international benchmark, dropped 4.2 per cent lower to USD 57.07 per barrel Tuesday, a 14-month low.
Meanwhile, foreign institutional investors (FIIs) bought shares to the tune of Rs 144.76 crore Tuesday, while domestic institutional investors (DIIs) sold shares worth a net of Rs 182.60, provisional data showed.
Elsewhere in Asia, Japan’s Nikkei fell 0.43 per cent, Shanghai Composite Index shed 0.25 per cent, while Hong Kong’s Hang Seng rose 0.10 per cent.
The US Dow Jones Industrial Average ended 0.35 per cent higher Tuesday.