Sensex and Nifty opened higher on Tuesday, extending their gains to a fourth consecutive session, as strong corporate earnings, easing crude oil prices and early signs of foreign investor inflows lifted sentiment.A view of the illuminated Bombay Stock Exchange (BSE) building and Chhatrapati Shivaji Maharaj Terminus (CSMT) at night on Oct 28. (PTI/File)Rising for the third straight session on Monday, the 30-share BSE Sensex jumped 1,233.25 points, or 1.66 per cent, to settle at the day's high of 75,692.78, a level not seen since September 7. Nifty, meanwhile, ended above 23,400 on Monday after sharp gains in Reliance Industries following its earnings and cooling crude oil prices.Brent crude traded flat at around $105 a barrel after falling seven per cent in the previous session, as talks between Iran and Qatari mediators raised hopes of an end to the US-Israeli war with Iran.However, reports that the US had struck Iran's Qeshm Island kept geopolitical tensions elevated.Foreign portfolio investors turned net buyers of Indian equities on Monday, bringing in ₹31,150 crore, while domestic institutional investors sold shares worth a net ₹3,920 crore, according to provisional NSE data.