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At 11:26 am, the Sensex was trading 86 points, or 0.3 per cent, higher at 33,933, while the Nifty was up 27 points at 10,174.
Top gainers on the 50-scrip Nifty index included Bajaj Finance, Bharat Petroleum, Indian Oil, Hindustan Petroleum and Hindalco Industries, trading between 2.8 per cent and 4.5 per cent higher in morning deals.
On the other hand, IT and pharma stocks declined, after the rupee touched a three-week high of 73.10 against the dollar. Strength in the rupee limits profitability for exporters such as IT and pharma companies.
The rupee rose as much as 47 paise against the dollar. It opened at 73.18 against the greenback, and advanced to an intraday high of 73.10 on increased selling of the dollar amid weakness in crude oil prices.
Wipro shares fell as much as 2.9 per cent to hit an intraday low of Rs 303.80 apiece on the NSE, ahead of release of earnings for the July-September quarter by the IT major.
However, HCL Technologies shares bucked the trend, jumping more than 4 per cent after the software services exporter reported a 14.8 per cent rise in net profit in the July-September quarter, beating analysts' estimates.
The rise in the domestic markets came despite weakness in Asian peers. MSCI's broadest index of Asia-Pacific shares outside Japan was down 0.2 per cent, extending the decline of more than 2 per cent in the previous session.
Global stocks have suffered this week on worries about US earnings, Italian government finances, US trade tensions and mounting pressure on Saudi Arabia over the death of dissident journalist Jamal Khashoggi.
If the Sensex and Nifty finish the day with gains, that would mean the first higher closing for the indices after four days of losses. The Sensex has lost 1,315 points, or 3.7 per cent, and the Nifty given up 437 points, or 4.1 per cent, in past four consecutive sessions.
(With agency inputs)