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Besides, lower crude prices and a weak American currency in overseas markets boosted the local unit, analysts said.
At the interbank foreign exchange, the rupee opened strong at 75.29 against the US dollar, then rose further to 75.26, registering a gain of 26 paise over the last close.
In initial deals, the rupee also touched a high of 75.25 against the American currency.
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Retail inflation fell to a five-month low of 4.35 per cent in September from 7.27 per cent in the year-ago period as prices of vegetables and other items declined.
Industrial production grew 11.9 per cent in August mainly due to a low-base effect and good performance by manufacturing, mining and power sectors that surpassed the pre-COVID level.
Meanwhile, the dollar index, which gauges the greenback”s strength against a basket of six currencies, slipped 0.18 per cent to 94.35.
Global oil benchmark Brent crude futures declined 0.16 per cent to USD 83.29 per barrel.
Foreign institutional investors were net sellers in the capital market on Tuesday as they offloaded shares worth Rs 278.32 crore, as per exchange data.
On the domestic equity market front, the 30-share Sensex was trading 302.33 points or 0.50 per cent higher at 60,586.64, while the broader NSE Nifty surged 114.75 points or 0.64 per cent to 18,106.70.