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The dollar index, which gauges the greenback's strength against a basket of six currencies, fell 0.02 per cent to 93.02.
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IndusInd Bank was the top loser in the Sensex pack, shedding around 3 per cent, followed by HDFC twins, Kotak Bank, SBI, Axis Bank and ICICI Bank.
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Surging crude oil prices in the overseas market added pressure to the domestic unit, dealers said.
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M&M was the top gainer, surging around 4 per cent, followed by Bajaj Finance, Kotak Bank, SBI, ONGC, L&T, Tata Steel, Bajaj Finserv and Maruti.
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Bajaj Finance was the top gainer in the Sensex pack, surging around 9 per cent, followed by IndusInd Bank, L&T, Bajaj Finserv, HDFC, SBI, ICICI Bank, HDFC Bank, ONGC and Axis Bank.
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At the interbank forex market, the domestic currency opened up at 74.04 against the US dollar, then edged slightly lower to 74.05 in early deals, a rise of 10 paise over its last close.
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The dollar index, which gauges the greenback's strength against a basket of six currencies, dipped 0.06 per cent to 92.16.
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ICICI Bank was the top gainer, surging around 3 per cent, followed by Infosys, HCL Tech, Axis Bank, Bharti Airtel and Bajaj Finance.
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Reliance Securities in a report said that the uptick in the rupee was supported by foreign portfolio flows.
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Reliance Industries was the top gainer in the Sensex pack, surging around 3 per cent, followed by M&M, Bajaj Auto, Tata Steel, NTPC, Titan and HDFC.
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At the interbank forex market, the domestic unit opened at 74.35 against the US dollar, then gained further ground and touched 74.29, registering a rise of 47 paise over its previous close.
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SBI was the top gainer in the Sensex pack, surging over 5 per cent, followed by HCL Tech, Tech Mahindra, Asian Paints, Infosys, Tata Steel, TCS and Reliance Industries.
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Traders said most Asian currencies opened weak against the US Dollar Index, which started with gains on Wednesday morning in Asian trade ahead of the US Presidential election results.
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ICICI Bank was the top gainer in the Sensex pack, surging around 4 per cent, followed by SBI, IndusInd Bank, HDFC Bank, Tata Steel and HDFC.
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The dollar index, which gauges the greenback's strength against a basket of six currencies, fell 0.14 per cent to 94.01.
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Losses in domestic stock markets and uncertainty ahead of US presidential election weighed on the investor sentiment, traders said.
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Reliance Industries was the top laggard, tanking over 4 per cent, followed by HCL Tech, TCS, Asian Paints, Bajaj Auto, Infosys and HUL.
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NTPC was the top gainer in the Sensex pack, rising around 2 per cent, followed by Nestle India, HCL Tech, ONGC, SBI, M&M, TCS and Reliance Industries.
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The dollar index, which gauges the greenback's strength against a basket of six currencies, rose 0.41 per cent to 93.31.
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On the equity market front, BSE index Sensex was trading 11.80 points higher at 40,157.30, and the broader NSE Nifty advanced 20.55 points to 11,788.30.