Among the 30 Sensex companies, UltraTech Cement, Reliance Industries, IndusInd Bank, Hindustan Unilever, Kotak Mahindra Bank and ICICI Bank were the biggest gainers.
Tata Steel, Mahindra & Mahindra, Titan and JSW Steel were among the laggards.
In Asian markets, Seoul, Tokyo, Shanghai and Hong Kong quoted with gains.
US markets ended mostly higher on Tuesday.
Global oil benchmark Brent crude climbed 0.45 per cent to USD 85.39 a barrel.
Foreign Institutional Investors (FIIs) bought equities worth Rs 1,175.91 crore on Tuesday, according to exchange data.
The BSE benchmark jumped 712.44 points or 0.92 per cent to settle at a new closing peak of 78,053.52 on Tuesday. The Nifty went up by 183.45 points or 0.78 per cent to settle at a record closing peak of 23,721.30.
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