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The benchmark BSE index climbed 0.36 percent to a record close of 37,692.46, while the broader NSE index rose 0.23 percent to a record close of 11,387.1.
ICICI Bank gained 3.3 percent, while Axis Bank rose 3.8 percent.
HDFC Asset Management Co Ltd's shares ended 65 percent higher in their first day of trade, following an initial public offering of 28 billion rupees ($408.10 million).