At the dinner break, India was strongly placed, having started the proceedings at 132 for one.
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The 25-year-old Mandhana became the first Indian woman to hit a century in day-night Tests and also the first from the country to reach three figures in the game’s traditional format on Australian soil.
Mandhana made 127 off 216 balls with the help of 22 boundaries and a six at the Carrara Oval, and added an Indian record of 102 runs in Australia for the second wicket with Punam Raut (36), continuing the good work after putting on 93 with Shafali Verma on a rain-marred opening day.
She brought her century with a short-arm pull shot off Ellyse Perry in the 52nd over.
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The India opener, however, overcame the early jitters and went about her business in a professional manner while playing some lovely shots, including a magnificent straight drive off Annabel Sutherland.
She looked set for more but was caught at short mid-off off the bowling Ash Gardner, after playing an uppish drive.
Raut walked off after a caught behind appeal despite the umpire not entertaining Alyssa Healy and Meg Lanning’s loud shouts.
Skipper Mithali Raj (15 batting) though got into the job straight away, sweeping and driving Gardner for fours.
Brief scores:
India 1st innings: 231/3 in 84 overs (Smriti Mandhana 127; Sophie Molineux 2/22).