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After Will Pucovski (62) and Marnus Labuschagne (91) gave the hosts their strongest start of the series, Steve Smith struck a gritty 131-run knock to ensure that the team had a fighting score on the board.
For India, all-rounder Ravindra Jadeja was the top wicket-taker with four scalps, conceding 62 runs in his 18 overs.
Pace spearhead Jasprit Bumrah and debutant Navdeep Saini chipped in with two wickets each to keep the visiting side firmly in the match after the hosts claimed the day one honours.
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Brief Scores:
Australia 1st innings: 338 all out in 105.4 overs (Will Pucovski 62, Marnus Labuschagne 91, Steve Smith 131, Ravindra Jadeja 4/62, Jasprit Bumrah 2/66).