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Mohammad Shami has made himself available for recall after a lengthy absence due to an injury.
India were 141/6 at stumps on day two after Australia were bowled out for 181.
During his absence, senior batter Virat Kohli took charge of the team.
Jasprit Bumrah won the toss, but Pat Cummins' pacers exploited the conditions in Sydney on day one.
Marnus Labuschagne, on 20 not out, and Steve Smith, on two, survived to the break.
India pacer gave a timely reminder about his qualities with the bat after a match-saving cameo in the Brisbane Test.
Akash Deep (27) and Jasprit Bumrah (10) helped India to 252/9 at stumps on day four.
The Australia batter has lavished praise on India's pace spearhead.
Australia also ensured that the Test was played on the fastest and bounciest pitch available in the country.
Bumrah overtook Kagiso Rabada and Josh Hazlewood for top spot in ICC bowlers rankings.
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