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A 147-run opening stand between David Warner (86) and Travis Head (69) effectively laid the platform for Australia's comprehensive victory.
Captain Jos Butter (80 not out) and his opening partner Alex Hales (86 not out) smashed the Indian bowlers to all parts of the ground in their chase of 169. England romped home with four overs to spare.
The International Cricket Council took to Twitter to share a picture of Warner enjoying himself with the kids.
Selectors will not add any replacements for Hazlewood to the current squad and will instead pick a new squad after the Adelaide Test.
Kohli should do well to remember that the captain of the Indian cricket team is required not only to lead the side to glory on the field of play, but also win friends off it.
Australia were 191 for seven, with Head batting on 61 and tailender Mitchell Starc unbeaten on eight, still 59 runs short of India's modest total of 250.
The 21-year-old is now level with Englishman Jack Russell and South Africa's AB de Villiers.
Set a target of 323, Australia crumbled to 291 in 119.5 overs at the Adelaide Oval.
Kohli's men have to be on their toes as the Aussies are expected to come hard at them in the next Test.
Cheteshwar Pujara and Virat Kohli thwarted Australia in a diligent partnership to push India to a position of strength and a 166-run lead at stumps on day three of the first Test.
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