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Devon Conway top scored with 91 as the Kiwis ended Day 2 on the front foot by posting 180/3.
Kuldeep, who is on a short family trip to Australia, visited the iconic Melbourne Cricket Ground, the home ground of his idol.
A top-order meltdown left England reeling at 49-5, and they capitulated before the Indian spin duo of Axar Patel and Kuldeep Yadav, who claimed three wickets apiece.
Since he is a centrally-contracted player and a T20 World Cup hopeful, National Cricket Academy's sports science and medical team will have a big say in Kuldeep's injury and rehab management.
India bowled England out for a below-par 218 and cruised to 135/1 at stumps on Day 1.
England were bowled out for 319 in their first innings, with seamer Mohammed Siraj (4/84) emerging as the most successful Indian bowler.
Jadeja had been recalled to the Indian squad with selectors keeping an eye on his fitness before the third Test, which begins on Thursday.
Kuldeep chose to side-step when asked whether rank turners should be there or not.
He played down an ankle injury that forced him from the field early in South Africa’s paltry reply of 95 to India’s total of 201/7 in 20 overs.
The left-arm wrist spinner said dealing with the setback was tough.
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