Agarwal, who played the series in the absence of KL Rahul and Rohit Sharma, failed in Kanpur but regained his form to score 150 and 62 in the second Test to win the 'Player of the Match' award.
The 33-year-old Mumbai-born Patel, who migrated to New Zealand as a seven-year-old, said it has been a "dream come true" to be able to play at the city of his birth and come up with a historic feat.
The Mumbai-born Ajaz joined Jim Laker and Anil Kumble in the rare 10-wicket club after taking all 10 wickets of India's first innings in the second Test which the hosts won by 372 runs.
After their tail-enders secured a thrilling draw in the Kanpur Test, New Zealand managed just 62 and 167 runs in the final game as India took less than an hour on the fourth day morning to walk away with a massive 372-run win -- their biggest winning margin at home.
Kumble had achieved the 300-wicket mark in 52 matches while Ashwin touched the same in 49 matches.
Kohli surpassed his own record that he had set as the skipper for the Indian team back then in 2015.
Ajinkya Rahane and Cheteshwar Pujara are under pressure to save their places in the side ahead of the South Africa tour and in that context, Dravid's comments assume significance.
Talking of the first Test in Kanpur, the right-handed batsman praised New Zealand for their valourous efforts for concluding the game in a draw.
Besides, the 48-year-old hailed the Indian players' efforts for having performed well especially when a few senior players were not in the team.
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The 33-year-old Patel, who had migrated to New Zealand from Mumbai with his parents back in 1996, ended the Indian innings with figures of 47.5-12-119-10 to equal England great Jim Laker and Indian legend Anil Kumble, who had earlier achieved the rarest of rare feat in Test cricket
Kohli was adjudged LBW by the on-field umpire on the fourth ball of his innings though the bat and pad appeared very close to the ball.
Shubman Gill while playing a shot in the ongoing second Test against New Zealand in Mumbai
Ajaz Patel scalped took a 10 wicket haul at an economy of just 2.49.
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The BCCI and the team management found an "exit route" which was honourable for both the distinguished senior cricketers as everyone associated wanted to be subtle while taking a tough decision, at least for this Test.
Tom Latham will lead the side in place of Williamson, who has been dealing with the tendon injury since it first emerged in the New Zealand home summer.
The match is expected to start later Friday amid wet weather.
LIVE India vs New Zealand, 2nd Test Day 1: Get all the Latest Score, Live Updates, Commentary, Scorecard and Live Updates from the India-New Zealand second Test match played at the Wankhede Stadium, Mumbai.
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