Having been put into bat on a notoriously seamer-friendly pitch in Wayanad, Duckett (80) and Max Holden (26) put on 82 in a crucial opening partnership facing the new ball. Holden fell just before lunch to bring Hain to the crease.
The pair put on 48 for the second wicket before Duckett was bowled by Shardul Thakur, getting a small inside edge onto his stumps.
Hain showed excellent fortitude as the Indian attack stemmed the early run-rate; the Warwickshire man reached his 50 off 142 balls and was eventually caught at short-leg off spinner Jalaj Saxena for 61.
Steven Mullaney (39*) and Will Jacks (40*) will resume their six-wicket partnership on Friday, having put on 65 in the final 20 overs of the day.
“I did all the hard work in the morning and got myself in in the second session. It was a day for me to get a big hundred, but it’s a nice start to the series.
“We bat on these wickets all the time [in England] when they do a bit with the new ball. I think I went into the mentality of being in England – I knew it would do a little bit but I think the wicket was a bit nicer [to bat on] than both teams expected. It was about going out and playing my natural game and it’s paid off.
“Potentially, early on, the bowlers tried too many things which allowed us to score freely. Something that our bowlers will do is bang a good length in the right areas. Maybe as they were expecting the new ball to do a lot they searched a little bit.”
© Cricket World 2019