Put into bat, Indian openers Lokesh Rahul (43) and Shikhar Dhawan (62) gave the visitors a solid 108-run start but the batting wobbled after their departure.
Rohit Sharma (7) and Kohli (8) fell in quick succession as medium-pacer Kasun Rajitha (3-47) made his presence felt in the President XI ranks as Indians lost four wickets for 25 runs in the post-lunch session.
Pujara and Rahane defied the hosts until tea with the scorecard reading 175 for four.
The two batsmen put on runs at a brisk pace, bringing up the 50-partnership in the 49th over. And then they kicked on, with Rahane bringing up his half-century off 59 balls, with five fours.
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Their 100-partnership came up in the 59th over and the duo scored at 4.75 per over during their 28.1-over stay together at the crease. Pujara slowed down a little as spin was introduced to make up for the slow over-rate and that hesitation cost him his wicket in the 66th over.
Rahane has struck 11 fours and a six in his 127-run stay so faras he helped India manage a healthy run-rate of 3.97 through the day.
The in-form batsman had got the company of Ravichnadran Ashwin (10 not out) at the end of the day's play as the duo managed an unbeaten 41-run partnership.