Opting to bat after winning the toss, India were provided a solid start by Dhawan (51) and Rahul (50), with the two putting on 93 runs for the first wicket before the left-handed Delhi dazzler was retired out.
At the end of a slow day during which 93 overs were bowled at the Warner Park wicket, Sharma was batting on 54 with the help of eight boundaries and a six.
Skipper Virat Kohli (14) and Ajinkya Rahane (5) failed to get what would have been some valuable batting practice before the start of the four-match Test series. The Indians, though, is slated to play another three-day warm-up game before the Test series gets going from July 21 at Antigua.
Like Dhawan, who struck seven boundaries during his 90-ball knock, Rahul was also called back after the batsman found the fence five times and cleared it once.
Sharma added 47 runs for the sixth wicket with Wriddhiman Saha (22) before putting on 45 runs for an unbroken seventh- wicket stand with Mishra.
Pujara's knock contained five boundaries and he spent 115 minutes at the crease while facing 102 balls.
Sharma then took charge and guided the lower middle-order in the company of Saha and Mishra.
For the West Indies, left-arm spinner Jomel Warrican was the most successful bower, returning figures of 2/61 in 26 overs.
Saha was the last Indian wicket to fall on day 1, when the wicketkeeper-batsman was dismissed by Damion Jacobs.
The rules allow 12 players to play while 11 could field. India decided to rest off-spinner Ravichandran Ashwin and opener Murali Vijay.
(REOPENS FGN 4)
On a slow Warner Park wicket, the right-arm pacers Marquino Mindley and Jason Dawes couldn't create much of an impact although the Indians did not take any undue risks.
The moment spinners were introduced, the Indian batsmen showed more intent in scoring runs and the footwork looked assured. Rahul swept a leg-break from Jacobs from outside the off-stump.
Like the openers, Pujara and Kohli too took their time to settle down as they knocked the ball around for singles and twos, with the occasional boundaries. The partnership, however, came to an end in the 48th over when Kohli was out caught-behind off Warrican.
Rohit then played some effective shots in the second half of the day.
Brief scores: India 258/3 in 93 overs (Rohit Sharma 54 not out, Shikhar Dhawan 51, KL Rahul 37, Cheteshwar Pujara 34; Jomel Warrican 2-61, Damion Jacobs 1-80) vs West Indies Cricket Board President's XI.
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