The 25-year-old Carter dominated the West Indies innings by smashing the Indian attack to all corners of the ground, scoring an impressive 133 off 132 balls.
He took his time in establishing control on a pitch that offered good bounce for the bowlers but was productive for batsmen who were willing to be patient.
Carter plundered 18 fours and two sixes in a fine display. His hundred came after he had been dropped on six Yusuf Pathan.
Carter attacked the Indian bowlers relentlessly and the West Indies reached their 200 in 43rd over. Medium pacer Jaydev Unadkat finally dismissed him as he trapped him LBW.
Choosing to bowl first, Indian seamer Vinay Kumar struck twice early on, dismissing openers Andre Fletcher (15) and captain Kieran Powell (4) to leave the visitors 21 for two in 8.4 overs.
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