West Indies have scored a healthy 466 in their first innings courtesy a patient 112 by veteran Shivnarine Chanderpaul and an impressive 94 by Narsingh Deonarine.
Right-arm medium pacer Imtiaz Ahmed was pick of the UP bowlers with figures of five for 117. Veteran India discard left-arm pacer Rudra Pratap Singh took three for 86.
The stockily built right-hander Parvinder quickly settled down after West Indies reduced UPCA to 96 for four as he remained undefeated on a well-crafted 78.
At stumps, Parvinder who hit 11 boundaries and two sixes was at the crease with wicketkeeper-batsman Amir Khan as UP still trail West Indies by 260 runs with warm-up game slowly and steadily seemed to be meandering towards a predictable draw.
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Earlier, the match began an hour late because of wet outfield as the West Indies, resuming the day at 333 for four went past 450-run mark which also gave them much needed batting practice ahead of two-Test series against India.
Seamer Ahmed, who had impressed on the first day by picking up a couple of wickets, including that of Chris Gayle, added wickets of Chanderpaul (112; 15x4, 2x6) and Deonarine (94; 10x4, 2x6) in successive overs after UPCA took the second new ball in the 81st over.