Overnight 325/5, J&K rode on Singh's 115 (184 balls) and Manhas' 135 (231 balls) to almost match upto the visiting side.
Lower down the order, Aamir Aziz (47) and Samad Bhat (42 not out) also made useful contributions.
For Goa, R P Singh and Shadab Jakati picked up four wickets apiece.
In their second innings, Goa were 82 for one wicket before stumps were drawn for the day. The visiting side picked up three points from the match owing to the first innings lead they managed.
Jammu and Kashmir: 501 in 140.5 overs (Ian Dev Singh 115, Mithun Manhas 135, R P Singh 4/118, Shadab Jakati 4/103)
Goa: 552/5d and 82/1 19 overs (Darshan Misal 41).
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