Earlier, Mukesh bowled with venom, taking three wickets to help India crawl back into the contest as England Lions stumbled to 333 for five at lunch on Day 3.
England Lions were 192 for 3 in 46 overs in reply to India A's 348 at stumps on the second day of their second unofficial Test, in Northampton on Saturday.
Tom Haines smashed an unbeaten century to lead England Lions' strong reply after Karun Nair's double century had powered India A to a massive 557 on Day 2 of the first Unofficial Test.
Nitish and Shardul were thrown into the playing XI for India A during both unofficial Tests against England Lions, and both all-rounders reaped mixed results across the two contests.
Andrew Flintoff's 17-year-old son Rocky and fit-again pacer Chris Woakes were on Wednesday named in England Lions squad for the two four-day games against India A at home.
India A batters enjoyed their time on a placid batting track with all the top four batters helping themselves to half-centuries as the first unofficial 'Test' against England Lions ended in a draw
K L Rahul would look to make the most of his first red-ball outing in months ahead of the upcoming Test series against England.
Earlier, Tanush Kotian (90 not out) and Anshul Kamboj (51 not out) brought up their respective half-centuries to take India A to 417 for 7 at tea on the fourth day of their second unofficial Test in Northampton on Monday.
India batter Cheteshwar Pujara's unbeaten 104 helped Sussex extend their first innings lead to 111 runs in their County Championship Division Two match against Derbyshire on Saturday.
'I am delighted that Cheteshwar is returning to Hove again for the first two months of the season.'
India international Cheteshwar Pujara has been suspended from one county game after his team Sussex was docked 12 points in the County Championship.
Cheteshwar Pujara continued his incredible form and hit a double century on captaincy debut for Sussex to put his side in a commanding position against Middlesex at Lord's on Wednesday.
Senior India batter Cheteshwar Pujara redeemed himself with an unbeaten double hundred in the second innings as Sussex snatched a draw against Derbyshire at the 2022 County Championship in Derby on Sunday.
Since joining Sussex last year, India's star batter made an enormous impact on the south coast side, scoring over 1000 County Championship runs, including a record-breaking three double centuries and finishing the season with an average of 109.4.