At stumps on the second day at the MA Chidambaram Stadium, Saurashtra, in reply to the hosts' massive first-innings total, were struggling at 12 for one.
Resuming on overnight 103, the 23-year-old Mukund went on to score 240 after facing 437 balls. He found the fence 20 times and cleared it once. Karthik made 133 off 192 balls, hitting 14 boundaries and a six.
After Tamil Nadu started at an overnight 268/2, the duo of Mukund and Karthik shared 240 runs for the fourth wicket to pile on the agony for Saurashtra. Overnight batsman Baba Aparajith got out immediately after reaching his half-century, falling to seamer Jaydev Unadkat, who finished with figures of four for 99 in 31.4 overs.
Mukund was bowled by Kamlesh Makvana after his monumental effort while skipper Karthik was one of Unadkat's four victims. When the stumps were drawn for the day, Bhushan Chauhan (3) and India player Cheteshwar Pujara (8) were at the crease for Saurashtra. They have already lost opener Sagar Jogiyani.
Brief scores: Tamil Nadu 1st innings: 565 for eight declared in 158.2 overs (Mukund 240, Karthik 133; Unadkat 4/99) vs Saurashtra eight for no loss.