Mukund scored 108 with the help of 13 fours in 242 balls while Badrinath continued his good form, stroking 106 in 262 balls that included 15 fours.
While only eight overs were possible on the first day, bad light stopped play with 11 still to be bowled on the second day as Railways toiled for meagre returns while Tamil Nadu laid foundation for a big score.
The only success for Railways Thursday was the wicket of opener KB Arun Karthik who fell to seamer Jai Prakash Yadav.
Thereafter, Mukund and Badrinath put their heads down to strike a profitable partnership worth 208 runs so far for the third wicket.
Scoreboard:
Tamil Nadu (1st Innings): Srikkanth Aniruda c Fazal b Yadav 1; Abhinav Mukund (batting) 108; KB Arun Karthick c Rawat b Yadav 10; Subramaniam Badrinath (batting) 106. Extras (nb-18, W-1): 19. Total (for 2 wkts , 87 overs): 244
Fall of wickets: 1-5, 2-36.
Bowling: Anureet Singh 18-6-38-0, Jai Prakash Yadav 18-6-55-2, Vikas Tokas 13-0-48-0, Sanjay Bangar 12-4-28-0, Murali Karthik 18-1-34-0, Marripuri Suresh 3-0-21-0, Prashant Awasthi 5-0-20-0.
Deccan Herald is on WhatsApp Channels| Join now for Breaking News & Editor's Picks