Having dismissed the visitors for 295 on a green-tinged pitch, England saw their way to 51 for the loss of Cook and Sam Robson at lunch, with Gary Ballance (7) and Ian Bell (11) to resume after the break.
Left-hander Cook has not passed three figures in over a year, and has now scored 93 runs in six test innings against Sri Lanka and India this season following his latest failure.
He looked comfortable at the crease in London's sweltering heat, before nibbling at a ball from the accurate Bhuvneshwar Kumar that was well taken by Mahendra Singh Dhoni behind the stumps.
Opening partner Robson was lucky to survive the previous over from Mohammed Shami, but second slip Ajinkya Rahane spilled a simple catch.
Dhoni ensured he did not have another life, claiming a simple catch when Australia-born Robson flailed at a ball outside off-stump on 17 to give Kumar a well-deserved second wicket and leave England's innings teetering at 31 for two.
Ballance and Bell dug in to ensure there was no further loss before the break and while they barely troubled the scorers, they showed appropriate discipline on a surface still offering encouragement to the seam attack.
Earlier India's first innings lasted only ten balls of the morning session before Ben Stokes had Shami caught by Cook, with five runs added to the overnight score.
The quick breakthrough was scant consolation for the hosts, who had India at 145 for seven just after tea on Thursday before Rahane (103) combined with the lower order to ensure their bowlers had a total to defend.
The first match of the five-test series at Trent Bridge was drawn.
- Sports & Recreation
- Sam Robson
- Gary Ballance
- Bhuvneshwar Kumar
- Mahendra Singh Dhoni
- Ian Bell
- Mohammed Shami
- Ajinkya Rahane