Cook won the toss and elected to bat on a wicket that looked like it would favour the fast bowlers and after being badly dropped at third slip on 15, he played with growing confidence. (Agencies)
He and Sam Robson shared the first half-century opening partnership for England in 11 innings before Mohammed Shami removed Robson for 26, the right-hander edging a simple catch to Ravindra Jadeja at third slip.
Jadeja clung on this time after dropping a straightforward opportunity presented by Cook off the bowling of Pankaj Singh.
Cook was joined by Gary Ballance who was unbeaten on four at the interval.
The decision to bat first was a brave one considering Cook's recent lack of form and with the surface offering a hint of movement for the bowlers, although it was not as quick as first anticipated.
After a steady start in which where England had few scares, tall fast bowler Singh got one to nip away from Cook and his edge carried at a nice height to the slips where Jadeja spilled it.
Shami tempted Robson into an awkward prod outside off stump that carried to Jadeja, who would have been grateful for the simplicity of the chance as he made up for his earlier mistake.
Both teams made changes from the second test at Lord's with wicketkeeper Jos Buttler, on debut, Chris Jordan and Chris Woakes replacing Matt Prior, Ben Stokes and Liam Plunkett for England.
India, 1-0 up in the series, handed a debut to Singh, who came in for the injured Ishant Sharma, and Rohit Sharma took the place of Stuart Binny.
Cook won the toss and elected to bat on a wicket that looked like it would favour the fast bowlers and after being badly dropped at third slip on 15, he played with growing confidence.