The home side won the toss and chose to bat first in the final Test match of the summer, with skipper Strauss and Cook at the crease.
India, who are 3-0 down in the Test series, failed to pick up any wickets before lunch after losing bowler Praveen Kumar to injury, while Strauss scored 30 runs and Cook hit 34.
While the early session was relatively comfortable for England, Indian bowler RP Singh appealed for an lbw on Cook but was denied as the ball was heading too high over the wicket.
Strauss escaped an injury after the ball struck him on the helmet just before the break of the bowling of Ishant Sharma.
England are on course to claim their fourth straight win over India after being crowned the world’s best Test team at Edgbaston.