Mohammed Shami (1/62) got Sam Robson's wicket but was the most disappointing of the pace trio erring in length on a number of occasions.
Ballance on his part hit 15 boundaries in his 204 ball unbeaten knock.
When the post-tea session began, Cook (82 batting) needed another few runs to score his first Test century in more than a year.
He began well, reaching the nervous 90s quickly, but once there the Indians mounted the pressure on him and it resulted in his dismissal.
Cook faced 231 balls and struck nine fours during his knock. It was his highest score since the 130 runs he made versus New Zealand in May 2013 and in doing so, reached 8257 runs in his career to overtake David Gower (8231 runs) and Kevin Pietersen (8181 runs) in the overall Test runs scored by Englishman.
Ballance on his part hit 15 boundaries in his 204 ball unbeaten knock.
When the post-tea session began, Cook (82 batting) needed another few runs to score his first Test century in more than a year.
He began well, reaching the nervous 90s quickly, but once there the Indians mounted the pressure on him and it resulted in his dismissal.
Cook faced 231 balls and struck nine fours during his knock. It was his highest score since the 130 runs he made versus New Zealand in May 2013 and in doing so, reached 8257 runs in his career to overtake David Gower (8231 runs) and Kevin Pietersen (8181 runs) in the overall Test runs scored by Englishman.