India in Delhi last year.
Kumar also shared in a 111 partnership with number 11 Mohammed Shami in India's first innings - a last-wicket record for India against England.
Even Cook himself had a bowl, much to the delight of the home crowd, and he was allowed a smile with the wicket of Ishant Sharma (13) when he edged to Prior.
India declared after his over and as stumps were drawn all eyes moved to the home of cricket next week.
The visitors have not played a five-match test series on English soil since 1959 and are in search of their first away win since 2011, while England are chasing their first victory of coach Peter Moores' second spell in charge.