England currently trail India by 244 runs with Gary Ballance (7) and Ian Bell (11) fighting it out in the middle.
Kumar (2/17) removed Alastair Cook (10) first, caught behind by a diving Mahendra Singh Dhoni, as the English skipper's horrible run with the bat continued.
It was brilliant bowling from the Indian medium-pacer who set up Cook beautifully in the previous over and then snapped him up with a huge out-swinger off the first ball of the 11th over.
It was quite disappointing for the batsman for he failed to make good on a life given by Ajinkya Rahane at third slip, when the first-innings' centurion dropped him off Mohammed Shami (0-21) in the 10th over. Robson was batting on 8 at that time and could only add 9 runs to his tally.
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Ishant Sharma (0-9) was the only other bowler used in this session by India as they dominated play on this second morning of the match. Kumar and Shami in particular bowled a fuller line as compared to the English bowlers yesterday and India reaped rewards for it.
On day one, Rahane's second Test ton had rescued India from collapse after they were reduced to 145/7 at one stage. He scored 103 runs on a green-top wicket and added 90 runs for the eight wicket with Bhuvneshwar (36) to guide his team to safety.
James Anderson, playing under allegations of physical abuse against Ravindra Jadeja, took 4-60 while Stuart Broad returned 2-79. Liam Plunkett (1-51) and Moeen Ali (1-38) were the other bowlers used.
Both sides were unchanged from the first Test in Nottingham that ended in a draw.