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After being bowled out for 319 with a first-innings lead of 24, England took their first wicket at the end of the 14th over when Shikhar Dhawan (31) was acrobatically caught at backward-point by Joe Root off the bowling of Ben Stokes.
Cheteshwar Pujara came in and steadied the Indians before England took three wickets for the loss of just five runs in the final session.
Kohli thought that the Yorkshireman's delivery was safely carrying through to Prior, but the ball clipped the top of off-stump to send Kohli straight back to the pavilion.
The last wicket of the day came when Stuart Broad's bouncer looped off Ajinkya Rahane and was caught by Prior. However, replays showed that Rahane shouldn't have been given out as the ball hit his forearm guard, not his glove.
England now have two days to bowl the Indians out and chase down the victory target to take a 1-0 series lead.