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Chasing an unlikely 405 for victory, wicketkeeper-batsman Jonny Bairstow (23) and Zafar Ansari (0) were battling for survival after Indian bowlers claimed five wickets in the morning session.
The visitors, who resumed the day on 87 for two, are 263 runs behind their victory target as India need three more wickets to take a 1-0 lead in the five-match series.