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They actually did (except new guys) and lost 2 test match series.
I do not remember that series but New Zealand is the only place they are yet to win a Test series if that is the case and if i remember correctly they already won in other countries or atleast drawn the series but i do not remember any good performance in New Zealand but i think the current India team can change that and win the series as they have the bowlers and if there is a support from the batting unit they can win, if not it is going to be really close matches.
England and New Zealand ended in a draw, if not for the rain delay i thought New Zealand could win the match.