The rupee shed 33 paise to close at a life-time low of 74.39 against the dollar on Tuesday. A surge in crude oil prices and strength in the American currency overseas pulled the rupee lower. The rupee had started the session on a stronger note, and hit an intraday high of 73.88 against the greenback in the morning session. However, it gave up those gains in the second half of the day. The rupee closed lower against the dollar for the sixth session in a row.