If HIV virus won't live more than 1min the how come vaginal fluid having HIV on cloth exposed outside wiped at tip of penis can cause HIV infection?

Wrong assumption! HIV virus can survive for weeks, outside the body, depending on the composition of the fluid containing the virus and ambient temperature. The infectivity depends on contact with skin that may have abrasions, open sore or other wounds. See this site for more info. http://www.aidsmap.com/Survival-outside-the-body/page/1321278/