No problem in praying half an hour before fajr.

Sheik.. my mother wanted to know that if fajr is 5.30 am and she prays tahajud at 5.00 am will it be accepted as tahajud or should she pray much earlier like 4.00 am?

Prayer | November 22, 2017 3:08 pm
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I wanna know whether this hadith is authentic there is thasbeeq nafil prayer which should be prayed at least once in a week or once in month or once in a year or atleast once in lifetime. This nafil prayer should be prayed in India as follows 4 raqats of nafil with 75 times of reciting Subhuhanallahi walhamdullilahi walahilah illalahu wallahu Akbar per raqats .
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Me and my mom everyday pray tahajjud together..but I just heard we should pray tahajjud alone. .is it true?