no, you definitely cannot take SOLVED ROUGH SHEETS or any other written materials from from the exam centre after the JEE mains with you home as these exam materials, including the rough sheet everything  remains the property of the national testing agency NTA. Once when the exam is over you must submit all these documents to the eXAM invigilator all the exam materials to the invigilator taking anything part of this exam material strictly prohibited and may lead to serious consequences.These rough sheets are basically kept as a backup. so that so that it does not create any problem when you are prepare is checked. Or they can check if you have cheated or not.