hi,

see one month is not too late to start preparation, and if you devote extra 2 hours per day for studying the previous lessons, I am pretty confident that you would complete it with in 2 months of past one month syllabus.

now coming to the points you should follow while competing any of the entrance exam is as follows:

never feel weak, always have the self confidence, unless it will not fruitful at the end of the long 1 year preparation.

make short notes and prepare notes for each chapters of pcm .

make a separate copy for theoretical and numerical problem.

for iits b.tech admission you need to clear jee main and jee advance score. even if your jee advance is not good enough you would get options for tier 1 nits if you score 99+ percentile in jee main exam.

since jee main and jee advance are national level entrance test, while you prepare for this two exams, you will eventually get perfect for the state level engineering test which would benefits you for the long run.

so there is many options available for you, all you have to do is studies and regularly maintain a routine for personal grooming and studies and daily necessary work.

hope you get my point. best of luck for your future endeavor.