Hello aspirant
As you have not mentioned about which exam you are talking about i m considering it for neet.No you are not allowed to wear watch in neet 2020 according to NTA guidlines. In every exam hall wall clock is present in classroom in alomost 80 % cases , so you can see time from there or you can ask your class invigilator he/ she will surely help you.
Don't be panick for time management because you can easily check that practice previous year papers and you will get an approximate idea and in worst case you have your invigilator. You will get pen in classroom itself . you can take your transparent bottle and hand sanitizer with your self.

This guideline is also for jee main .

Hope this will help you

Guidline for neet 2020 here

Thank you

See Candidate If You are talking about JEE MAINS examination that is going to be held in September (1-6) 2020 then you can take your own pen but it should be transparent one . Now talking about watch then it is not allowed.  It is strictly prohibited. In every room there Will be clock to cross-check time .You can take sanitizer bottle and Drinking water to centre this time due to COVID 19 Outbreak.

All the Best!
If you want that you should predict your rank after giving JEE MAINS exam then you can predict it here.