can anyone tell me that will i be eligible for State counselling ''mop up round'' if i have took admission through 2nd round state counselling in Bihar( for neet 2020)
Yes, you will be eligible for mop up round.
Once you attend a round of counselling ie you are physically present there, it does not matter whether you get a seat or not. You are automatically eligible for the subsequent round, and you can attend it either for up gradation or to avail a seat for the first time. Just make sure to attend the counselling till the end.