Hello , 

As your query is you appeared in an entrance exam and completed with 1st round of counselling and you are not satisfied with the college alloted to you so you want to for 2nd round of counselling.

I would like to tell you that in many of the cases students have found that they waited for few more rounds of counselling and at the end they get a good college as per their choice but in some of the cases they don't get one. So yes if you fell that you can get better college as compared to what you have got in 1st round of counselling so definitely you can apply for the 2nd round of counselling. But in my opinion it would be better to keep the seat alloted to you in 1st round of counselling on float so that in any case if you don't get any better college so at least you would have that option left with you.

Further, if you have any other query regarding the same you can let me know in the comment section below.

I hope your query is solved.

Thank you