Is branch sliding option there at MNNIT Allahabad?

Yes, at the end of the first year, you can apply for branch sliding. However, in order to be eligible, you must have a CPI of at least 7.5.

My brother also applied for branch sliding. There are only a few seats available in the branches (3 or 4), despite the fact that 90% of the students applied for branch sliding. 

The competition in-branch sliding is similar to that in JEE Main because there are only a limited number of seats available. To be eligible for a branch such as IT or CSE, your CPI must be greater than 9.0.

The date of the result of branch sliding is totally the mismanagement of academics. For 2 or 3 weeks after commencement of classes, you will have to first attend lectures of your own branch and after the result declaration you will go to the other branch, and slowly you will realize its importance. You have to catch up with what the teacher is teaching.

So branch sliding is possible, but it is a difficult problem to confront, as you will see when you attend the lectures.