Hello, Manya.

I'm Afraid the cut offs for some of Kolkata's best BA colleges is in the upper high range i.e. 82%-95%

Some of the best colleges include

1) St. Xavier's College

2) Lady Brabourne College

3) Presidency College etc

However, if you want to go for it,  you might apply anyway. Sometimes an availability of seats or cap round selections can get you admission.

Hope this helped,

Good luck!