Cut off for BA(Hons.) in Social Science isn't available still. But according to be data of 2019 you can estimate how much can it be.

For General candidates: cut-off rank: 1504 & Cut-off marks: 170

For OBC candidates : Cut off rank: 1106 & cut-off marks: 147

For SC candidates: Cut off rank :474 & cut off marks: 113

For ST candidates: Cut off rank : 294 & cut off marks: 80

For PH-OH candidates: Cut off rank : 228 & cut off marks: 0

For PH-VI candidates: Cut off rank : 222 & cut off marks: 14

For PH-HI candidates: Cut off rank : 224 & cut off marks: 10

For Employee Rank candidates: Cut off rank :252 & cut off marks: -17

Hope my answer helps you to get a rough estimate about how the cut off can be this year. Although , the cut off fluctuates every year but it's the standard way to get a prediction of what it will be this year.

Wish you a prosperous career ahead!