Well, you can prepare for BHU’s BA entrance exam by studying any General Knowledge book along with a reasoning book.I would recommend you to study from -

1-Lucent’s General Knowledge

2-Arihant’s reasoning question book (one that comes with a red cover)

3-Some previous years question papers (BHU’s BA Entrance Exam)

My friend studied from these two books along with the question papers for just a month and he got 263 marks and secured a seat. Hope that’ll help & best of luck.

Thank you.