I am getting 87 marks in JEE Mains shift 1 and I am an OBC candidate. What would be my rank and percentile?

Percentile depends on various factors like the difficulty of the paper, number of candidates appearing in the JEE examination and many more. So, according to the last year trends, your percentile should be nearly between 94.47 to 95.74, looking at your JEE score. Moreover, your rank may be around IN

The rank might be above INR 1 Lacs, but I don't know about the percentile. It depends upon the people in that slot.