Whenever a new baby arrives, the other children in the family have to make many adjustments. They see that the mother's time is totally taken up for the baby and that they do not get much attention. Also all the visitors come with presents for the baby and not for them. They are told that the new baby will play with them, but if they try to start playing, the baby cries and they get scolded. This is the usual picture.
I think you are not right in using the adjective – arrogant, in describing your 7 year old. He is upset with the changing dynamics of the family, where suddenly no one bothers about him. You should not be beating him for not concentrating on his studies. Surely you can use a gentler and friendlier technique to persuade him to study.
Please remember your child is a person, not an examination-passing machine. Take some time off to cuddle him, talk to him and even more important, listen to him. Get him a surprise present. Do something for him that he finds interesting. Get the cooperation of others in the family to see that your older son does not feel neglected.