Will there be any problems if I drop a year for IIT-JEE as I've heard that in interviews, they ask us the valid reasons for the same?

No, there would not be any problem in dropping an year for JEE. And I am not sure about which interview you are talking about but No one will ask about reason for your drop and even then somebody asks you then the answer is obvious "I want to improve my JEE score" You just have to give an affidavit

Hi, But why do you want to drop a year. Were't your scores good. It's actually not a good note of dropping a year. Of course they'll ask as they're giving you the job, they'd surely want to know the reason. Think once again whether you really need a drop or so. All the Best!

No, there will not be any problem regarding the same as many students take drop for entering into IIT.