I am not sure, if the sentence ""I knew that you are busy in a meeting" is correct. I think it is incorrect as it has past tense(knew) and present (are). pls. correct me
You can mix tenses, but this particular mix wouldn't be quite appropriate to a native English speaker. "I knew that you were busy" says that you knew the person was busy, but they aren't now. "I know that you were busy in a meeting" would be used if you are acknowledging that someone was previously busy, and have something else to say ("I know you were busy, but you still needed to send me that report"). "I know you are busy in a meeting" would be used if they are in a meeting right now, and you're contacting them while they're in that meeting.
It is incorrect, you're right. "I knew that you are busy in a meeting" implies that you somehow saw the future and knew that the person was going to be busy ahead of time. Which is doubly rude, since you knowingly interrupted their meeting!
"I know you're busy in a meeting" would be appropriate if you're contacting someone in the middle of a meeting with something important. Otherwise, it would be "I knew you were busy in a meeting" if the meeting happened some time ago, and you decided to wait until afterwards to contact the person, since you knew they were busy at the time.