On iTunes 40 out of 83 of apps were deleted because I hadn't authorized the computer is there any way to get them back?

Yes, there is a way to get them back. As long as you are using the same iTunes account, you can get all of your apps back for free. If you remember all of the apps you need back, just download all of them again through iTunes, and since you already downloaded them once (if they're not in your computer's system), it will download them for free.