Question of Applications

Hello i placed a passcode on my iPhone 4s and forgot it. Didn't have a backup so i just restore it to defualt with itunes, but i lost my all paid application. Before i restored the phone i did backup of all my installed application by using a software name iTools which is storing applcation in my laptop in .ipa format and the size also was the same shown in my iphone so i was a bit satisified and restore it to defualt to remove the passcode. Now when i try to import backup application in my phone using iTools it shown in my phone but when i click on it, its not working ...i have many paid application and games so any way to restore it back from my laptop to iphone .

Thankyou