After updating to Yosemite, following apps not opening. App Store, Mail, Contacts, Calendars... About the Mac

Question

After updating to Yosemite, following apps not opening.
App Store
Mail
Contacts
Calendars
Reminders
Maps
Preview
About the Mac
I recently updated to Yosemite and now I am having problems with the above mentioned apps, not opening at all.
I am unable to check to which version its update to, or even update to next version.

Answer 1

You ran a defective third-party "utility" such as "CleanMyMac" or "MacCleanse" that purports to "clean up" "junk" files. What it really does is to corrupt the operating system and many applications.   
The first thing you need to do is remove that software according to the developer's instructions. Never install it, or anything like it, again. Then see below. If you use any iWork applications, you may need to delete them and redownload them from the App Store.
If you don't already have a current backup, back up all data, then reinstall the OS.* You don't need to erase the startup volume, and you won't need the backup unless something goes wrong. If the system was upgraded from an older version of OS X, you may need the Apple ID and password you used.
If you use FileVault 2, then before running the Installer you must launch Disk Utility and select the icon of the FileVault startup volume ("Macintosh HD," unless you gave it a different name.) It will be nested below another icon, usually with the same name. Click the Unlock button in the toolbar and enter your login password when prompted. Then quit Disk Utility to be returned to the main Recovery screen.
There are ways to back up a computer that isn't fully functional. Ask if you need guidance.
If you installed the Java runtime distributed by Apple and still need it, you'll have to reinstall it. The same goes for Xcode. All other data will be preserved.
*The linked support article refers to OS X 10.10 ("Yosemite"), but the procedure is the same for OS X 10.7 ("Lion") and later.