The simple and quick solution by "dale from sf" worked for me. No reboot needed.
If you do not know how to "terminate" Settings, here is the gory detail. Many words to read, just a few seconds to do.
Press the "Settings" icon to open the Settings app. Observe that Airplane Mode is OFF and Cellular Data is (improperly) grayed out.
Press the Home button once to exit Settings.
Double-tap the Home button. (The contents of the screen will slide up an inch and look like it's behind smoked glass. The bottom row of the screen--which won't look like smoked glass--will display the icons of the last few apps you have run. The Settings icon, run most recently, will be the leftmost of those icons.)
Press and hold the Settings icon (at the left end of the bottom row) for about 2 seconds until a "minus badge" (red circle with white minus sign inside) appears near the top left corner of the Settings icon.
Tap the red "minus badge". (This will "terminate" the current run of the Settings app but leave the app installed on your iPad. Your settings won't change, but if you were in the middle of a process such as joining a wi-fi network or setting up a mail account, it may not complete and you may need to restart that process from the beginning.)
Press the "Settings" icon to open the Settings app. Confirm that Cellular Data is no longer grayed out. (If it is still grayed out, this method did not work folr you, Power off the iPad and power it back on.)