Hiya!
Do you speak of the app in which you referred to in your title,
https://play.google.com/store/apps/details?id=sagar.advancedgooglesearch

or some other Google app like the real Google app :
https://play.google.com/store/apps/details?id=com.google.android.googlequicksearchbox&hl=en

Either way, how are you exiting the app? With the "Home" button, or the "Back" key?

Some apps, depending on how they are written, and what permissions are granted, may run in the background. Killing/cleaning RAM in Android is pointless as any app will just restart again....the more ram, the better in Android.

 

If you force stop an app, it may misbehave. You really don't need to force stop an app unless it is acting weird.
If you do indeed force stop it, it either will act funny, or just start up by itself if needed.
Now, again, clearing ram is pointless....yes initially your device may run slightly quicker, but the ram will just build back up....the more ram used in Android the better. As opposed to Windows, the less ram, the better...(someone correct me if I'm wrong about the Windows ram bit )


Interesting, well written thread to check out about ram and such:
http://androidforums.com/threads/pu...k-killers-ram-optimizers-and-the-like.896663/


Anyhoo, is the Google app causing an issue?

 

It's because Google apps covers so many things. You might not realise that you used something that's classed as Google apps but you did. Did you ever get a gmail? There you go. There's more examples. Seriously though don't worry about RAM management on Android. It sorts itself out. Closing them usually just makes the system re-open them a few minutes later when it was needed