How to compare the context objects of the two different Activities..?

Ten activities seems like a lot to have at once.

What are you trying to do by comparing context objects? Sometimes the answer to the question "How do I do this?" is "Don't do this! Tell us what you want, and we'll suggest another path to follow."

I hope you aren't holding on to these Context references longer than necessary, I found out what a wonderful source of memory leaks this can be if not handled correctly!

If they are all Activity instances you can treat them as such and use:

if ( activity instanceof MyClassActivityOne ) {
// do something
}