[milind]

Is a non metal with more electronegativity more reactive than a non metal with less electronegativity? I mean can the former displace the latter in a displacement reaction?  And is there any exception to this rule?

[Borek]

There is no such rule.

To some extent that's how it will work for at least some of the binary compounds (metal/nonmetal), but in general chemistry of nonmetals is way too diverse for such a simple rule.