Correct Answer - Option 4 : Avoid and Seek
In each option meaning of the first word and the second word is similar except in option 4.
Beautiful → very pretty or attractive; Handsome → having an attractive, well-proportioned
Bother → to disturb, annoy or worry somebody; Worry → to think that something bad might happen or has happened
Cold → having a low temperature; not hot or warm; Chilly → too cold to be comfortable
Avoid → to prevent something happening or to try not to do something; Seek → try to find or get something
Hence, Avoid and Seek is odd among all