Parametrized maximum independent clauses problem:
Input : A k-CNFSAT formula F having n variables and m clauses, k
Ques : Does there exists at least k clauses such that they are mutually independent i.e. no variable occurs more than once in all these clauses combined.
I would like to know whether this problem is in FPT or not. In both situations, an idea to proceed forward will be appreciated.

Parametrized maximum independent clauses problem:
Input : A r-CNFSAT formula F having n variables and m clauses, k
Ques : Does there exists at least k clauses such that they are mutually independent i.e. no variable occurs more than once in all these clauses combined.
Parameter : k
I would like to know whether this problem is in FPT or not. In both situations, an idea to proceed forward will be appreciated.