Is parametrized maximum independent clauses problem in FPT?
The problem is known as r-Set Packing:
Instance: A collection $\mathcal{C}$ of subsets of size at most $r$ of a finite set $S$ and an integer $k$.
Parameter: $k$
Question: Is there a subcollection $\mathcal{C'} \subseteq \mathcal{C}$ which consists of at least $k$ mutually disjoint subsets?

For unbounded $r$, the problem is W[1]-hard by an easy reduction from Independent Set (see for example [1]).
However, for constant $r$, the problem becomes fixed parameter tractable (see for example [2]).

[1]: Rodney G. Downey, Michael R. Fellows: Parameterized Complexity. Springer, 1999.
[2]: Michael R. Fellows, Christian Knauer, Naomi Nishimura, Prabhakar Ragde, Frances A. Rosamond, Ulrike Stege, Dimitrios M. Thilikos, Sue Whitesides: Faster Fixed-Parameter Tractable Algorithms for Matching and Packing Problems. Algorithmica 52(2): 167-176 (2008)