Intersection of two CFL's is CFL is undecideable.
Lets take example suppose we have 2 CFL
L1=( a^n b^n c^m |m,n≥0)
L2=(a^m b^m c^n |m,n≥0)
Then L1∩ L2
L3=(a^n b^n c^n |m,n≥0) is csl
But
L1=( a^m b^m c^n |m,n≥0)
L2=(a^m b^n c^n |m,n≥0)
L3=(a^p b^q c^r |m,n≥0)
Is cfl
so sometimes it may be cfl or sometimes it may be non cfl
hence we can say that intersection of two cfl is cfl is undecideable.