The maximum number of points into which 4 circles and 4straight lines intersect, is

4 lines intersect each other in 4C2=6  points. 4 circles intersect each other in 2×4C2=12  points. Further, one line and one circle intersect in two points. So, 4 lines will intersect four circles in 32 points. ∴  Maximum number of points =6+12+32=50.