Given a collection of points P in the plane, a 1 – set is a point in P that can be separated from the rest by a line, .i.e that point lies on one side of the line while the others lie on the other side. The number of 1-sets of P is denoted by n1(P). The minimum value of n1(P) over all configurations P of 5 points in P lie on a line ) is a) 3 b) 5 c) 2 d) 8

• For Maximize: The number of methods, Points should be drawn in the circumference of the CIRCLE So answer would be the number of total point in the plane.
  
  For minimize: The number of methods we should draw 3 points in a TRIANGLE and all other point inside this triangle in such a way that no 3 points could be in a line.
  
  If it will be allowed to draw the points in a line then minimum possibilities will be 2 only, because if we take all points in a line then you can separate only the corner points from the others.
  
  For example
  If we have 10 points then maximum possibilities = 10
  and minimum = 3
  
  similarly for 5 points
  Max = 5, Min = 3
  
  for 19
  max= 19 Min = 3
  
  Answer is 3
• 12 years agoHelpfull: Yes(3) No(0)