UPSEE Solved Model Paper 1

Case :Only intermediate points are used
Using(AB, BC, CD→ 3 x 4 x 5 = 60
Using (BC, CD,DA → 4 x 5 x 6 = 120
Using (CD, DA,AB) → 5 x 6 x 3 = 90
Using (DA,AB, BC) - 6 x 3 x 4 = 72
Total ways = 342
Case ll: One vertex of quadrilateral is used
Using vertex A, other two points must be taken from intermediate points on BC and CD.
No. of ways = 4 x 5 = 20.
Similarly using vertex B.No. of ways = 5 x 6 = 30
Using vertex C.No. of ways = 6 x 3 = 18
Using vertex D.No. of ways = 3 x 4 = 12
Total ways = 80
Combining casel and Il, there are 422 possible triangles that have no side common with quadrilateral.