Question

# Let there be 16 points in a plane out of which 6 lie on one line and 5 lie on other line, then the correct option(s) among the following is/areTotal straight lines that can be formed using these points are 95Total triangles that can be formed using these points are 530Total circles that can be formed using these points are 256Total quadrilaterals that can be formed using these points are 1490

Solution

## The correct options are B Total triangles that can be formed using these points are 530 D Total quadrilaterals that can be formed using these points are 1490Total straight lines that can be formed from 16 points = 16C2 Required number of ways Since total points are 16, but 6 are collinear and other 5 are also collinear. ∴ Required number of ways = 16C2− 6C2− 5C2+1+1=97 (two lines will be obtained from collinear points) Total triangles that can be formed from 16 points = 16C3 Since total points are 16, but 6 are collinear and other 5 are also collinear. ∴ Required number of ways = 16C3− 6C3− 5C3=530 Total circles that can be formed from 16 points = 16C3 Since total points are 16, but 6 are collinear and other 5 are also collinear. ∴ Required number of ways = 16C3− 6C3− 5C3=530 Total quadrilaterals that can be formed from 16 points = 16C4 Since total points are 16, but 6 are collinear and other 5 are also collinear. Also, for making quadrilaterals three collinear points can't be taken, ∴ Required number of ways = 16C4− 6C4− 5C4− 6C3× 10C1− 5C3× 11C1=1490

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