1.

ABCD is a convex quadrilateral and 3, 4, 5, and 6points are marked on the sides AB, BC, CD, and DA, respectively. The numberof triangles with vertices on different sides isa. `270`b. `220`c. `282`d. `342`A. 220B. 270C. 282D. 342

Answer» Correct Answer - D
Total number of triangles=Number of triangles with vertices on sides
`[(AB,BC,CD)+(AB,BC,DA)+(AB,CD,DA)+(BC,CD,DA)]`
`=.^(3)C_(1)xx.^(4)C_(1)xx.^(5)C_(1)+.^(3)C_(1)xx.^(4)C_(1)xx.^(6)C_(1)+.^(3)C_(1)xx.^(5)C_(1)xx.^(6)C_(1)+.^(4)C_(1)xx.^(5)C_(1)xx.^(6)C_(1)`
`=60+72+90+120=342`


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