jee-main 2021 Q62

jee-main · India · session2_16mar_shift2 Combinations & Selection Geometric Combinatorics
Consider a rectangle $ABCD$ having $5,6,7,9$ points in the interior of the line segments $AB , BC , CD , DA$ respectively. Let $\alpha$ be the number of triangles having these points from different sides as vertices and $\beta$ be the number of quadrilaterals having these points from different sides as vertices. Then $(\beta - \alpha)$ is equal to
(1) 795
(2) 1173
(3) 1890
(4) 717
Consider a rectangle $ABCD$ having $5,6,7,9$ points in the interior of the line segments $AB , BC , CD , DA$ respectively. Let $\alpha$ be the number of triangles having these points from different sides as vertices and $\beta$ be the number of quadrilaterals having these points from different sides as vertices. Then $(\beta - \alpha)$ is equal to\\
(1) 795\\
(2) 1173\\
(3) 1890\\
(4) 717