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JEE Main 2025 Apr 8 Shift 2, Mathematics Q13: Combinations

JEE Main2025Apr 8, Shift 2Mathematics
Q.

There are 12 points in a plane, no three of which are in the same straight line, except 5 points which are collinear. Then the total number of triangles that can be formed with the vertices at any three of these 12 points is

  1. A

  2. B

  3. C

  4. D

Solution

Choosing any 3 of the 12 points gives possible triples.

A triple fails to form a triangle only when all three chosen points are collinear, and the only collinear set available consists of the 5 given points.

The number of collinear triples is .

Valid triangles: , matching option (4).

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