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JEE Main20253 Apr 2025Evening ShiftMathematicsPermutation and CombinationActual

Line L₁ of slope 2 and line L₂ of slope 1 2 intersect at the origin O . In the first quadrant, P ₁, P ₂, . P ₁₂ are 12 points on line L₁ and Q₁, Q₂, . . Q₉ are 9 points on line L₂ . Then the total number of triangles, that can be formed having vertices at three of the 22 points O , P ₁, P ₂, P ₁₂ , Q ₁, Q ₂, . Q ₉ , is:

Options

  1. A1080
  2. B1134
  3. C1026
  4. D1188

Correct answer

B. 1134

Step-by-step solution

Total number of are aligned & = ^9 C ₁ ¹² C ₂+ ^9 C ₂ ¹² C ₁+ ^1 C ₁ ^9 C ₁ ¹² C ₁ & =594+432+108 & =1134 aligned

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