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JEE Main 20253 AprilEvening Shift
Exam
JEE Main
Year
2025
Date
3 April
Shift
Evening Shift
Subject
Mathematics
Chapter
Permutation and Combination

JEE Main 2025 · 3 April · Evening Shift · Mathematics · Permutation and Combination

Line L_1 of slope 2 and line L_2 of slope (1)/(2) intersect at the...

Line L1L_1 of slope 2 and line L2L_2 of slope 12\frac{1}{2} intersect at the origin O . In the first quadrant, P1,P2,….P12\mathrm{P}_1, \mathrm{P}_2, \ldots . \mathrm{P}_{12} are 12 points on line L1L_1 and Q1,Q2,…..Q9Q_1, Q_2, \ldots . . Q_9 are 9 points on line L2L_2. Then the total number of triangles, that can be formed having vertices at three of the 22 points O,P1,P2,…P12\mathrm{O}, \mathrm{P}_1, \mathrm{P}_2, \ldots \mathrm{P}_{12}, Q1,Q2,….Q9\mathrm{Q}_1, \mathrm{Q}_2, \ldots . \mathrm{Q}_9, is:

Options

  1. A10801080
  2. B11341134
  3. C10261026
  4. D11881188

Correct answer

B. 11341134

Step-by-step solution

Total number of Δ\Delta are
<br/>=9C112C2+9C212C1+1C19C112C1=594+432+108=1134<br/>\begin{aligned}<br/>& ={ }^9 \mathrm{C}_1{ }^{12} \mathrm{C}_2+{ }^9 \mathrm{C}_2{ }^{12} \mathrm{C}_1+{ }^1 \mathrm{C}_1{ }^9 \mathrm{C}_1{ }^{12} \mathrm{C}_1 \\ & =594+432+108 \\ & =1134<br/>\end{aligned}
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