Line L₁ of slope 2 and line L₂ of slope 1/2 intersect at the origin O. In the first quadrant, P₁,P₂,,P₁₂ are 12 points on L₁ and Q₁,Q₂,,Q₉ are 9 points on L₂. Then the total number of triangles that can be formed with vertices chosen from the 22 points O,P₁,,P₁₂,Q₁,,Q₉ is:

Permutations and Combinations: JEE Main 2025 Mathematics question

JEE Main 2025 · April, Unspecified (session-level dataset) · Q58

JEE Main 2025April, Unspecified (session-level dataset)MathematicsMediumPermutations and Combinations98× since 2002

Line

L_1

of slope

2

and line

L_2

of slope

\tfrac12

intersect at the origin

O

. In the first quadrant,

P_1,P_2,\dots,P_{12}

are 12 points on

L_1

and

Q_1,Q_2,\dots,Q_9

are 9 points on

L_2

. Then the total number of triangles that can be formed with vertices chosen from the 22 points

O,P_1,\dots,P_{12},Q_1,\dots,Q_9

is:

JEE Main 2025 Permutations and Combinations Question with Solution (April Unspecified (session-level dataset), Q58) | JEE Arc

JEE Main 2025 · April, Unspecified (session-level dataset) · Q58

JEE Main 2025April, Unspecified (session-level dataset)MathematicsMediumPermutations and Combinations98× since 2002

Line

L_1

of slope

2

and line

L_2

of slope

\tfrac12

intersect at the origin

O

. In the first quadrant,

P_1,P_2,\dots,P_{12}

are 12 points on

L_1

and

Q_1,Q_2,\dots,Q_9

are 9 points on

L_2

. Then the total number of triangles that can be formed with vertices chosen from the 22 points

O,P_1,\dots,P_{12},Q_1,\dots,Q_9

is: