JEE Main 2026 — Permutation Combination Question with Solution
JEE Main 2026 (22 January Shift 1)
Question
Let ABC be a triangle. Consider four points on the side AB, five points on the side , and four points on the side AC. None of these points is a vertex of the triangle ABC. Then the total number of pentagons, that can be formed by taking all the vertices from the points , is
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Show full solutionCorrect answer: 660
Correct answer
660
Step-by-step explanation
Points: 4 on AB, 5 on BC, 4 on AC. For a valid pentagon, no 3 vertices can be collinear, so at most 2 points from each side.
Only valid distribution with and each is permutations of :
:
:
:
Total .
Only valid distribution with and each is permutations of :
:
:
:
Total .
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This is a previous-year question from JEE Main 2026, covering the Permutation Combination chapter of Mathematics. PrepSharp catalogues every PYQ from JEE Main with a verified answer key and step-by-step solution prepared by IIT alumni — so you can search by chapter, topic or year and revise efficiently.