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MathsJEE Main 22 Jan 2026, Shift 1·Q25·Numerical·Moderate

Permutations & Combinations · Selection of points on triangle sides

Let ABCABC be a triangle. Consider four points p1p_1, p2p_2, p3p_3, p4p_4 on the side ABAB, five points p5p_5, p6p_6, p7p_7, p8p_8, p9p_9 on the side BCBC and four points p10p_{10}, p11p_{11}, p12p_{12}, p13p_{13} on the side ACAC. None of these points is a vertex of the triangle ABCABC. Then the total number of pentagons, that can be formed by taking all the vertices from the points p1p_1, p2p_2, …\ldots, p13p_{13}, is .

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See the full 22 Jan 2026, Shift 1 paper