6-Letter Words From MATHS Where Every Letter Appears Twice
How many 6-letter words can be formed from MATHS if every letter used must appear at least twice? A JEE Main 2025 permutations problem, solved fully.
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Position Vectors 4p+q-3r, -5p+q+2r, 2p-q+2r: Find α+2β+5γ
A JEE Main 2025 vector geometry problem solved using the Euler line property that the centroid divides the orthocenter-circumcenter segment 2:1.
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Two Ellipses, Eccentricity 1/√3: Area of Quadrilateral ABCD
Two ellipses with the same eccentricity, a given latus rectum product, and a known focal distance intersect at four points. A JEE Main 2025 area problem, solved.
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Unit Vector Perpendicular to b, c at Angles cos⁻¹(-1/3) and π/3
Find alpha when a unit vector perpendicular to two given vectors also satisfies two angle conditions. A JEE Main 2025 3D vector problem, solved fully.
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3-Digit Numbers Divisible by 2 and 3, Not 4 and 9
How many 3-digit numbers are divisible by both 2 and 3, but not by 4 or 9? Solved using LCMs and arithmetic progressions, JEE Main 2025 style.
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The Length of the Chord of the Ellipse x²/4 + y²/2 = 1 Whose Mid-Point Is (1, 1/2) Is
Given only the midpoint of a chord of an ellipse, find its length using the T = S1 equation of a chord — a JEE Main 2025 conic sections problem, solved.