If Sn=1/2+1/6+1/12+… to n Terms, A.P. Sum is √(2026·S2025)
A JEE Main 2025 problem combining a telescoping series with an arithmetic progression, solved by simplifying Sn first, then using it to pin down the AP.
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Distance From C to Angle Bisector of OA, OB is 9/√2, Find a
Three points given by position vectors, a distance from an angle bisector — solved fastest by switching to plain coordinate geometry. JEE Main 2025.
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If I(m,n)=∫x^(m-1)(1-x)^(n-1)dx, Find I(9,14)+I(10,13)
A beta-function-style JEE Main 2025 integral solved without ever evaluating the integral itself — just substitution, addition, and pattern matching.
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Complex Roots of x²-(3-2i)x-(2i-2)=0, Find αγ+βδ
A quadratic with complex coefficients and complex roots is easier factorised directly than approached through Vieta’s formulas. JEE Main 2025, solved.
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5-Digit Numbers >50000, Digits 0-7, First+Last Digit ≤8
How many 5-digit numbers above 50,000, built from digits 0-7 with repetition, have first-plus-last digit at most 8? JEE Main 2025, fully solved.
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Group A: 7 Boys 3 Girls, Group B: 6 Boys 5 Girls — Picnic Selection
A JEE Main 2025 combinatorics problem: invite 4 boys and 4 girls for a picnic with 5 from one group and 3 from another. Solved case by case.
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Words From KANPUR in Dictionary Order: 440th Word
All arrangements of the letters of KANPUR are sorted like a dictionary. Which word sits at position 440? A JEE Main 2025 permutations shortcut, solved.
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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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Value of 36(4cos²9°-1)(4cos²27°-1)(4cos²81°-1)(4cos²243°-1)
A JEE Main 2023 trigonometric product that telescopes to a single value once each factor is rewritten using the sin 3θ triple-angle identity.
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Chord Length of Ellipse x²/4+y²/2=1 With Midpoint (1,½)
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.