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 Consists of 7 Boys and 3 Girls, Group B Consists of 6 Boys and 5 Girls. The Number of Ways 4 Boys and 4 Girls Can Be Invited for a Picnic if 5 of Them Must Be From Group A and the Remaining 3 From Group B
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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If All the Words, With or Without Meaning, Made Using All the Letters of the Word KANPUR Are Arranged as in a Dictionary, Then the Word at the 440th Position Is
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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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.