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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Let A, B, C Have Position Vectors OA = √3i + j, OB = i + √3j and OC = ai + (1−a)j. If the Distance of C From the Line Bisecting the Angle Between OA and OB Is 9/√2, the Sum of All Possible Values of a Is
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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If the Sum From r = 1 to 30 of r²(³⁰Cᵣ)²/(³⁰Cᵣ₋₁) = α·2²⁹, Then the Value of α Is
A JEE Main 2025 binomial coefficient summation simplified by rewriting the ratio of consecutive coefficients, then splitting into two telescoping sums.
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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 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 I = ∫96x²cos²x/(1+eˣ)dx = π(απ²+β), Find (α+β)²
A JEE Main 2025 definite integral solved using the King’s property trick for limits symmetric about zero, avoiding a direct, messier computation.
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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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The Value of (sin 70°)(cot 10° cot 70° − 1) Is Equal To
A short JEE Main 2025 trigonometry problem solved by converting cotangents to cosines and sines, then applying the cos(A+B) identity.