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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Let A=[0 -2,2 0], M=ΣA²ᵏ, N=ΣA²ᵏ⁻¹ (k=1 to 10): Find MN²
Find MN² for a 2×2 matrix A where M and N are sums of its even and odd powers. Solved by spotting that A² is a scalar multiple of the identity.
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Let A, B=A−I, ω=(√3i−1)/2: Count n With Aⁿ+(ωB)ⁿ=A+B
Given A^n + (ωB)^n = A + B for ω a complex cube root of unity, how many n in 1..100 satisfy it? JEE Main 2022 matrix and complex numbers problem.
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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.
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If sin²10°sin20°sin40°sin50°sin70°=α−1/16sin10°, Find 16+1/α
A five-term trigonometric product from JEE Main 2022, reduced step by step using complementary angles and the sin a cos a identity.
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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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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.