Wheel Making 360 Revolutions per Minute — Radians Turned in 1 Second
A wheel makes 360 revolutions in one minute. Find how many radians it turns through in 1 second, converting revolutions per minute into radians per second.
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Find the Positive Square Root of 3+√5
Find the positive square root of 3+√5 by expressing it as √x+√y, splitting the equation into a rational and irrational part, and solving for x and y.
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Direction Cosines of the Line 5x−3=15y+7=3−10z
Find the direction cosines of 5x−3=15y+7=3−10z and a point through which it passes, by converting to symmetric form with equal-magnitude denominators.
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Aryan and Babban’s Monthly Incomes in Ratio 3:4, Solved Using Matrix Method
The monthly incomes of Aryan and Babban are in the ratio 3:4 and expenditures in the ratio 5:7. If each saves ₹15,000, find their incomes using the matrix method.
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Value of (sin 70°)(cot 10° cot 70° − 1)
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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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.