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Jee Main 2025 — Hard JEE math MCQ

Let \(y = y(x)\) be the solution of the differential equation \((xy - 5x^2 \sqrt{1 + x^2}) \, dx + (1 + x^2) \, dy = 0, y(0) = 0\). Then \(y(\sqrt{3})\) is equal to
  1. A. \(\sqrt{15} \div 2\)
  2. B. \(\frac{1}{2} \sqrt{\frac{3}{2}}\)
  3. C. \(2\sqrt{2}\)
  4. D. \(\sqrt{\frac{14}{3}}\)

Solution

The correct option is **B**. (B. \(\frac{1}{2} \sqrt{\frac{3}{2}}\))

MATH

hard • PYQ Reworded
Question
Read carefully, then pick the best option.
Let y=y(x)y = y(x) be the solution of the differential equation (xy−5x21+x2) dx+(1+x2) dy=0,y(0)=0(xy - 5x^2 \sqrt{1 + x^2}) \, dx + (1 + x^2) \, dy = 0, y(0) = 0. Then y(3)y(\sqrt{3}) is equal to
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Jee Main 2025 — Hard JEE Mathematics MCQ | MyGoalPrep