MyGoalPrep LogoMyGoalPrep.com

Jee Main 2025 — Hard JEE math MCQ

If for the solution curve \( y = f(x) \) of the differential equation \( \frac{dy}{dx} + (\tan x)y = \frac{2 + \sec x}{(1 + 2\sec x)^2} \), \( x \in \left(-\frac{\pi}{2}, \frac{\pi}{2}\right) \), then \( f\left(\frac{\pi}{4}\right) \) is equal to
  1. A. \( \frac{\sqrt{3} - 1}{10(4+\sqrt{3})} \)
  2. B. \( \frac{\sqrt{3} - 1}{2\sqrt{3} - 2} \)
  3. C. \( \frac{\sqrt{3} - 1}{10(4+\sqrt{3})} \)
  4. D. \( \frac{5 - \sqrt{3}}{14} \)

Solution

The correct option is **D**. (D. \( \frac{5 - \sqrt{3}}{14} \))

MATH

hard • PYQ Reworded
Question
Read carefully, then pick the best option.
If for the solution curve y=f(x) y = f(x) of the differential equation dydx+(tan⁡x)y=2+sec⁡x(1+2sec⁡x)2 \frac{dy}{dx} + (\tan x)y = \frac{2 + \sec x}{(1 + 2\sec x)^2} , x∈(−π2,π2) x \in \left(-\frac{\pi}{2}, \frac{\pi}{2}\right) , then f(π4) f\left(\frac{\pi}{4}\right) is equal to
AI hints
Ask for a nudge. Keep it specific.