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Friday, 9 October

JEE Main 2025 · MathsMultiple choiceSingle correctHardMulti-step

JEE Main 3 April 2025, Shift 1, Maths Q20

Question 20 of 75 in this shift, Maths question 20 of 25, Section A.

Let gg be a differentiable function such that ∫0xg(t) dt=x−∫0xt g(t) dt\int_0^x g(t)\,dt = x - \int_0^x t\,g(t)\,dt, x≥0x \ge 0 and let y=y(x)y = y(x) satisfy the differential equation dydx−ytan⁡x=2(x+1)sec⁡x  g(x)\frac{dy}{dx} - y\tan x = 2(x+1)\sec x\; g(x), x∈[0,π2)x \in \left[0, \frac{\pi}{2}\right). If y(0)=0y(0) = 0, then y(π3)y\left(\frac{\pi}{3}\right) is equal to
  1. (1)4π3\frac{4\pi}{3}Official answer
  2. (2)2π3\frac{2\pi}{3}
  3. (3)2π33\frac{2\pi}{3\sqrt{3}}
  4. (4)4π33\frac{4\pi}{3\sqrt{3}}

Official answer

Option 1

NTA final key.

Chapter
Differential Equations
Topic
Linear Differential Equations
Idea tested
Integrating Factor Calculation

Same idea in other shifts

Asked 3× in all
  1. 4 Apr 2026, Shift 2 · Q19Let y=y(x)y=y(x) be the solution of the differential equation:…HardSingle correct
  2. 13 Apr 2023, Shift 2 · Q27If y=y(x)y=y(x) is the solution of the differential equation dydx+4x(x2−1)y=x+2(x2−1)52\frac{dy}{dx}+\frac{4x}{(x^2-1)}y=\frac{x+2}{(x^2-1)^{\frac{5}{2}}}, x>1x>1 such…HardNumerical value

Question text from the official JEE Main paper published by NTA; answer from the final answer key. Chapter, topic and idea tags, difficulty and skill are Lumi’s. Lumi analyses 42 of the 174 JEE Main shifts held from 2017 to 2026.