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Saturday, 31 October

JEE Main 2024 · MathsMultiple choiceSingle correctHardMulti-step

JEE Main 31 January 2024, Shift 1, Maths Q11

Question 11 of 90 in this shift, Maths question 11 of 30, Section A.

Let y=y(x)y=y(x) be the solution of the differential equation dydx=(tan⁡x)+ysin⁡x(sec⁡x−sin⁡xtan⁡x), x∈(0,π2)\frac{dy}{dx}=\frac{(\tan x)+y}{\sin x(\sec x-\sin x\tan x)},\ x\in\left(0,\frac{\pi}{2}\right) satisfying the condition y(π4)=2y\left(\frac{\pi}{4}\right)=2. Then, y(π3)y\left(\frac{\pi}{3}\right) is
  1. (1)3(2+log⁡e3)\sqrt{3}\left(2+\log_e3\right)
  2. (2)32(2+log⁡e3)\frac{\sqrt{3}}{2}\left(2+\log_e3\right)
  3. (3)3(2+log⁡e3)\sqrt{3}\left(2+\log_e\sqrt{3}\right)Official answer
  4. (4)3(1+2log⁡e3)\sqrt{3}\left(1+2\log_e3\right)

Official answer

Option 3

NTA final key.

Chapter
Differential Equations
Topic
Linear Differential Equations
Idea tested
Integrating Factors with Trigonometric Functions

Same idea in other shifts

Asked 7× in all
  1. 2 Apr 2026, Shift 1 · Q20Let y=y(x)y=y(x) be the solution curve of the differential equation (1+sin⁡x)dydx+(y+1)cos⁡x=0(1+\sin x)\frac{dy}{dx}+(y+1)\cos x=0, y(0)=0y(0)=0. If the curve y=y(x)y=y(x)…MediumSingle correct
  2. 2 Apr 2025, Shift 2 · Q25Let y=y(x)y = y(x) be the solution of the differential equation…MediumNumerical value
  3. 3 Apr 2025, Shift 2 · Q20Let y=y(x)y = y(x) be the solution of the differential equation…MediumSingle correct
  4. 29 Jan 2024, Shift 1 · Q13A function y=f(x)y=f(x) satisfies f(x)sin⁡2x+sin⁡x−(1+cos⁡2x)f′(x)=0f(x)\sin 2x+\sin x-(1+\cos^2x)f'(x)=0 with condition f(0)=0f(0)=0. Then, f(π2)f\left(\frac{\pi}{2}\right) is…MediumSingle correct
  5. 28 Jul 2022, Shift 1 · Q10If y=y(x), x∈(0,π/2)y=y(x),\ x\in(0,\pi/2) be the solution curve of the differential equation…HardSingle correct
  6. 27 Jun 2022, Shift 2 · Q28Let y=y(x)y=y(x) be the solution of the differential equation (1−x2)dy=(xy+(x3+2)1−x2)dx\left(1-x^2\right)dy=\left(xy+\left(x^3+2\right)\sqrt{1-x^2}\right)dx,…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 108 of the 174 JEE Main shifts held from 2017 to 2026.