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Saturday, 31 October

JEE Main 2024 · MathsMultiple choiceSingle correctMediumCalculation

JEE Main 6 April 2024, Shift 1, Maths Q14

Question 14 of 90 in this shift, Maths question 14 of 30, Section A.

Let y=y(x)y=y(x) be the solution of the differential equation (2xlog⁡ex)dydx+2y=3xlog⁡ex(2x\log_e x)\frac{dy}{dx}+2y=\frac{3}{x}\log_e x, x>0x>0 and y(e−1)=0y(e^{-1})=0. Then, y(e)y(e) is equal to
  1. (1)−2e-\frac{2}{e}
  2. (2)−3e-\frac{3}{e}Official answer
  3. (3)−32e-\frac{3}{2e}
  4. (4)−23e-\frac{2}{3e}

Official answer

Option 2

NTA final key.

Chapter
Differential Equations
Topic
Linear Differential Equations
Idea tested
Coefficient Normalization for Standard Form

Same idea in other shifts

Asked 3× in all
  1. 6 Apr 2026, Shift 1 · Q25Let y=y(x)y=y(x) be the solution of the differential equation…HardNumerical value
  2. 28 Jun 2022, Shift 1 · Q11Let y=y(x)y=y(x) be the solution of the differential equation x(1−x2)dydx+(3x2y−y−4x3)=0, x>1x(1-x^2)\frac{dy}{dx}+(3x^2y-y-4x^3)=0,\ x>1, with y(2)=−2y(2)=-2. Then y(3)y(3) is…HardSingle correct

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.