/

Learn

Friday, 9 October

/

JEE Main 2023 · MathsNumerical answerNumerical valueHardMulti-step

JEE Main 8 April 2023, Shift 2, Maths Q28

Question 28 of 90 in this shift, Maths question 28 of 30, Section B.

Let the solution curve

x = x(y)

,

0 < y < \frac{\pi}{2}

, of the differential equation

(\log_e(\cos y))^2 \cos y\,dx - (1 + 3x\log_e(\cos y))\sin y\,dy = 0

satisfy

x\left(\frac{\pi}{3}\right) = \frac{1}{2\log_e 2}

. If

x\left(\frac{\pi}{6}\right) = \frac{1}{\log_e m - \log_e n}

, where

m

and

n

are coprime, then

mn

is equal to

Official answer

12

NTA final key.

Chapter: Differential Equations
Topic: Linear Differential Equations
Idea tested: Linear in x Form

Same idea in other shifts

Asked 3× in all

24 Jun 2022, Shift 1 · Q14If $x=x(y)$ is the solution of the differential equation $y\frac{dx}{dy}=2x+y^3(y+1)e^y,\ x(1)=0$ ; then $x(e)$ is equal to :MediumSingle correct
3 Aug 2021, Shift 2 · Q87If the solution $y = y(x)$ of the differential equation $\left(y + 3x^4\right)\frac{dx}{dy} = x,\ x > 0$ , satisfies $y(1) = -1$ , then the…MediumNumerical 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.