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

NTA final key.

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

Same idea in other shifts

Asked 6× in all

1 Feb 2024, Shift 2 · Q27If $\frac{dx}{dy}=\frac{1+x-y^2}{y}$ , $x(1)=1$ , then $5x(2)$ is equal to ________.MediumNumerical value
15 Apr 2023, Shift 1 · Q11Let $x=x(y)$ be the solution of the differential equation $2(y+2)\log_e(y+2)dx+\left(x+4-2\log_e(y+2)\right)dy=0$ , $y>-1$ with…HardSingle correct
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
27 Aug 2021, Shift 2 · Q73If the solution curve of the differential equation $(2x - 10y^3)dy + y\,dx = 0$ , passes through the points $(0, 1)$ and $(2, \beta)$ , then…MediumSingle 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.