JEE Main 2023 · MathsMultiple choiceSingle correctHardMulti-step

JEE Main 15 April 2023, Shift 1, Maths Q11

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

Let

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

x\left(e^4-2\right)=1

. Then

x\left(e^9-2\right)

is equal to

(1) $3$
(2) $\frac{10}{3}$
(3) $\frac{4}{9}$
(4) $\frac{32}{9}$ Official answer

Official answer

Option 4

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
8 Apr 2023, Shift 2 · Q28Let the solution curve $x = x(y)$ , $0 < y < \frac{\pi}{2}$ , of the differential equation…HardNumerical value
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.