JEE Main 2024 · MathsMultiple choiceSingle correctMediumMulti-step

JEE Main 27 January 2024, Shift 1, Maths Q13

Question 13 of 90 in this shift, Maths question 13 of 30, Section A.

Let

x=x(t)

and

y=y(t)

be solutions of the differential equations

\dfrac{dx}{dt}+ax=0

and

\dfrac{dy}{dt}+by=0

respectively,

a, b\in\mathbf{R}

. Given that

x(0)=2

;

y(0)=1

and

3y(1)=2x(1)

, the value of t, for which

x(t)=y(t)

, is :

(1) $\log_{\frac{2}{3}}2$
(2) $\log_4 3$
(3) $\log_{\frac{4}{3}}2$ Official answer
(4) $\log_3 4$

Official answer

Option 3

NTA final key.

Chapter: Differential Equations
Topic: Variable Separable Form
Idea tested: Initial Value Problem

Same idea in other shifts

Asked 15× in all

4 Apr 2026, Shift 1 · Q20Let $y=y(x)$ be the solution of the differential equation $\frac{dy}{dx}=(1+x+x^2)(1-y+y^2)$ , $y(0)=\frac12$ . Then $(2y(1)-1)$ is equal toMediumSingle correct
8 Apr 2024, Shift 1 · Q13Let $y=y(x)$ be the solution of the differential equation $(1+y^2)e^{\tan x}dx+\cos^2x\,(1+e^{2\tan x})dy=0$ , $y(0)=1$ . Then…MediumSingle correct
9 Apr 2024, Shift 1 · Q11The solution curve, of the differential equation $2y\frac{dy}{dx}+3=5\frac{dy}{dx}$ , passing through the point $(0,1)$ is a conic, whose…MediumSingle correct
29 Jan 2024, Shift 1 · Q26If the solution curve $y=y(x)$ of the differential equation $(1+y^2)(1+\log_e x)dx+x\,dy=0$ , $x>0$ passes through the point $(1,1)$ and…MediumNumerical value
13 Apr 2023, Shift 1 · Q14Let $y=y_1(x)$ and $y=y_2(x)$ be the solution curves of the differential equation $\frac{dy}{dx}=y+7$ with initial conditions $y_1(0)=0$ …EasySingle correct
26 Jun 2022, Shift 1 · Q30Let $S = (0, 2\pi) - \left\{\frac{\pi}{2}, \frac{3\pi}{4}, \frac{3\pi}{2}, \frac{7\pi}{4}\right\}$ . Let $y = y(x)$ , $x \in S$ , be the…HardNumerical value
29 Jun 2022, Shift 2 · Q9If $y = y\,(x)$ is the solution of the differential equation $\left(1 + e^{2x}\right)\frac{dy}{dx} + 2\left(1 + y^2\right)e^x = 0$ and…MediumSingle correct
25 Jul 2021, Shift 2 · Q86Let a curve $y=f(x)$ pass through the point $(2,(\log_e 2)^2)$ and have slope $\frac{2y}{x\log_e x}$ for all positive real value of $x$ .…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 108 of the 174 JEE Main shifts held from 2017 to 2026.