JEE Main 2023 · MathsMultiple choiceSingle correctEasyConceptual

JEE Main 13 April 2023, Shift 1, Maths Q14

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

Let

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

and

y_2(0)=1

respectively. Then the curves

y=y_1(x)

and

y=y_2(x)

intersect at

(1)no pointOfficial answer
(2)one point
(3)two points
(4)infinite number of points

Official answer

Option 1

NTA final key.

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

Same idea in other shifts

Asked 15× in all

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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
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27 Jan 2024, Shift 1 · Q13Let $x=x(t)$ and $y=y(t)$ be solutions of the differential equations $\dfrac{dx}{dt}+ax=0$ and $\dfrac{dy}{dt}+by=0$ respectively,…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
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.