JEE Main 2023 · MathsNumerical answerNumerical valueHardMulti-step

JEE Main 10 April 2023, Shift 2, Maths Q27

Question 27 of 90 in this shift, Maths question 27 of 30, Section B.

Let the tangent at any point P on a curve passing through the points

(1, 1)

and

\left(\frac{1}{10}, 100\right)

, intersect positive

x

- axis and

y

-axis at the points A and B respectively. If

PA : PB = 1 : k

and

y = y(x)

is the solution of the differential equation

e^{\frac{dy}{dx}} = kx + \frac{k}{2},\ y(0) = k

, then

4y(1) - 5\log_e 3

is equal to ________.

Official answer

NTA final key.

Chapter: Differential Equations
Topic: Variable Separable Form
Idea tested: Substitution of Ratio (u = y/x)

Same topic in other shifts

All Variable Separable Form questions

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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

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.