JEE Main 2024 · MathsNumerical answerNumerical valueHardMulti-step

JEE Main 31 January 2024, Shift 2, Maths Q27

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

Let

y=y(x)

be the solution of the differential equation

\sec^2x\,dx+\left(e^{2y}\tan^2x+\tan x\right)dy=0

0<x<\frac{\pi}{2}

y\left(\frac{\pi}{4}\right)=0

. If

y\left(\frac{\pi}{6}\right)=\alpha

, then

e^{8\alpha}

is equal to ________.

Official answer

NTA final key.

Chapter: Differential Equations
Topic: Linear Differential Equations
Idea tested: Bernoulli Equation Reduction

Same idea in other shifts

Asked 4× in all

25 Feb 2021, Shift 2 · Q82If the curve, $y = y(x)$ represented by the solution of the differential equation $(2xy^2 - y)dx + x\,dy = 0$ , passes through the…HardNumerical value
26 Feb 2021, Shift 2 · Q65Let slope of the tangent line to a curve at any point $P(x, y)$ be given by $\frac{xy^2+y}{x}$ . If the curve intersects the line $x+2y=4$ …MediumSingle correct
18 Mar 2021, Shift 2 · Q69Let $y=y(x)$ be the solution of the differential equation $\frac{dy}{dx}=(y+1)\left((y+1)e^{x^2/2}-x\right)$ , $0<x<2.1$ , with $y(2)=0$ .…HardSingle 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.