If $\log_e y=3\sin^{-1}x$, then $(1-x^2)y''-xy'$ at $x=\frac{1}{2}$ is equal to

JEE Main 2024 · MathsMultiple choiceSingle correctMediumMulti-step

JEE Main 9 April 2024, Shift 2, Maths Q8

Question 8 of 90 in this shift, Maths question 8 of 30, Section A.

\log_e y=3\sin^{-1}x

, then

(1-x^2)y''-xy'

x=\frac{1}{2}

is equal to

(1) $9e^{\pi/2}$ Official answer
(2) $9e^{\pi/6}$
(3) $3e^{\pi/2}$
(4) $3e^{\pi/6}$

Official answer

Option 1

NTA final key.

Chapter: Continuity and Differentiability
Topic: Chain Rule
Idea tested: Second Order Implicit Chain Rule

Same idea in other shifts

Asked 5× in all

27 Jun 2022, Shift 1 · Q8If $\cos^{-1}\left(\frac{y}{2}\right) = \log_e\left(\frac{x}{5}\right)^5$ , $|y|<2$ , then :MediumSingle correct
26 Aug 2021, Shift 1 · Q86If $y=y(x)$ is an implicit function of $x$ such that $\log_e(x+y)=4xy$ , then $\frac{d^2y}{dx^2}$ at $x=0$ is equal to __________.MediumNumerical value
27 Aug 2021, Shift 1 · Q84If $y^{1/4}+y^{-1/4}=2x$ , and $(x^2-1)\frac{d^2y}{dx^2}+\alpha x\frac{dy}{dx}+\beta y=0$ , then $|\alpha-\beta|$ is equal to __________.HardNumerical value
3 Sep 2020, Shift 1 · Q57If $y^2+\log_e(\cos^2x)=y$ , $x\in\left(-\frac{\pi}{2},\frac{\pi}{2}\right)$ , 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.