JEE Main 2024 · MathsNumerical answerNumerical valueMediumMulti-step

JEE Main 9 April 2024, Shift 1, Maths Q27

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

Let the set of all positive values of

\lambda

, for which the point of local minimum of the function

(1+x(\lambda^2-x^2))

satisfies

\frac{x^2+x+2}{x^2+5x+6}<0

, be

(\alpha,\beta)

. Then

\alpha^2+\beta^2

is equal to ________.

Official answer

NTA final key.

Chapter: Application of Derivatives
Topic: Maxima and Minima
Idea tested: First Derivative Test

Same idea in other shifts

Asked 3× in all

25 Jul 2022, Shift 1 · Q7The curve $y(x)=ax^3+bx^2+cx+5$ touches the $x$ -axis at the point $\mathrm{P}(-2,0)$ and cuts the $y$ -axis at the point $\mathrm{Q}$ ,…MediumSingle correct
6 Sep 2020, Shift 2 · Q60The set of all real values of $\lambda$ for which the function $f(x)=(1-\cos^2 x)\cdot(\lambda+\sin x)$ ,…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 42 of the 174 JEE Main shifts held from 2017 to 2026.