JEE Main 2024 — Application of Derivatives Question with Solution
JEE Main 2024 (09 Apr Shift 1)
Question
Let the set of all positive values of , for which the point of local minimum of the function satisfies , be . Then is equal to _________
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Show full solutionCorrect answer: 39
Correct answer
39
Step-by-step explanation
$\begin{aligned} & x \in(-3,-2) \ldots \ldots \ldots . .(1) \\ & f(x)=1+x\left(\lambda^2-x^2\right) \end{aligned}$
Finding local minima Put $\begin{aligned} & \Rightarrow \lambda^2=3 x^2 \\ & \Rightarrow x= \pm \frac{\lambda}{\sqrt{3}} \end{aligned}$
We want local min
from (1)
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This is a previous-year question from JEE Main 2024, covering the Application of Derivatives chapter of Mathematics. PrepSharp catalogues every PYQ from JEE Main with a verified answer key and step-by-step solution prepared by IIT alumni — so you can search by chapter, topic or year and revise efficiently.