JEE Main 2025 · MathsMultiple choiceSingle correctMediumMulti-step

JEE Main 2 April 2025, Shift 1, Maths Q8

Question 8 of 75 in this shift, Maths question 8 of 25, Section A.

If the function

f(x)=2x^3-9ax^2+12a^2x+1

, where

a>0

, attains its local maximum and local minimum values at p and q, respectively, such that

p^2=q

, then

f(3)

is equal to :

(1)37Official answer
(2)55
(3)10
(4)23

Official answer

Option 1

NTA final key.

Chapter: Application of Derivatives
Topic: Maxima and Minima
Idea tested: Finding Parameters from Given Extrema

Same idea in other shifts

Asked 3× in all

4 Apr 2025, Shift 2 · Q17Let $a>0$ . If the function $f(x)=6x^3-45ax^2+108a^2x+1$ attains its local maximum and minimum values at the points $x_1$ and $x_2$ …MediumSingle correct
3 Aug 2021, Shift 2 · Q71If the function $f : \mathbb{R} \to \mathbb{R}$ defined by $f(x) = \frac{x^3}{3} - (2a+3b)x^2 + 24abx + 5$ has a local maxima at $-4$ and…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 42 of the 174 JEE Main shifts held from 2017 to 2026.