JEE Main 2025 · MathsMultiple choiceSingle correctMediumMulti-step

JEE Main 4 April 2025, Shift 2, Maths Q17

Question 17 of 75 in this shift, Maths question 17 of 25, Section A.

Let

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

respectively such that

x_1x_2=54

, then

a+x_1+x_2

is equal to :

(1)13
(2)15
(3)18Official answer
(4)24

Official answer

Option 3

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

2 Apr 2025, Shift 1 · Q8If 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…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.