JEE Main 2021 · MathsMultiple choiceSingle correctMediumMulti-step

JEE Main 3 August 2021, Shift 2, Maths Q71

Question 71 of 90 in this shift, Maths question 11 of 30, Section A.

If 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 a local minima at 4, then a value of

4a + 3b

(1) $\frac{1}{2}$
(2) $2$ Official answer
(3) $0$
(4) $1$

Official answer

Option 2

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
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

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.