JEE Main 2023 · MathsMultiple choiceTwo statementsHardMulti-step

JEE Main 11 April 2023, Shift 1, Maths Q10

Question 10 of 90 in this shift, Maths question 10 of 30, Section A.

Let

f : [2, 4] \to \mathbb{R}

be a differentiable function such that

(x \log_e x) f'(x) + (\log_e x) f(x) + f(x) \ge 1,\ x \in [2, 4]

with

f(2) = \frac{1}{2}

and

f(4) = \frac{1}{4}

. Consider the following two statements : (A) :

f(x) \le 1

, for all

x \in [2, 4]

(B) :

f(x) \ge \frac{1}{8}

, for all

x \in [2, 4]

Then,

(1)Only statement (A) is true
(2)Only statement (B) is true
(3)Both the statements (A) and (B) are trueOfficial answer
(4)Neither statement (A) nor statement (B) is true

Official answer

Option 3

NTA final key.

Chapter: Application of Derivatives
Topic: Monotonicity
Idea tested: Proving Inequalities

Same topic in other shifts

All Monotonicity questions

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.