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) \geq 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) \leq 1, for all x \in[2,4] (B) : f(x) \geq \frac{1}{8}, for all x \in[2,4] Then, [11-Apr-2023 shift 1]

Correct Answer is : Both the statements (A) and (B) are true

Neither statement (A) nor statement (B) is true

Both the statements (A) and (B) are true

JEE Mains 11-Apr-2023 Shift 1 Solved Paper

Section: Mathematics

Question : 5 of 90

Marks: +1, -0

Let f:[2,4]→ℝ be a differentiable function such that (xlogex)f′(x)+(logex)f(x)+f(x)≥1,x∈[2,4] with f(2)=‌

and f(4)=‌

. Consider the following two statements :
(A) : f(x)≤1, for all x∈[2,4]
(B) : f(x)≥‌

, for all x∈[2,4]
Then,

[11-Apr-2023 shift 1]

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