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Saturday, 31 October

JEE Main · Maths · Application of Derivatives

Proving Inequalities

JEE Main asked Proving Inequalities once in the 108 shifts Lumi analysed, on 11 Apr 2023, Shift 1. It belongs to Monotonicity, in Application of Derivatives (Maths).

Updated 2026-10-24

Times asked
1
in 1 shift
Years
1 of 8
First asked
2023
the only year
Pattern
Occasional
asked once so far

Questions on this idea a shift, by year

2017–2026. Asked in 2023. Years differ in how many shifts Lumi analysed, so each year is scaled to one shift of 25 Maths questions.

00.050.10’170’200’210’220.07’230’240’250’26

Raw count: 2017: 0 in 1 shift · 2020: 0 in 12 shifts · 2021: 0 in 24 shifts · 2022: 0 in 24 shifts · 2023: 1 in 12 shifts · 2024: 0 in 18 shifts · 2025: 0 in 8 shifts · 2026: 0 in 9 shifts.

Shift by shift

Each square is one analysed shift, in date order. Open a filled one for that paper.

  • 20260 of 9
  • 20250 of 8
  • 20240 of 18
  • 20231 of 12
  • 20220 of 24
  • 20210 of 24
  • 20200 of 12
  • 20170 of 1

Asked in that shift More than once Not asked

How JEE Main framed it

Two statements is the usual form. Skill tested: multi-step.

  • Statement a/b on bounds of function from derivative inequality

Difficulty

Easy 0Medium 0Hard 1

The question was multiple choice.

Every question

The question

From the official JEE Main shift papers, newest first. Open one for the full question, the options and the official answer.

  1. 11 Apr 2023, Shift 1 · Q10Let f:[2,4]→Rf : [2, 4] \to \mathbb{R} be a differentiable function such that (xlog⁡ex)f′(x)+(log⁡ex)f(x)+f(x)≥1, x∈[2,4](x \log_e x) f'(x) + (\log_e x) f(x) + f(x) \ge 1,\ x \in [2, 4]…HardTwo statements

Shift: 11 Apr 2023, Shift 1.

Same topic

Other ideas in Monotonicity

Monotonicity has 12 ideas JEE Main has asked; 4 of them came up in more than one question.

Topic analysisChapter analysisStudy this chapterAll repeated ideas