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Saturday, 31 October

JEE Main · Maths · Continuity and Differentiability

Proving Inequalities via LMVT

JEE Main asked Proving Inequalities via LMVT 3 times in 3 of the 108 shifts Lumi analysed, all in 2020. It belongs to Mean Value Theorem, in Continuity and Differentiability (Maths). In 2020 it came in more than one shift of the same year.

Updated 2026-10-24

Times asked
3
in 3 shifts
Years
1 of 8
First asked
2020
the only year
Pattern
Gone quiet
across the analysed shifts

Questions on this idea a shift, by year

2017–2026. Asked in 2020. Years differ in how many shifts Lumi analysed, so each year is scaled to one shift of 25 Maths questions.

00.150.30’170.25’200’210’220’230’240’250’26

Raw count: 2017: 0 in 1 shift · 2020: 3 in 12 shifts · 2021: 0 in 24 shifts · 2022: 0 in 24 shifts · 2023: 0 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
  • 20230 of 12
  • 20220 of 24
  • 20210 of 24
  • 20203 of 12
  • 20170 of 1

Asked in that shift More than once Not asked

How JEE Main framed it

Single correct is the usual form. Skill tested: conceptual.

  • Bounds on f from derivative inequalities
  • Inequality from concavity and monotonic derivative

Difficulty

Easy 0Medium 0Hard 3

Every question was multiple choice.

Every question

All 3 questions

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

  1. 4 Sep 2020, Shift 1 · Q58Let ff be a twice differentiable function on (1,6)(1, 6). If f(2)=8f(2) = 8, f′(2)=5f'(2) = 5, f′(x)≥1f'(x) \ge 1 and f′′(x)≥4f''(x) \ge 4, for all…HardSingle correct
  2. 9 Jan 2020, Shift 1 · Q60Let ff be any function continuous on [a, b] and twice differentiable on (a, b). If for all x∈(a,b)x\in(\mathrm{a, b}), f′(x)>0f'(x)>0 and…HardSingle correct
  3. 8 Jan 2020, Shift 2 · Q59Let S be the set of all functions f:[0,1]→Rf : [0, 1] \to \mathbf{R}, which are continuous on [0,1][0, 1] and differentiable on (0,1)(0, 1). Then for…HardSingle correct

Shifts: 8 Jan 2020, Shift 2, 9 Jan 2020, Shift 1, 4 Sep 2020, Shift 1.

Same topic

Other ideas in Mean Value Theorem

Mean Value Theorem has 5 ideas JEE Main has asked; 1 of them came up in more than one question.

Topic analysisChapter analysisStudy this chapterAll repeated ideas