JEE Main · Maths · Continuity and Differentiability

Mean Value Theorem: JEE Main previous year questions

Name: Mean Value Theorem: JEE Main previous year questions
Creator: Lumi

7 questions in the 108 JEE Main shifts Lumi analysed, in 3 of 8 years. Pattern: Frequent. 1 came in 2024–26. Here is how it is asked and which ideas come back.

Questions: 7; in 6 of 108 shifts
Years asked: 3/8; last asked 2026
Chance in a shift: 13%; calibrated model, how we compute it
Weighted estimate: 0.1; model; history: 0.1 a shift on average, typically 0.0–0.1

Key findings

01
Asked in 3 of 8 years with analysed shifts and in 6 of 108 shifts: 7 questions, #184 of 196 topics. The years that asked it were 3.0 apart on average.
02
100% of its questions since 2020 tested an idea no earlier year had asked; none repeated an idea from the year before.
03
The most repeated idea is Proving Inequalities via LMVT, asked 3 times in 3 shifts (2020), most often as “bounds on f from derivative inequalities”.
04
JEE Main has asked 5 of the 61 ideas in this topic; 51 have never been asked, directly or inside another question.
05
Mostly asked as single correct (100%); 0% need a numerical answer, 0% are easy and 43% hard.
06
The skill tested most is multi-step (43%), then conceptual (43%).

Questions a shift, year by year

Out of the 25 Maths questions in a shift. Years differ in how many shifts Lumi analysed, so each year is scaled to one shift.

Raw count: 2017: 0 in 1 shift · 2020: 5 in 12 shifts · 2021: 1 in 24 shifts · 2022: 0 in 24 shifts · 2023: 0 in 12 shifts · 2024: 0 in 18 shifts · 2025: 0 in 8 shifts · 2026: 1 in 9 shifts.

Up to 2023: 0.1; a shift, of 25
Since 2024: 0.0; 0.0
Usual gap: 3.0 yrs; between years asking it
Shifts with it: 6/108; 6% of analysed shifts

How it is asked

Difficulty, format and skill

Across all 7 questions on Mean Value Theorem since 2017.

Difficulty

QUESTIONS

Easy0 · 0%
Medium4 · 57%
Hard3 · 43%

Format

Single correct · 7 Q100%

Skill tested

Multi-step · 3 Q43%
Conceptual · 3 Q43%
Application · 1 Q14%

Repeats

New idea, or one asked before?

Each column is a year. Blue questions tested an idea no earlier year had asked; navy ones went back to an idea from an earlier year. 2017 is the first year, so everything in it counts as new. Heights are question counts, and Lumi analysed 1 to 24 shifts a year, so compare the split inside a column rather than heights across years.

’17’20’21’22’23’24’25’26

Idea asked for the first time
Idea asked in an earlier year

Coverage of the topic

JEE Main has asked 5 of the 61 ideas in this topic. 51 have never been asked yet.

Asked directly5 · 8%
Touched inside another question5 · 8%
Never asked51 · 84%

Ideas come from Lumi’s JEE syllabus map. A never-asked idea is not a safe skip: across all of JEE Main, 22% of questions since 2024 tested an idea no earlier year had asked.

Drill down

Chapter, idea, question

Every idea JEE Main tested in this topic, with its eight years. Open one to read the questions.

chapterAskedShareYears’17’20’21’22’23’24’25’26

Open4 · 57%57%2/83
3 ideas inside
- Open2 · 50%50%1/82
- Open1 · 25%25%1/8
- Open1 · 25%25%1/8
Open3 · 43%43%2/82

Squares are the 8 years with analysed shifts, 2017 to 2026. A number is the questions that year when there is more than one; the shade is scaled to one shift, so a year with more analysed shifts (1 to 24 a year) does not look darker. Share is of the level above.

Ideas

Every idea inside this topic

5 different ideas were tested; 1 came more than once.

Proving Inequalities via LMVT3×
bounds on f from derivative inequalities
Single correct · 3 shifts
Zero Derivative Implies Constant Function1×
difference of functions with equal second derivatives
Single correct · 1 shift
Proving Lipschitz Condition via LMVT1×
bound on f(b) from bounded derivative
Single correct · 1 shift
Finding the Mean Value Point1×
point c from tangent parallel to chord
Single correct · 1 shift
Rolle's Theorem for Second Derivative1×
existence of point where second derivative vanishes
Single correct · 1 shift

Idea	Times	Shifts	Format	Numerical
Proving Inequalities via LMVTbounds on f from derivative inequalities	3	3	Single correctConceptual	–
Zero Derivative Implies Constant Functiondifference of functions with equal second derivatives	1	1	Single correctMulti-step	–
Proving Lipschitz Condition via LMVTbound on f(b) from bounded derivative	1	1	Single correctApplication	–
Finding the Mean Value Pointpoint c from tangent parallel to chord	1	1	Single correctMulti-step	–
Rolle's Theorem for Second Derivativeexistence of point where second derivative vanishes	1	1	Single correctConceptual	–

Times and shifts count every analysed shift. Across JEE Main, 78% of questions since 2024 went back to an idea an earlier year had asked; the rest were new. All repeated ideas

Every question

Mean Value Theorem questions, year by year

The opening words of each question as it appeared in the official paper, with the idea it tested. Open one for its options and the official answer.

Questions from the official JEE Main Paper 1 shifts published by NTA (CBSE for 2017). Questions NTA dropped are left out. Topic and idea tags, counts and notes are Lumi’s.