JEE Main Maths · Continuity and Differentiability

Mean Value Theorem in JEE Main

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

Mean Value Theorem (Maths, Continuity and Differentiability) came 4 times in 3 of the 42 JEE Main shifts Lumi analysed, across 4 distinct ideas. 1 of them came in 2024–26; it was last asked in 2026.

Questions: 4; in 3 shifts
Ideas asked: 4; 0 asked more than once
Numerical answer: 0; 0% of its questions
Pattern: Frequent; last asked 2026

Questions each year

In the shifts Lumi analysed for each year.

Difficulty and format

Easy 0Medium 4Hard 0

Format

Single correct4 Q

Ideas inside the topic

4 ideas

Finding the Mean Value Point1 Q
Zero Derivative Implies Constant Function1 Q
Proving Lipschitz Condition via LMVT1 Q
Rolle's Theorem for Second Derivative1 Q

Where it sits

Part of Continuity and Differentiability, which had 48 questions in all. Mean Value Theorem accounts for 8% of them. In Lumi's JEE taxonomy it belongs to Calculus.

Some questions sit in other chapters too: Application of Derivatives.

Every question

All 4 Mean Value Theorem questions

Newest first, each with its options and official answer.

5 Apr 2026, Shift 2 · Q20Let $f(x)$ and $g(x)$ be twice differentiable functions satisfying $f''(x)=g''(x)$ for all $x \in \mathbf{R}$ , $f'(1)=2g'(1)=4$ and…MediumSingle correct
3 Aug 2021, Shift 2 · Q70Let $f : \mathbb{R} \to \mathbb{R}$ be a differentiable function such that $f(0) = 2$ . If $\left|\frac{df}{dx}\right| \le 3$ , for all…MediumSingle correct
6 Sep 2020, Shift 2 · Q57For all twice differentiable functions $f:\mathbf{R}\to\mathbf{R}$ , with $f(0)=f(1)=f'(0)=0$ ,MediumSingle correct
6 Sep 2020, Shift 2 · Q59If the tangent to the curve, $y=f(x)=x\log_e x$ , $(x>0)$ at a point $(c, f(c))$ is parallel to the line - segment joining the points…MediumSingle correct