Applications of Derivatives JEE Main PYQs PDF, 2020–2026

Applications of Derivatives has 156 questions in JEE Main papers from 2020 to 2026, about 22 per year across all shifts. The free PDF has 153 of them, each with its answer. The most asked topic is Maxima and Minima (68 questions), followed by Increasing and Decreasing Functions (25) and Tangents and Normals (21).

Asked in JEE Main: 1562020–2026, all shifts
In this free PDF: 153with answers
Asked in 2026: 9Latest paper: 2026 Apr S1
Most asked topic: Maxima and Minima68 Qs · 44% of the chapter
Difficulty mix: 3% easy · 84% medium · 13% hardof the questions in the PDF

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Source: official NTA JEE Main papers · Updated 25 Oct 2026

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5 of this chapter's questions came back in a later paper (2021–2026). See the most repeated.

How often it's asked in JEE Main

Applications of Derivatives had about 0.8 questions per shift in recent JEE Main papers (2024–26). Its share has fallen since 2020–22. Most asked topic: Maxima and Minima. About 9 questions in the 2026 papers. (Some topics were cut in 2024; see what changed.)

It came up in most 2024–26 shifts in our bank (about 38 shifts). Question types in 2020–2026: about 120 MCQs and about 36 numerical.

How many questions from Applications of Derivatives in JEE Main, year by year

Year	Questions	Per shift	MCQ	Numerical
2026	9	0.5	7	2
2025	14	0.7	12	2
2024	23	1.2	17	6
2023	16	0.7	11	5
2022	36	1.6	29	7
2021	31	1.2	20	11
2020	27	1.7	24	3
2020–2026	156	1.1	120	36

Most asked Applications of Derivatives topics, 2020–2026

Topic	Questions
Maxima and Minima	68
Increasing and Decreasing Functions	25
Tangents and Normals	21
Optimization Problems	20
Rolle's and Mean Value Theorems	16

Every topic, year by year, is in the topic-wise table further down.

Counted from PrepWiser's question bank of JEE Main papers, 2020–2026. Per shift = questions that year ÷ shifts in our bank. Updated 25 Oct 2026.

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Two free sheets, made from the past JEE Main questions on this chapter.

Revision notes11 pages, 22 ideas with the usual mistakes.Open the revision notes Formula sheet2 pages, all 24 formulas.Open the formula sheet

Applications of Derivatives questions per year

Year	Asked	In PDF
2026	9	9
2025	14	14
2024	23	23
2023	16	16
2022	36	33
2021	31	31
2020	27	27

in the free PDF asked, not in the PDFThe PDF only has questions we can print in full with a checked answer, so it holds 153 of the 156 asked.

Topic-wise weightage by year

How many Applications of Derivatives questions each topic had in every JEE Main year (all shifts), counting every question asked, including ones not in the PDF. Darker cells mean more questions.

Topic	Asked	Share	2026	2025	2024	2023	2022	2021	2020
Maxima and Minima	68	44%	8	9	14	6	14	10	7
Increasing and Decreasing Functions	25	16%	1	2	6	1	6	7	2
Tangents and Normals	21	13%	·	·	·	5	5	4	7
Optimization Problems	20	13%	·	2	2	3	6	6	1
Rolle's and Mean Value Theorems	16	10%	·	·	1	1	2	4	8
Rate of Change	6	4%	·	1	·	·	3	·	2
All topics	156	100%	9	14	23	16	36	31	27

Swipe the table sideways for older years.

Newest questions (2026)

All 9 JEE Main 2026 Applications of Derivatives questions in the free PDF, latest shift first.

JEE Main 2026 · 5 Apr · Shift 1 · Maxima and Minima

Let $f:{\mathbb{R}}\rightarrow {\mathbb{R}}$ be a differentiable function such that $f\left(\frac{x+y}{3}\right)=\frac{f(x)+f(y)}{3}$ for all $x,y\in {\mathbb{R}}$ , and $f^{{'}}(0)=3$ . Then the minimum value of the function $g(x)=3+e^{x}f(x)$ , is:

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JEE Main 2026 · 4 Apr · Shift 2 · Maxima and Minima

$\max\limits_{0\le x\le \pi}\left(16\sin\left(\frac{x}{2}\right)\cos^{3}\left(\frac{x}{2}\right)\right)$ is equal to:
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JEE Main 2026 · 2 Apr · Shift 1 · Maxima and Minima

The number of critical points of the function

$f(x)=\left\{\begin{array}{cc}|\frac{\sin x}{x}|, & x\neq 0 \\ 1, & x=0\end{array}\right.$ in the interval $(-2\pi,2\pi)$ is equal to :
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JEE Main 2026 · 2 Apr · Shift 2 · Maxima and Minima

Let $f(x)$ be a polynomial of degree 5, and have extrema at $x=1$ and $x=-1$ . If $\underset{{x\rightarrow 0}}{lim}\left(\frac{f(x)}{x^{3}}\right)=-5$ , then $f(2)-f(-2)$ is equal to:
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JEE Main 2026 · 24 Jan · Shift 1 · Maxima and Minima

Let $(2\alpha,\alpha)$ be the largest interval in which the function $f(t)=\frac{|t+1|}{t^{2}},t<0$ , is strictly decreasing. Then the local maximum value of the function $g(x)=2\log_{{{\mathrm{e}}}}(x-2)+\alpha x^{2}+4x-\alpha,x>2$ , is $\_\_\_\_$
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JEE Main 2026 · 24 Jan · Shift 2 · Maxima and Minima

Consider the following three statements for the function $f:(0,\infty)\rightarrow {\mathbb{R}}$ defined by $f(x)=|\log_{e}x|-|x-1|$ :

(I) $f$ is differentiable at all $x>0$ .

(II) $f$ is increasing in $(0,1)$ .

(III) $f$ is decreasing in $(1,\infty)$ .

Then.
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JEE Main 2026 · 22 Jan · Shift 1 · Maxima and Minima

Let $f(x)=x^{{2025}}-x^{{2000}},x\in [0,1]$ and the minimum value of the function $f(x)$ in the interval $[0,1]$ be $(80)^{{80}}(n)^{{-81}}$ . Then $n$ is equal to

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JEE Main 2026 · 21 Jan · Shift 1 · Maxima and Minima

Let $f:{\mathbf{R}}\rightarrow {\mathbf{R}}$ be a twice differentiable function such that the quadratic equation $f(x){\mathrm{m}}^{2}-2f^{{'}}(x){\mathrm{m}}+f^{{''}}(x)=0$ in m , has two equal roots for every $x\in {\mathbf{R}}$ . If $f(0)=1,f^{{'}}(0)=2$ , and ( $\alpha,\beta$ ) is the largest interval in which the function $f(\log_{{{\mathrm{e}}}}x-x)$ is increasing, then $\alpha+\beta$ is equal to

$\_\_\_\_$ .
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JEE Main 2026 · 21 Jan · Shift 2 · Increasing and Decreasing Functions

Let $f:{\mathbb{R}}\rightarrow {\mathbb{R}}$ be a twice differentiable function such that $f''(x)>0$ for all $x\in {\mathbb{R}}$ and $f'(a-1)=0$ , where $a$ is a real number.

Let $g(x)=f(\tan^{2}x-2\tan x+a),\ 0<x<\frac{\pi}{2}$ .

Consider the following two statements:

(I) g is increasing in $\left(0,\frac{\pi}{4}\right)$

(II) g is decreasing in $\left(\frac{\pi}{4},\frac{\pi}{2}\right)$

Then,
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Sample questions from recent papers

JEE Main 2025 · 8 Apr · Shift 2 · Increasing and Decreasing Functions

Let the function $f(x) = \frac{x}{3} + \frac{3}{x} + 3, x \neq 0$ be strictly increasing in $(-\infty, \alpha_1) \cup (\alpha_2, \infty)$ and strictly decreasing in $(\alpha_3, \alpha_4) \cup (\alpha_4, \alpha_5)$ . Then $\sum\limits_{i=1}^{5} \alpha_i^2$ is equal to

(A)
48
(B)
40
(C)
36
(D)
28

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Answer: (C)

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JEE Main 2025 · 3 Apr · Shift 2 · Optimization Problems

Let

C

be the circle of minimum area enclosing the ellipse

E: \frac{x^2}{a^2}+\frac{y^2}{b^2}=1

with eccentricity

\frac{1}{2}

and foci

( \pm 2,0)

. Let

P Q R

be a variable triangle, whose vertex

P

is on the circle

C

and the side

Q R

of length

2 a

is parallel to the major axis of

E

and contains the point of intersection of

E

with the negative

y

-axis. Then the maximum area of the triangle

P Q R

is :

(A) $8(3+\sqrt{2})$
(B) $8(2+\sqrt{3})$
(C) $6(3+\sqrt{2})$
(D) $6(2+\sqrt{3})$

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Answer: (B)

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JEE Main 2025 · 23 Jan · Shift 2 · Rate of Change

A spherical chocolate ball has a layer of ice-cream of uniform thickness around it. When the thickness of the ice-cream layer is 1 cm , the ice-cream melts at the rate of $81 \mathrm{~cm}^3 / \mathrm{min}$ and the thickness of the ice-cream layer decreases at the rate of $\frac{1}{4 \pi} \mathrm{~cm} / \mathrm{min}$ . The surface area (in $\mathrm{cm}^2$ ) of the chocolate ball (without the ice-cream layer) is :

(A) $128 \pi$
(B) $196 \pi$
(C) $225 \pi$
(D) $256 \pi$

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Answer: (D)

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JEE Main 2024 · 4 Apr · Shift 2 · Rolle's and Mean Value Theorems

Let $f: \mathbb{R} \rightarrow \mathbb{R}$ be a thrice differentiable function such that $f(0)=0, f(1)=1, f(2)=-1, f(3)=2$ and $f(4)=-2$ . Then, the minimum number of zeros of $\left(3 f^{\prime} f^{\prime \prime}+f f^{\prime \prime \prime}\right)(x)$ is __________.

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Answer: 5

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JEE Main 2023 · 10 Apr · Shift 2 · Tangents and Normals

Let the quadratic curve passing through the point $(-1,0)$ and touching the line $y=x$ at $(1,1)$ be $y=f(x)$ . Then the $x$ -intercept of the normal to the curve at the point $(\alpha, \alpha+1)$ in the first quadrant is __________.

Show answer

Answer: 11

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Frequently asked

How many questions come from Applications of Derivatives in JEE Main?

156 questions from 2020 to 2026, about 22 per year. In 2026 it had 9. The free PDF has 153 of them.

Which Applications of Derivatives topics are most important for JEE Main?

By past papers: Maxima and Minima (44%), Increasing and Decreasing Functions (16%) and Tangents and Normals (13%) of all Applications of Derivatives questions.

Is the Applications of Derivatives PYQ PDF free?

Yes. The PDF and its answer key are free, and you can practise the questions online with no login, with step-by-step solutions where available.

Prefer to solve online? Practise Applications of Derivatives online with step-by-step solutions where available, or work through JEE Main papers shift by shift.

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JEE Main PYQs by year: 2026 · 2025 · 2024 · 2023 · 2022 · 2021 · 2020

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Applications of Derivatives JEE Main PYQs PDF, 2020–2026

How often it's asked in JEE Main

How many questions from Applications of Derivatives in JEE Main, year by year

Most asked Applications of Derivatives topics, 2020–2026

Revise Applications of Derivatives before you practise

Send this chapter to your study group

Applications of Derivatives questions per year

Topic-wise weightage by year

Newest questions (2026)

Sample questions from recent papers

Practise these online, free, no login

Frequently asked

How many questions come from Applications of Derivatives in JEE Main?

Which Applications of Derivatives topics are most important for JEE Main?

Is the Applications of Derivatives PYQ PDF free?

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