Application Of Derivatives — JEE Main Previous Year Questions

146 solved PYQs · 2016–2026 · Mathematics

Solved PYQs: 146
Years covered: 2016–2026
Avg / year: ~13
Subject: Mathematics

How many JEE Main questions come from Application Of Derivatives?

Application Of Derivatives has contributed 146 questions to Joint Entrance Examination (Main) papers between 2016 and 2026 — an average of about 13 questions a year. That count is measured from EByAi’s bank of 55,289 JEE Main questions, not estimated from a syllabus. Every one of the 146 questions carries a written, step-by-step solution, and each is tagged to Application Of Derivatives within Mathematics, so you can drill this chapter across every year at once instead of hunting through paper PDFs. Practising a chapter’s full PYQ history is the fastest way to learn the patterns examiners reuse.

Sample Application Of Derivatives questions from real JEE Main papers

These are 5 real questions from the bank — exactly as asked, with the answer one tap away. All 146 Application Of Derivatives questions (with full written solutions) are available in practice.

Question 1 · JEE Main 2022
Consider a cuboid of sides 2x, 4x and 5x and a closed hemisphere of radius r. If the sum of their surface areas is a constant k, then the ratio x : r, for which the sum of their volumes is maximum, is :
1. (A) $2 : 5$
2. (B) $19 : 45$
3. (C) $3 : 8$
4. (D) $19 : 15$
Show answerAnswer
$Answer: (B) 19 : 45$
Question 2 · JEE Main 2022
The surface area of a balloon of spherical shape being inflated, increases at a constant rate. If initially, the radius of balloon is 3 units and after 5 seconds, it becomes 7 units, then its radius after 9 seconds is :
1. (A) $9$
2. (B) $10$
3. (C) $11$
4. (D) $12$
Show answerAnswer
$Answer: (A) 9$
Question 3 · JEE Main 2020
If the point P on the curve, 4x 2 + 5y 2 = 20 is farthest from the point Q(0, -4), then PQ 2 is equal to:
1. (A) $36$
2. (B) $48$
3. (C) $21$
4. (D) $29$
Show answerAnswer
$Answer: (A) 36$
Question 4 · JEE Main 2020
If p(x) is a polynomial of degree three that has a local maximum value 8 at x = 1 and a local minimum value 4 at x = 2; then p(0) is equal to :
1. (A) $6$
2. (B) $12$
3. (C) $-12$
4. (D) $-24$
Show answerAnswer
$Answer: (C) -12$
Question 5 · JEE Main 2020
If the surface area of a cube is increasing at a rate of 3.6 cm^2/sec, retaining its shape; then the rate of change of its volume (in cm^3/sec), when the length of a side of the cube is 10 cm, is :
1. (A) $9$
2. (B) $10$
3. (C) $18$
4. (D) $20$
Show answerAnswer
$Answer: (A) 9$

Application Of Derivatives questions by year

Year	Questions	Share of chapter questions
2026	10
2025	14
2024	26
2023	13
2022	23
2021	24
2020	14
2019	14
2018	3
2017	2
2016	3

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FAQs

How many JEE Main questions have been asked from Application Of Derivatives?

EByAi's bank holds 146 real JEE Main questions from Application Of Derivatives, asked between 2016 and 2026 — about 13 per year on average. Every count is measured from actual papers, not estimated.

Is Application Of Derivatives important for JEE Main?

146 questions over 11 papers make Application Of Derivatives a moderate-weightage chapter in JEE Main Mathematics. The year-wise table above shows exactly how often it appears.

Can I solve Application Of Derivatives PYQs online for free?

Yes. EByAi lets you solve JEE Main past-year questions in the browser with written solutions — free daily practice, no card needed.

More JEE Main Mathematics chapters

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