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JEE Advanced Differentiation and Application of Derivatives questions with solutions

Continuity, differentiability, differentiation techniques, tangents, maxima and minima and monotonicity. 23 questions from our 2016–2025 JEE Advanced pattern papers, from the Class 12 Mathematics syllabus. Each has the answer and a full solution.

Also practise: Differentiation and Application of Derivatives for JEE Main

JEE Advanced 2025

Let d be the least distance between a point of the ellipse (x^2/(4)+y^2=1 and a point of the line x+y=4. Find d.JEE Advanced 2025 Paper 1 · medium
Let g(x)=(ln x)/(x) for x>0.JEE Advanced 2025 Paper 2 · hard

JEE Advanced 2024

Let f:mathbb R→mathbb R be defined by f(x)=∫0^x t |t-1| dt.JEE Advanced 2024 Paper 1 · medium

JEE Advanced 2023

Let h(x)=(ln x)/(x) for x>0. Using properties of h, decide which of the following statements is/are correct.JEE Advanced 2023 Paper 1 · medium
Match each function in List-I with the number of real points at which it is not differentiable (List-II). For the function in (S), consider only the…JEE Advanced 2023 Paper 1 · medium
Find the number of real values of x satisfying 2^x=x^2+1.JEE Advanced 2023 Paper 2 · hard

JEE Advanced 2022

Let f:mathbb R→mathbb R be defined by f(x)=lfloor xrfloorsin (π x), where lfloor xrfloor is the greatest integer not exceeding x.JEE Advanced 2022 Paper 1 · hard

JEE Advanced 2021

Let f(x)=x^2sin 1/x for x≠0 and f(0)=0.JEE Advanced 2021 Paper 1 · medium
The number of real solutions of the equation e^x=2x^2 is ____.JEE Advanced 2021 Paper 1 · hard

JEE Advanced 2020

A point P moves on the parabola y^2=4x and a point Q moves on the circle x^2+y^2-12x+35=0. The least possible value of PQ is ____.JEE Advanced 2020 Paper 1 · medium

JEE Advanced 2019

Let f(x)=lfloor xrfloorsin (π x) for real x, where lfloor xrfloor is the greatest integer not exceeding x.JEE Advanced 2019 Paper 1 · medium
A right circular cone of maximum volume is inscribed in a sphere of radius 3. A right circular cylinder of maximum volume is then inscribed in this…JEE Advanced 2019 Paper 1 · medium
Paragraph 1: Let f(x)=x^3-6x^2+9x. List-II is the following list of numbers: (1) -3, (2) 2, (3) 3, (4) 4, (5) 27/4, (6) 6. In each of the two…JEE Advanced 2019 Paper 2 · 2-question set

JEE Advanced 2017

Define f(x)=∫0^x(t-1)(t-2) e^-t dt for x∈mathbbR.JEE Advanced 2017 Paper 1 · hard
Paragraph 2: Column 1 gives four functions through their derivatives, on the stated domains (with an initial value), Column 2 gives the abscissa of…JEE Advanced 2017 Paper 1 · 3-question set
Let pk(x)=x^3-12x+k, where k is a real constant, and let N(k) denote the number of distinct real roots of pk(x)=0.JEE Advanced 2017 Paper 2 · medium
Consider four real functions, each defined on the whole real line, and examine differentiability at the stated point. Which conclusions hold?JEE Advanced 2017 Paper 2 · medium

JEE Advanced 2016

Let f(x)=∫0^x (t-1)(t-3)(t-2)^2 dt.JEE Advanced 2016 Paper 1 · hard
Let f(x)=begincasesx^2sin 1/x,&x≠0\\[2mm]0,&x=0endcases, g(x)=f(x)+|x| and F(x)=∫0^xf(t) dt. ThenJEE Advanced 2016 Paper 2 · hard
Let varphi(x)=(ln x)/(x) for x>0.JEE Advanced 2016 Paper 2 · hard

Other Mathematics topics

Area Under Curves 13 Binomial Theorem 10 Complex Numbers 24 Conic Sections 34 Differential Equations 18 Indefinite and Definite Integrals 18 Limits 19 Matrices and Determinants 28 Permutations and Combinations 18 Probability 38 Quadratic Equations 12 Sequences and Series 11 Sets, Relations and Functions 8 Straight Lines and Circles 10 Three Dimensional Geometry 22 Trigonometry and Inverse Trigonometric Functions 18 Vector Algebra 9