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JEE Advanced Sets, Relations and Functions questions with solutions

Set operations, relations, functions and their types. 8 questions from our 2019–2025 JEE Advanced pattern papers, from the Class 11 Mathematics syllabus. Each has the answer and a full solution.

Also practise: Sets, Relations and Functions for JEE Main

JEE Advanced 2025

A function f:mathbb Rsetminus\0\→mathbb R satisfies f(x)+2f (1/x)=3x for all x≠0. Then ∫1^2 f(x) dx equalsJEE Advanced 2025 Paper 2 · medium

JEE Advanced 2024

Let f(x)=x^2-2 for real x. The number of real values of x for which f(f(f(x)))=x but f(x)≠ x is ______.JEE Advanced 2024 Paper 2 · hard

JEE Advanced 2023

A sequence is defined by a1=1 and an+1=an+1/an for n≥1. Find lfloor a100rfloor, where lfloor·rfloor denotes the greatest integer function.JEE Advanced 2023 Paper 1 · hard
Let f(x)=x^3+x+1 for real x and let g=f^-1 be its inverse function. The value of ∫1^3 g(y) dy isJEE Advanced 2023 Paper 2 · medium

JEE Advanced 2022

Let f(x)=∫0^xt(t-1)(t-2) dt for x∈mathbb R.JEE Advanced 2022 Paper 2 · medium

JEE Advanced 2020

Let f(x)=|x^2-1|+|x-2| for x∈mathbb R.JEE Advanced 2020 Paper 1 · medium
Let f(x)=∫0^x^2(t-1)(t-4) dt for real x.JEE Advanced 2020 Paper 2 · medium

JEE Advanced 2019

Let f:mathbb R→mathbb R be differentiable with f(x+y)=f(x)+f(y)+2xy for all real x,y, and f'(0)=-2. The area of the region bounded by the curve…JEE Advanced 2019 Paper 1 · medium

Other Mathematics topics

Area Under Curves 13 Binomial Theorem 10 Complex Numbers 24 Conic Sections 34 Differential Equations 18 Differentiation and Application of Derivatives 20 Indefinite and Definite Integrals 18 Limits 19 Matrices and Determinants 28 Permutations and Combinations 18 Probability 38 Quadratic Equations 12 Sequences and Series 11 Straight Lines and Circles 10 Three Dimensional Geometry 22 Trigonometry and Inverse Trigonometric Functions 18 Vector Algebra 9