JEE Advanced Relations and Functions (Class 12) — previous year questions

19 questions from 2026, 2025, 2020, 2018, 2015, 2014, 2013, 2012, 2011, 2010.

• Let S = {1, 2, 3, ..., 10}. Consider the set X = {R : R is an equivalence relation on the set S such that R…2026JEE Advanced
• Let N denote the set of all positive integers. Consider the sets A = {1, 2, 3, 4, 5} and B = {1, 2, 3, 4, 5,…2026JEE Advanced
• Let the set of all relations R on the set {a, b, c, d, e, f}, such that R is reflexive and symmetric, and R…2025JEE Advanced
• Let N denote the set of all natural numbers, and Z denote the set of all integers. Consider the functions…2025JEE Advanced
• Let R denote the set of all real numbers. Let f : R → R and g : R → (0,4) be functions defined by f(x) =…2025JEE Advanced
• If the function f : R → R is defined by f(x) = |x|(x - sin x), then which of the following statements is TRUE?2020JEE Advanced
• Let X be a set with exactly 5 elements and Y be a set with exactly 7 elements. If α is the number of one-one…2018JEE Advanced
• The value of ((log₂ 9)²)^(1/(log₂(log₂ 9))) × (√7)^(1/(log₄ 7)) is ________.2018JEE Advanced
• Let E₁ = { x ∈ R : x ≠ 1 and x/(x-1) > 0 } and E₂ = { x ∈ E₁ : sin⁻¹( logₑ( x/(x-1) ) ) is a real number }.…2018JEE Advanced
• Let f(x)=sin(π/6sin(π/2sin x)) for all x ∈ R and g(x)=π/2sin x for all x ∈ R. Let (fog)(x) denote f(g(x)) and…2015JEE Advanced
• Let a ∈ R and let f : R → R be given by f(x) = x⁵ - 5x + a. Then2014JEE Advanced
• Let f : [0, 4π] → [0, π] be defined by f(x) = cos⁻¹(cos x). The number of points x in [0, 4π] satisfying the…2014JEE Advanced
• Let f : (-π/2, π/2) → R be given by f(x) = (log(sec x + tan x))³. Then2014JEE Advanced
• The function f(x) = 2|x| + |x + 2| - ||x + 2| - 2|x|| has a local minimum or a local maximum at x=2013JEE Advanced
• The function f : [0, 3] → [1, 29], defined by f(x) = 2x³ - 15x² + 36x + 1, is2012JEE Advanced
• Let f: (-1, 1) → R be such that f(cos 4θ) = 2/(2 - sec² θ) for θ ∈ (0, π/4) ∪ (π/4, π/2). Then the value(s)…2012JEE Advanced
• Let f(x) = x² and g(x) = sin x for all x ∈ R. Then the set of all x satisfying (f ∘ g ∘ g ∘ f)(x) = (g ∘ g ∘…2011JEE Advanced
• Let f : (0, 1) → R be defined by f(x) = (b - x)/(1 - bx), where b is a constant such that 0 < b < 1. Then2011JEE Advanced
• Let f, g and h be real-valued functions defined on the interval [0, 1] by f(x) = e^(x²) + e^(-x²), g(x) = x…2010JEE Advanced

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