JEE Mathematics
Differentiability: JEE Questions & Solutions
12 previous-year JEE Mathematics questions on Differentiability, each with a worked step-by-step solution.
Previous-year questions
- 01Let α,β∈ℝ be such that the function f(x)= 2α(x²-2)+2β x, x<1 (α+3)x+(α-β), x≥1 is differentiable at all x∈ℝ. Then 34(α+β) is equal toMCQMediumJEE 2026
- 02Let the function, f(x) = -3ax² - 2, x < 1 a² + bx, x ≥ 1 Be differentiable for all x ∈ ℝ, where a > 1, b ∈ ℝ. If the area of the region…NVAMediumJEE 2025
- 03Let [x] denote the greatest integer function, and let m and n respectively be the numbers of the points, where the function f(x) = [x] + |x…MCQMediumJEE 2025
- 04Let the function f(x) = (x² - 1)|x² - ax + 2| + cos|x| be not differentiable at the two points x = α = 2 and x = β. Then the distance of…MCQMediumJEE 2025
- 05Let m and n be the number of points at which the function f(x) = max { x, x³, x⁵, …, x²¹ } is not differentiable and not continuous,…NVAMediumJEE 2025
- 06Consider the function f: (0,2) → R defined by f(x) = x/2 + 2/x, and the function g(x) by min{f(t)} for 0 < t ≤ x, 0 < x ≤ 1 and g(x) = 3/2…MCQMediumJEE 2024
- 07Let g: ℝ → ℝ be a non-constant twice differentiable function such that g'(1/2) = g'(3/2). If a real-valued function f is defined as f(x) =…MCQMediumJEE 2024
- 08If the function f(x) = 1/|x|, |x| ≥ 2 ax² + 2b, |x| < 2 is differentiable on ℝ, then 48(a + b) is equal to:NVAMediumJEE 2024
- 09Let a and b be real constants such that the function f defined by f(x)= x²+3x+a, x≤ 1 bx+2, x>1 is differentiable on ℝ. Then, the value of…MCQMediumJEE 2024
- 10Let f(x) = |2x² + 5|x| - 3|, x ∈ ℝ. If m and n denote the number of points where f is not continuous and not differentiable respectively,…MCQMediumJEE 2024
- 11Let a ∈ Z and [t] be the greatest integer ≤ t. Then the number of points, where the function f(x) = [a + 13sin x], x ∈ (0,π) is not…NVAMediumJEE 2023
- 12Let f(x) be defined as: f(x) = x⌊ x⌋, -2 < x < 0, and f(x) = (x - 1)⌊ x⌋, 0 ≤ x < 2. If m and n are the number of points in (-2, 2) where y…NVAMediumJEE 2023
Frequently asked questions
Our bank has 12 previous-year JEE Mathematics questions tagged to Differentiability, drawn from JEE papers between 2023 and 2026, including 1 from 2026 alone. Each comes with a full step-by-step solution.
Differentiability is rated Advanced overall for JEE Mathematics. The PYQs on this page break down as 12 medium.
Of the 12 previous-year questions on Differentiability, 7 are multiple-choice (MCQ) and 5 are numerical-value (NVA) questions.
Based on recent paper analysis, Differentiability is worth about 1 mark in JEE Main. It sits in Limits, Continuity & Differentiability, a Class 12 Mathematics chapter.
More Limits, Continuity & Differentiability topics
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