Limits and Differentiability JEE Advanced PYQ Chapter Wise

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Answer first

Limits, Continuity and Differentiability PYQs (previous year questions) for JEE Advanced: Limits, Continuity and Differentiability (Mathematics) had 55 questions across the 22 official JEE Advanced papers we tagged (2016–2026), and appeared in 22 of them. Asked in 11 of 11 years. The concepts asked in the most papers: Limits, Maxima and Minima, Monotonicity.

Year-wise question count

Asked in 11 of 11 years, with 2 papers each year.

Most-asked concepts

Sorted by the number of papers a concept appeared in.

How to practise Limits, Continuity and Differentiability PYQs

1. Start with the concepts at the top of the table. They have come back the most.
2. Solve one year’s Limits, Continuity and Differentiability questions from the official PDF against the clock, then check the answer listed below.
3. Log every miss as a concept gap, a calculation slip or a misread. Each needs a different fix.
4. Once a concept is clean in two papers, move to the next. Then sit a full paper from the year pages.

Questions by year

Each line gives the question number and paper, type, concept, our one-line summary and the official answer, with a link to the official PDF.

JEE Advanced2026

• Q.1 (Paper 1) · MCQ · Maxima and Minima: Monotonicity and extrema of a function with root x times log x (official answer: D) PDF
• Q.7 (Paper 1) · MSQ · Differentiability: Continuity and differentiability of x f(x) at zero (official answer: B, D) PDF
• Q.10 (Paper 1) · Numerical · Continuity: Points of discontinuity and non-differentiability with greatest integer (official answer: 5) PDF
• Q.14 (Paper 2) · Numerical · Continuity: Count discontinuities of functions with greatest integer parts (official answer: 56) PDF

JEE Advanced2025

• Q.3 (Paper 1) · MCQ · Monotonicity: Differentiability, monotonicity and extrema of a piecewise function with sin(1/x) (official answer: C) PDF
• Q.11 (Paper 1) · Numerical · Limits: Find constants from a limit involving an integral and x cos x (official answer: 2.35–2.45) PDF
• Q.15 (Paper 1) · Matching · Monotonicity: Match n values for continuity, increasing nature and extrema conditions (official answer: B) PDF
• Q.1 (Paper 2) · MCQ · Limits: Limit of a ratio near the root of e^x + x = 0 for given alpha (official answer: C) PDF
• Q.8 (Paper 2) · MSQ · Maxima and Minima: Local extrema and monotonicity of a function with sine terms (official answer: B, C, D) PDF
• Q.14 (Paper 2) · Numerical · Derivative of Inverse: Derivative of f composed with inverse of a logistic-type function (official answer: 0.2–0.3) PDF

JEE Advanced2024

• Q.17 (Paper 1) · Matching · Continuity and Differentiability: Continuity and differentiability of combinations of two functions (official answer: C) PDF
• Q.3 (Paper 2) · MCQ · Limits: Value of k from a 1-power-infinity limit equal to e^6 (official answer: B) PDF
• Q.4 (Paper 2) · MCQ · Continuity and Differentiability: Statements on zeros and derivative of x^2 sin(pi/x^2) (official answer: D) PDF
• Q.5 (Paper 2) · MSQ · Limits: Parameter pairs for which a log-trig limit at infinity is zero (official answer: B, C) PDF

JEE Advanced2023

• Q.4 (Paper 1) · MCQ · Limits: Limit of f(x)g(x) at 0 for a step function and an integral bound (official answer: C) PDF
• Q.6 (Paper 2) · MSQ · Continuity and Differentiability: Discontinuities and non-differentiable points of a floor-based function (official answer: A, B) PDF
• Q.7 (Paper 2) · MSQ · Concavity: Number of fixed points of functions with positive second derivative (official answer: A, B, C) PDF
• Q.8 (Paper 2) · Integer · Maxima and Minima: Minimum of a function defined by an integral with inverse-tan limit (official answer: 0) PDF

JEE Advanced2022

• Q.2 (Paper 1) · Numerical · Limits: Right-hand limit of sine of a log-ratio function at x = alpha (official answer: 0.49–0.51) PDF
• Q.5 (Paper 2) · Integer · Limits: Value of 6 beta from a limit with exponential and root terms (official answer: 5) PDF
• Q.10 (Paper 2) · MSQ · Maxima and Minima: Extreme values of a function defined via an infinite trig series (official answer: A, B, C) PDF
• Q.18 (Paper 2) · MCQ · Limits: Limit of a finite sum f(n) as n tends to infinity (official answer: B) PDF

JEE Advanced2021

• Q.12 (Paper 1) · MSQ · Monotonicity: Monotonicity, onto-ness and range of a rational function PDF
• Q.9 (Paper 2) · Numerical · Maxima and Minima: Count of local extrema for an integral-defined function PDF
• Q.10 (Paper 2) · Numerical · Maxima and Minima: Count of local extrema for a polynomial in (x-1) PDF
• Q.15 (Paper 2) · MCQ · Mean Value Theorem: True statement on functions defined by integrals and MVT PDF
• Q.16 (Paper 2) · MCQ · Monotonicity: Inequality bounds on functions defined by integrals PDF

JEE Advanced2020

• Q.6 (Paper 1) · MCQ · Maxima and Minima: Area of the max-perimeter rectangle under y = 2 sin 2x PDF
• Q.7 (Paper 1) · MSQ · Differentiability: Differentiability of a product fg at x = 1 PDF
• Q.17 (Paper 1) · Numerical · Roots of Polynomials: Minimum of total distinct real roots of a polynomial and its derivative PDF
• Q.18 (Paper 1) · Numerical · Limits: Exponent for which a limit involving (1-x)^(1/x) is finite and nonzero PDF
• Q.5 (Paper 2) · Integer · Continuity: Points of discontinuity and non-differentiability of f(g(x)) PDF
• Q.6 (Paper 2) · Integer · Limits: Value of a trigonometric limit as x tends to pi/2 PDF
• Q.9 (Paper 2) · MSQ · Functional Equations: Differentiability of f defined by a functional equation PDF
• Q.18 (Paper 2) · Numerical · Maxima and Minima: Sum of points of local minima of a trigonometric function PDF

JEE Advanced2019

• Q.10 (Paper 1) · MSQ · Monotonicity: Monotonicity and differentiability of a piecewise function (official answer: B, C, D) PDF
• Q.4 (Paper 2) · MSQ · Limits: Functions satisfying two limit-based properties at zero (official answer: A, B) PDF
• Q.5 (Paper 2) · MSQ · Maxima and Minima: Locations of local extrema of sin(pi x)/x^2 (official answer: B, C, D) PDF
• Q.7 (Paper 2) · MSQ · Maxima and Minima: Local extrema of an integral of a cubic (official answer: A, B, D) PDF

JEE Advanced2018

• Q.4 (Paper 1) · MSQ · Rolle's Theorem: Properties of a bounded twice differentiable function PDF
• Q.11 (Paper 2) · Numerical · Functional Equations: Value of log f(4) from a functional equation PDF
• Q.18 (Paper 2) · Matching · Continuity and Differentiability: Match functions with continuity and differentiability properties PDF

JEE Advanced2017

• Q.39 (Paper 1) · MSQ · Continuity: Points of discontinuity of a function with greatest integer (official answer: Marks to all) PDF
• Q.52 (Paper 1) · Matching · Monotonicity: Zeros, limits and monotonicity of x+log x - x log x (official answer: B) PDF
• Q.53 (Paper 1) · Matching · Monotonicity: Correct combination of properties of f and its derivatives (official answer: B) PDF
• Q.54 (Paper 1) · Matching · Monotonicity: Incorrect combination of properties of f and its derivatives (official answer: C) PDF
• Q.40 (Paper 2) · MCQ · Mean Value Theorem: Bound on f'(1) for a convex function with given values (official answer: D) PDF
• Q.46 (Paper 2) · MSQ · Monotonicity: Behaviour of f given f' > 2f and f(0)=1 (official answer: A, C) PDF
• Q.47 (Paper 2) · MSQ · One-sided Limits: Left and right limits of a function at x=1 (official answer: A, D) PDF

JEE Advanced2016

• Q.41 (Paper 1) · MCQ · Maxima and Minima: Least a so a quadratic-plus-reciprocal inequality holds (official answer: C) PDF
• Q.47 (Paper 1) · MSQ · Inverse Functions: Derivatives and values of functions defined via a cubic inverse (official answer: B, C) PDF
• Q.53 (Paper 1) · Integer · Limits: Parameters making a trigonometric limit equal 1 (official answer: 7) PDF
• Q.44 (Paper 2) · MSQ · Differentiability: Differentiability of a cosine-sine combination at 0 and 1 (official answer: A, B) PDF
• Q.45 (Paper 2) · MSQ · Local Extrema: Nature of f at x=2 from a product limit condition (official answer: A, D) PDF
• Q.46 (Paper 2) · MSQ · Continuity: Discontinuities of floor function and non-differentiable points of g (official answer: B, C) PDF

Limits, Continuity and Differentiability in other exams

The same chapter in other official papers we tagged: JEE Main (24 questions).

Other Mathematics chapters

• Sets, Relations and Functions PYQs
• Complex Numbers and Quadratic Equations PYQs
• Matrices and Determinants PYQs
• Permutations and Combinations PYQs
• Binomial Theorem PYQs
• Sequences and Series PYQs
• Integral Calculus PYQs
• Differential Equations PYQs
• Coordinate Geometry PYQs
• Three-Dimensional Geometry PYQs
• Vector Algebra PYQs
• Statistics and Probability PYQs
• Trigonometry PYQs

FAQ

How many Limits, Continuity and Differentiability questions come in JEE Advanced?

In the official papers we tagged: 4 in 2026, 6 in 2025, 4 in 2024, 4 in 2023, 4 in 2022, 5 in 2021, 8 in 2020, 4 in 2019, 3 in 2018, 7 in 2017 and 6 in 2016 (2 papers each year). That is 55 questions in all, about 14% of Mathematics.

Which Limits, Continuity and Differentiability topics repeat in JEE Advanced?

Asked in the most papers: Limits, Maxima and Minima, Monotonicity. The concept table lists every one with its count.

Are these official JEE Advanced questions?

Yes. Every question is from an official JEE Advanced paper hosted on our year pages. The one-line summaries are ours; open the PDF linked beside each question for the full text.