Continuity & Differentiability JEE Main PYQs, 2020 to 2025

Continuity & Differentiability has 62 questions in JEE Main papers from 2020 to 2025, about 10 per year across all shifts. The most asked topic is Continuity at a Point (31 questions), followed by Differentiability (23) and Continuity and Differentiability Relation (4).

Updated 26 Sep 2026

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62Total PYQs

6Years covered

4Topics

2025 Apr S2Latest paper

Continuity & Differentiability questions per year

Year	Questions
2025	5
2024	12
2023	5
2022	11
2021	20
2020	9

Topic-wise weightage

Topic	Questions	Share of chapter	Last asked
Continuity at a Point	31	50%	2025
Differentiability	23	37%	2025
Continuity and Differentiability Relation	4	7%	2024
Types of Discontinuities	4	6%	2025

Sample questions from recent papers

JEE Main 2025 · 7 Apr · Shift 2 · Continuity at a Point

If the function

f(x)=\frac{\tan (\tan x)-\sin (\sin x)}{\tan x-\sin x}

is continuous at

x=0

, then

f(0)

is equal to ____________.

Answer: 2

Step-by-step solution

JEE Main 2025 · 7 Apr · Shift 1 · Types of Discontinuities

The number of points of discontinuity of the function $f(x)=\left[\frac{x^2}{2}\right]-[\sqrt{x}], x \in[0,4]$ , where $[\cdot]$ denotes the greatest integer function, is ________.

Answer: 8

Step-by-step solution

JEE Main 2025 · 29 Jan · Shift 2 · Differentiability

Let the function

f(x)=\left(x^2-1\right)\left|x^2-a x+2\right|+\cos |x|

be not differentiable at the two points

x=\alpha=2

and

x=\beta

. Then the distance of the point

(\alpha, \beta)

from the line

12 x+5 y+10=0

is equal to :

(A)
5
(B)
2
(C)4
(D)
3

Answer: (D)

Step-by-step solution

JEE Main 2024 · 31 Jan · Shift 1 · Continuity and Differentiability Relation

Let $g(x)$ be a linear function and $f(x)=\left\{\begin{array}{cl}g(x) & , x \leq 0 \\ \left(\frac{1+x}{2+x}\right)^{\frac{1}{x}} & , x>0\end{array}\right.$ , is continuous at $x=0$ . If $f^{\prime}(1)=f(-1)$ , then the value $g(3)$ is

(A) $\log _e\left(\frac{4}{9}\right)-1$
(B) $\frac{1}{3} \log _e\left(\frac{4}{9 e^{1 / 3}}\right)$
(C) $\log _e\left(\frac{4}{9 e^{1 / 3}}\right)$
(D) $\frac{1}{3} \log _e\left(\frac{4}{9}\right)+1$

Answer: (C)

Step-by-step solution

All 62 questions are in the free PDF above, grouped by topic.

Frequently asked

How many questions come from Continuity & Differentiability in JEE Main?

62 questions from 2020 to 2025, about 10 per year. In 2025 it had 5.

Which Continuity & Differentiability topics are most important for JEE Main?

By past papers: Continuity at a Point (50%), Differentiability (37%) and Continuity and Differentiability Relation (7%) of all Continuity & Differentiability questions.

Is the Continuity & Differentiability PYQ PDF free?

Yes. The PDF, the answer key and every step-by-step solution on PrepWiser are free, with no login needed to practise.

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JEE Main PYQs by year: 2025 · 2024 · 2023 · 2022 · 2021 · 2020

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