Limits JEE Main PYQs PDF, 2020–2026

Limits has 110 questions in JEE Main papers from 2020 to 2026, about 16 per year across all shifts. All 110 are in the free PDF, with an answer key. The most asked topic is Indeterminate Forms (50 questions), followed by Standard Limits (27) and L'Hopital's Rule (16).

Asked in JEE Main: 1102020–2026, all shifts
In this free PDF: 110all of them, with answers
Asked in 2026: 9Latest paper: 2026 Apr S1
Most asked topic: Indeterminate Forms50 Qs · 45% of the chapter
Difficulty mix: 1% easy · 79% medium · 20% hardof the questions in the PDF

Answer key includedNo loginPractise online

Source: official NTA JEE Main papers · Updated 17 Oct 2026

Practise these 110 questions free, no login Download PDF (0.3 MB)

5 of this chapter's questions came back in a later paper (2021–2026). See the most repeated.

How often it's asked in JEE Main

Limits had about 0.8 questions per shift in recent JEE Main papers (2024–26). Most asked topic: Indeterminate Forms. About 9 questions in the 2026 papers.

It came up in most 2024–26 shifts in our bank (about 42 shifts). Question types in 2020–2026: about 84 MCQs and about 26 numerical.

How many questions from Limits in JEE Main, year by year

Year	Questions	Per shift	MCQ	Numerical
2026	9	0.5	9	0
2025	15	0.8	10	5
2024	21	1.1	13	8
2023	12	0.5	11	1
2022	15	0.7	11	4
2021	26	1.0	21	5
2020	12	0.8	9	3
2020–2026	110	0.7	84	26

Most asked Limits topics, 2020–2026

Topic	Questions
Indeterminate Forms	50
Standard Limits	27
L'Hopital's Rule	16
Concept of Limit	15
Sandwich Theorem	2

Counted from PrepWiser's question bank of JEE Main papers, 2020–2026. Per shift = questions that year ÷ shifts in our bank. Updated 17 Oct 2026.

Download these numbers (CSV)

See all chapters' weightage →

Revise Limits before you practise

Two free sheets, made from the past JEE Main questions on this chapter.

Revision notes10 pages, 22 ideas with the usual mistakes.Open the revision notes Formula sheet2 pages, all 22 formulas.Open the formula sheet

Limits questions per year

Year	Asked	In PDF
2026	9	9
2025	15	15
2024	21	21
2023	12	12
2022	15	15
2021	26	26
2020	12	12

Topic-wise weightage by year

How many Limits questions each topic had in every JEE Main year (all shifts), counting every question asked, including ones not in the PDF. Darker cells mean more questions.

Topic	Asked	Share	2026	2025	2024	2023	2022	2021	2020
Indeterminate Forms	50	45%	5	9	5	5	8	11	7
Standard Limits	27	25%	3	4	5	2	3	7	3
L'Hopital's Rule	16	14%	1	·	8	1	1	5	·
Concept of Limit	15	14%	·	2	2	4	3	2	2
Sandwich Theorem	2	2%	·	·	1	·	·	1	·
All topics	110	100%	9	15	21	12	15	26	12

Swipe the table sideways for older years.

Newest questions (2026)

All 9 JEE Main 2026 Limits questions in the free PDF, latest shift first.

JEE Main 2026 · 6 Apr · Shift 1 · Indeterminate Forms

$\text{ The value of}\underset{{x\rightarrow 0}}{lim}\left(\frac{x^{2}\sin^{2}x}{x^{2}-\sin^{2}x}\right)\text{ is:}$
Solve it online →
JEE Main 2026 · 5 Apr · Shift 2 · Standard Limits

Let $f(x)=\underset{{y\rightarrow 0}}{lim}\frac{(1-\cos (xy))\tan (xy)}{y^{3}}$ . Then the number of solutions of the equation $f(x)=\sin x$ , $x\in {\mathbf{R}}$ is :
Solve it online →
JEE Main 2026 · 5 Apr · Shift 1 · Standard Limits

The product of all possible values of $\alpha$ , for which

$\underset{{x\rightarrow 0}}{lim}\left(\frac{1-\cos (\alpha x)\cos ((\alpha+1)x)\cos ((\alpha+2)x)}{\sin^{2}((\alpha+1)x)}\right)=2$ , is :

Solve it online →
JEE Main 2026 · 2 Apr · Shift 1 · Indeterminate Forms

If $\underset{{x\rightarrow 2}}{lim}\frac{\sin \left(x^{3}-5x^{2}+ax+b\right)}{\left(\sqrt{x-1}-1\right)\log_{e}(x-1)}=m$ , then $a+b+m$ is equal to :
Solve it online →
JEE Main 2026 · 28 Jan · Shift 1 · Standard Limits

The value of

$\underset{{x\rightarrow 0}}{lim}\frac{\log_{e}\left(\sec (ex)\cdot \sec \left(e^{2}x\right)\cdot \ldots \cdot \sec \left(e^{{10}}x\right)\right)}{e^{2}-e^{{2\cos x}}}$

is equal to
Solve it online →
JEE Main 2026 · 24 Jan · Shift 1 · Indeterminate Forms

If the function $f(x)=\frac{e^x\left(e^{\tan x-x}-1\right)+\log _e(\sec x+\tan x)-x}{\tan x-x}$ is continuous at $x=0$ , then the value of $f(0)$ is equal to

Solve it online →
JEE Main 2026 · 23 Jan · Shift 1 · Indeterminate Forms

Let $f(x)=\left\{\begin{array}{cc}\frac{{\mathrm{a}}x^{2}+2{\mathrm{a}}x+3}{4x^{2}+4x-3} &,x\neq -\frac{3}{2},\frac{1}{2} \\ {\ \mathrm{b}} &,x=-\frac{3}{2},\frac{1}{2}\end{array}\right.$ be continuous at $x=-\frac{3}{2}$ . If $f\circ f(x)=\frac{7}{5}$ , then $x$ is equal to:

Solve it online →
JEE Main 2026 · 22 Jan · Shift 2 · Indeterminate Forms

If $\underset{{x\rightarrow 0}}{lim}\frac{{\mathrm{e}}^{{({\mathrm{a}}-1)x}}+2\cos {\ \mathrm{b}}x+({\mathrm{c}}-2){\mathrm{e}}^{{-x}}}{x\cos x-\log_{{{\mathrm{e}}}}(1+x)}=2$ , then ${\mathrm{a}}^{2}+{\mathrm{b}}^{2}+{\mathrm{c}}^{2}$ is equal to :

Solve it online →
JEE Main 2026 · 21 Jan · Shift 1 · L'Hopital's Rule

Let $f:{\mathbf{R}}\rightarrow (0,\infty)$ be a twice differentiable function such that $f(3)=18,f^{{'}}(3)=0$ and $f^{{''}}(3)=4$ .

Then $\underset{{x\rightarrow 1}}{lim}\left(\log_{e}\left(\frac{f(2+x)}{f(3)}\right)^{{\frac{18}{(x-1)^{2}}}}\right)$ is equal to :

Solve it online →

Practise the 2026 Limits questions online

Sample questions from recent papers

JEE Main 2025 · 29 Jan · Shift 1 · Concept of Limit

Let [t] be the greatest integer less than or equal to t. Then the least value of p ∈ N for which

$\lim\limits_{x \to 0^+} \left( x (\left[ \frac{1}{x} \right] + \left[ \frac{2}{x} \right] + \ldots + \left[ \frac{p}{x} \right] \right) - x^2 \left( \left[ \frac{1}{x^2} \right] + \left[ \frac{2^2}{x^2} \right] + \ldots + \left[ \frac{9^2}{x^2} \right] \right) \geq 1$ is equal to _______.

Show answer

Answer: 24

Solve online

JEE Main 2024 · 9 Apr · Shift 2 · L'Hopital's Rule

$\lim \limits_{x \rightarrow \frac{\pi}{2}}\left(\frac{\int_{x^3}^{(\pi / 2)^3}\left(\sin \left(2 t^{1 / 3}\right)+\cos \left(t^{1 / 3}\right)\right) d t}{\left(x-\frac{\pi}{2}\right)^2}\right)$ is equal to

(A) $\frac{3 \pi^2}{2}$
(B) $\frac{9 \pi^2}{8}$
(C) $\frac{5 \pi^2}{9}$
(D) $\frac{11 \pi^2}{10}$

Show answer

Answer: (B)

Solve online

JEE Main 2024 · 31 Jan · Shift 2 · Sandwich Theorem

Let $f: \rightarrow \mathbb{R} \rightarrow(0, \infty)$ be strictly increasing function such that $\lim \limits_{x \rightarrow \infty} \frac{f(7 x)}{f(x)}=1$ . Then, the value of $\lim \limits_{x \rightarrow \infty}\left[\frac{f(5 x)}{f(x)}-1\right]$ is equal to

(A)0
(B)4
(C)1
(D)7/5

Show answer

Answer: (A)

Solve online

The free PDF above has all 110 questions grouped by topic, with an answer key.

Practise these online, free, no login

Answer Limits PYQs in the browser, get each one checked instantly and open the step-by-step solution where there is one.

Practise Limits online

Frequently asked

How many questions come from Limits in JEE Main?

110 questions from 2020 to 2026, about 16 per year. In 2026 it had 9.

Which Limits topics are most important for JEE Main?

By past papers: Indeterminate Forms (45%), Standard Limits (25%) and L'Hopital's Rule (14%) of all Limits questions.

Is the Limits PYQ PDF free?

Yes. The PDF and its answer key are free, and you can practise the questions online with no login, with step-by-step solutions where available.

Prefer to solve online? Practise Limits online with step-by-step solutions where available, or work through JEE Main papers shift by shift.

More Mathematics chapters

Applications of Derivatives (156 asked · 153 in PDF)
Area Under Curves (138 asked · 136 in PDF)
Binomial Theorem (197 asked · 196 in PDF)
Circles (117 asked · all in PDF)
Complex Numbers (162 asked · 161 in PDF)
Continuity & Differentiability (94 asked · all in PDF)
Definite Integration (225 asked · 223 in PDF)
Determinants (188 asked · all in PDF)
Differential Equations (204 asked · 202 in PDF)
Differentiation (38 asked · all in PDF)
Ellipse (100 asked · all in PDF)
Functions (Advanced) (71 asked · all in PDF)
Hyperbola (63 asked · 62 in PDF)
Indefinite Integration (60 asked · all in PDF)
Inverse Trigonometric Functions (94 asked · all in PDF)
Matrices (111 asked · all in PDF)
Parabola (107 asked · 104 in PDF)
Permutations & Combinations (163 asked · 162 in PDF)
Probability: Advanced (97 asked · all in PDF)
Probability: Basic (79 asked · 78 in PDF)
Quadratic Equations & Polynomial Inequalities (129 asked · 128 in PDF)
Relations & Functions (Basic) (139 asked · 137 in PDF)
Sequences & Series (247 asked · 246 in PDF)
Sets (39 asked · all in PDF)
Statistics (104 asked · all in PDF)
Straight Lines (130 asked · 123 in PDF)
Three Dimensional Geometry (297 asked · all in PDF)
Trigonometric Equations (48 asked · all in PDF)
Trigonometric Ratios & Identities (85 asked · 63 in PDF)
Vectors (216 asked · 212 in PDF)

JEE Main PYQs by year: 2026 · 2025 · 2024 · 2023 · 2022 · 2021 · 2020

Practise these 110 questions free, no login

Answers follow NTA's final answer keys. Typing errors are possible, so check doubtful answers against the official key. Spotted a mistake? prepwiser.in/feedback · Terms: prepwiser.in/terms

Limits JEE Main PYQs PDF, 2020–2026

How often it's asked in JEE Main

How many questions from Limits in JEE Main, year by year

Most asked Limits topics, 2020–2026

Revise Limits before you practise

Send this chapter to your study group

Limits questions per year

Topic-wise weightage by year

Newest questions (2026)

Sample questions from recent papers

Practise these online, free, no login

Frequently asked

How many questions come from Limits in JEE Main?

Which Limits topics are most important for JEE Main?

Is the Limits PYQ PDF free?

More Mathematics chapters