Limits Continuity And Differentiability — JEE Main Previous Year Questions

How many JEE Main questions come from Limits Continuity And Differentiability?

Limits Continuity And Differentiability has contributed 247 questions to Joint Entrance Examination (Main) papers between 2016 and 2026 — an average of about 22 questions a year. That count is measured from EByAi’s bank of 55,289 JEE Main questions, not estimated from a syllabus. Every one of the 247 questions carries a written, step-by-step solution, and each is tagged to Limits Continuity And Differentiability within Mathematics, so you can drill this chapter across every year at once instead of hunting through paper PDFs. Practising a chapter’s full PYQ history is the fastest way to learn the patterns examiners reuse.

Sample Limits Continuity And Differentiability questions from real JEE Main papers

These are 5 real questions from the bank — exactly as asked, with the answer one tap away. All 247 Limits Continuity And Differentiability questions (with full written solutions) are available in practice.

1. Question 1 · JEE Main 2021

   Let f be any continuous function on [0, 2] and twice differentiable on (0, 2). If f(0) = 0, f(1) = 1 and f(2) = 2, then
   1. (A)f''(x) = 0 for all x $\in$ (0, 2)
   2. (B)f''(x) = 0 for some x $\in$ (0, 2)
   3. (C)f'(x) = 0 for some x $\in$ [0, 2]
   4. (D)f''(x) > 0 for all x $\in$ (0, 2)
   Show answerAnswer

   Answer: (B) f''(x) = 0 for some x $\in$ (0, 2)

2. Question 2 · JEE Main 2026

   $$\text{ The value of }\underset{x\to 0}{\lim }\left(\frac{x^2{\sin }^{2}x}{x^2-{\sin }^{2}x}\right)\text{ is : }$$
   1. (A)2
   2. (B)3
   3. (C)4
   4. (D)6
   Show answerAnswer

   Answer: (B) 3

3. Question 3 · JEE Main 2026

   Let $\alpha ,\beta \in \mathbb{R}$ be such that the function $f(x)= \begin{cases}2 \alpha\left(x^2-2\right)+2 \beta x & , x
   1. (A)48
   2. (B)84
   3. (C)36
   4. (D)24
   Show answerAnswer

   Answer: (A) 48

4. Question 4 · JEE Main 2026

   If $\underset{x\to 2}{\lim }\frac{\sin \left(x^3-5x^2+ax+b\right)}{\left(\sqrt{x-1}-1\right){\log }_e(x-1)}=m$, then $a+b+m$ is equal to :
   1. (A)5
   2. (B)6
   3. (C)8
   4. (D)10
   Show answerAnswer

   Answer: (B) 6

5. Question 5 · JEE Main 2026

   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
   1. (A)$\frac{2}{3}$
   2. (B)$\frac{1}{2}$
   3. (C)2
   4. (D)$\frac{3}{2}$
   Show answerAnswer

   Answer: (D) $\frac{3}{2}$

Limits Continuity And Differentiability questions by year

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