Continuity & Differentiability JEE Main PYQs PDF, 2020–2026

Continuity & Differentiability questions per year

Topic-wise weightage by year

How many Continuity & Differentiability 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.

Swipe the table sideways for older years.

Newest questions (2026)

All 10 JEE Main 2026 Continuity & Differentiability questions in the free PDF, latest shift first.

1. JEE Main 2026 · 8 Apr · Shift 2 · Differentiability

   For the function $f(x)={\mathrm{e}}^{{\sin |x|}}-|x|,x\in {\mathbf{R}}$, consider the following statements :

   Statement I : $f$ is differentiable for all $x\in {\mathbf{R}}$.

   Statement II : $f$ is increasing in $\left(-\pi,-\frac{\pi}{2}\right)$.

   In the light of the above statements, choose the correct answer from the options given below :

   Solve it online →

2. JEE Main 2026 · 6 Apr · Shift 2 · Continuity at a Point

   Let $f(x)=\left\{\begin{array}{cc}x^{3}+8; & x<0, \\ x^{2}-4; & x\geq 0,\end{array}\right.$ and $g(x)=\left\{\begin{array}{cc}(x-8)^{{1/3}}; & x<0, \\ (x+4)^{{1/2}}; & x\geq 0.\end{array}\right.$

   Then the number of points, where the function $g\circ f$ is discontinuous, is $\_\_\_\_$ .

   Solve it online →

3. JEE Main 2026 · 4 Apr · Shift 1 · Differentiability

   The number of points, at which the function $f(x)=max\left\{6x,2+3x^{2}\right\}+|x-1|\cos \left|x^{2}-\frac{1}{4}\right|,x\in (-\pi,\pi)$, is not differentiable, is

   $\_\_\_\_$ .

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4. JEE Main 2026 · 4 Apr · Shift 2 · Differentiability

   Let $f(x)=\left\{\begin{array}{cc}e^{{x-1}} &,x<0 \\ x^{2}-5x+6 &,x\geq 0\end{array}\right.$ and $g(x)=f(|x|)+|f(x)|$. If the number of points where $g$ is not continuous and is not differentiable are $\alpha$ and $\beta$ respectively, then $\alpha+\beta$ is equal to $\_\_\_\_$

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5. JEE Main 2026 · 2 Apr · Shift 2 · Continuity at a Point

   The number of points in the interval $[2,4]$, at which the function $f(x)=\left[x^{2}-x-\frac{1}{2}\right]$, where $[\cdot]$ denotes the greatest integer function, is discontinuous, is ________.

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6. JEE Main 2026 · 28 Jan · Shift 2 · Continuity at a Point

   Let $f(x)=\underset{{\theta\rightarrow 0}}{lim}\left(\frac{\cos \pi x-x^{\left(\frac{2}{\theta}\right)}\sin (x-1)}{1+x^{\left(\frac{2}{\theta}\right)}(x-1)}\right),\ x\in {\mathbb{R}}$. Consider the following two statements :

   (I) $f(x)$ is discontinuous at $x=1$.

   (II) $f(x)$ is continuous at $x=-1$.

   Then,

   Solve it online →

7. JEE Main 2026 · 24 Jan · Shift 1 · Differentiability

   Let $\alpha, \beta \in \mathbb{R}$ be such that the function $f(x)= \begin{cases}2 \alpha\left(x^2-2\right)+2 \beta x & , x<1 \\ (\alpha+3) x+(\alpha-\beta) & , x \geq 1\end{cases}$ be differentiable at all $x \in \mathbb{R}$. Then $34(\alpha+\beta)$ is equal to

   Solve it online →

8. JEE Main 2026 · 24 Jan · Shift 2 · Continuity at a Point

   Let $[t]$ denote the greatest integer less than or equal to $t$. If the function

   $$f(x)=\left\{\begin{array}{cl} b^2 \sin \left(\frac{\pi}{2}\left[\frac{\pi}{2}(\cos x+\sin x) \cos x\right]\right), & x<0 \\ \frac{\sin x-\frac{1}{2} \sin 2 x}{x^3} & , x>0 \\ a & , x=0 \end{array}\right.$$

   is continuous at $x=0$, then $a^2+b^2$ is equal to :

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9. JEE Main 2026 · 23 Jan · Shift 2 · Continuity at a Point

   If $f(x)=\left\{\begin{array}{cc}\frac{a|x|+x^{2}-2(\sin |x|)(\cos |x|)}{x} &,x\neq 0 \\ b &,x=0\end{array}\right.$
   
   is continuous at $x=0$, then $a+b$ is equal to :

   Solve it online →

10. JEE Main 2026 · 22 Jan · Shift 2 · Continuity at a Point

    Let $[\cdot]$ denote the greatest integer function, and let $f(x)=min\left\{\sqrt{2}x,x^{2}\right\}$.

    Let ${\mathrm{S}}=\{x\in (-2,2)$ : the function ${\mathrm{g}}(x)=|x|\left[x^{2}\right]$ is discontinuous at $x\}$.

    Then $\sum_{{x\in {\ \mathrm{S}}}}f(x)$ equals

    Solve it online →

Practise the 2026 Continuity & Differentiability questions online

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