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Continuity and Differentiability

Get chapter-wise JEE Main & Advanced questions with solutions

Q JEE MAIN
Let f:(0,π)→R be a function given by Where a,b∈Z. If f is continuous at $\mathrm{x}=\frac{\pi}{2}$,...
JEE Main Mathematics Easy
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Q JEE MAIN 2024
If the function $f(x)=\frac{\sin 3 x+\alpha \sin x-\beta \cos 3 x}{x^3}, x \in R$, is continuous at $x=0$, then $f(0)$ is equal to :
JEE Main Mathematics Easy
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Q JEE MAIN 2024
If the function $f(x)=\left\{\begin{array}{cl}\frac{1}{|x|} & , \\ a x^2+2 b, & |x| \geq 2\end{array}\right.$ is differentiable on R , then $48(\mathrm{a}+\mathrm{b})$ is equal to
JEE Main Mathematics Easy
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Q JEE MAIN 2024
Let $g(x)$ be a linear function and $f(x)=\left\{\begin{array}{ll}g(x) & , x \leq 0 \\ \left(\frac{1+x}{2+x}\right)^{\frac{1}{x}} & , x>0\end{array}\right.$, is continuous at $x=0$. If $f^{\prime}(1)=f(-1)$, then...
JEE Main Mathematics Hard
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Q JEE-Main 2024
Let f:R→R be defined as
$...
JEE Main Mathematics Easy
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Q JEE MAIN 2024
Consider the function
$f(x)=\left\{\begin{array}{cl} \frac{a\left(7 x-12-x^2\right)}{b\left|x^2-7 x+12\right|} & , x<3 \\ 2^{\frac{\sin (x-3)}{x-[x]}} & , x>3 \\ b & , x=3 \end{array}\right.$
Where $[\mathrm{x}]$ denotes...
JEE Main Mathematics Medium
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Q JEE MAIN 2025
Let the function $f(x)=\left(x^{2}-1\right)\left|x^{2}-\mathrm{a} x+2\right|+\cos |x|$ be not differentiable at the two points $x=\alpha=2$ and $x=\beta$. Then the distance of the point ( $\alpha, \beta$...
JEE Main Mathematics Medium
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Q JEE MAIN 2025
Let $f: \mathbf{R}-\{0\} \rightarrow(-\infty, 1)$ be a polynomial of degree 2 , satisfying $f(x) f\left(\frac{1}{x}\right)=f(x)+f\left(\frac{1}{x}\right)$. If $f(\mathrm{~K})=-2 \mathrm{~K}$, then the sum of squares of all...
JEE Main Mathematics Medium
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Q JEE MAIN 2025
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...
JEE Main Mathematics Medium
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Q JEE MAIN 2025
Let $m$ and $n$ be the number of points at which the function $f(x) = \max \left\{ {x,{x^3},{x^5}, \ldots ,{x^{21}}} \right\},x \in \mathbb{R}$, is not...
JEE Main Mathematics Easy
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