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Continuity and Differentiability

Get chapter-wise JEE Main & Advanced questions with solutions

Q JEE MAIN 2025
Let $f: \mathbb{R} \rightarrow \mathbb{R}$ be a continuous function satisfying $f(0) = 1$ and $f(2x) - f(x) = x$ for all $x \in \mathbb{R}$. If...
JEE Main Mathematics Hard
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Q JEE MAIN 2025
Let $[\mathrm{x}]$ denote the greatest integer function, and let m and n respectively be the numbers of the points, where the function $f(x)-[x]+|x-2|,-2
JEE Main Mathematics Easy
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Q JEE MAIN 2025
Let $f:R \to R$ be a twice differentiable function such that $...
JEE Main Mathematics Hard
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Q JEE MAIN 2025
Let $...
JEE Main Mathematics Medium
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Q JEE MAIN 2025
Let $f: \mathbb{R} \rightarrow \mathbb{R}$ be a function defined by
$...
JEE Main Mathematics Medium
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Q JEE MAIN 2025
If the function $...
JEE Main Mathematics Medium
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Q JEE MAIN 2025
Let $f(x)$ be a real differentiable function such that $f(0)=1$ and $f(x+y)=f(x){{f}^{\prime }}(y)+{{f}^{\prime }}(x)f(y)$ for all $x,y\in \mathbf{R}$. Then $\sum\limits_{{\text{n}=1}}^{{100}}{{{{{\log }}_{\text{e}}}}}f(\text{n})$ is equal to
JEE Main Mathematics Medium
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Q JEE MAIN 2025
Let the function,
$f(x)= \begin{cases}-3 a^2-2, & x<1 \\ a^2+b x, & x \geqslant 1\end{cases}$ be differentiable for all $x \in \mathbf{R}$, where $...
JEE Main Mathematics Medium
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