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Continuity and Differentiability

Get chapter-wise JEE Main & Advanced questions with solutions

Q JEE MAIN 2021
Let $f: R \rightarrow R$ satisfy the equation $f(x+y)=f(x)$. $f(y)$ for all $x, y \in R$ and $f(x) \neq 0$ for any $x \in R$....
JEE Main Mathematics Medium
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Q JEE MAIN 2021
Let a function $\mathrm{g}:[0,4] \rightarrow R$ be defined as $...
JEE Main Mathematics Medium
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Q JEE MAIN 2021
Let $f: R \rightarrow R$ be a function defined as
$...
JEE Main Mathematics Medium
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Q JEE MAIN_2021
If the function $f(x)=\frac{\cos (\sin x)-\cos x}{x^4}$ is continuous at each point in its domain and $f(0)=\frac{1}{k}$, then $k$ is $\_\_\_\_$ .
JEE Main Mathematics Medium
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Q JEE MAIN 2021
Let $f: R \rightarrow R$ and $g \mid: R \rightarrow R$ be defined as $$ \begin{aligned} & f(x)=\left\{\begin{array}{ll} x+a, & x<0 \\ |x-1|, & x...
JEE Main Mathematics Medium
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Q JEE MAIN 2021
Let $f: S \rightarrow$ Swhere $S=(0, \infty)$ be a twice differentiable function such that $\mathrm{f}(\mathrm{x}+1)= \mathrm{xf}(\mathrm{x})$. If $\mathrm{g}: \mathrm{S} \rightarrow \mathrm{R}$ be defined as $...
JEE Main Mathematics Easy
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Q JEE MAIN 2021
Let $\alpha \in \mathrm{R}$ be such that the function $$ f(x)= \begin{cases}\frac{\cos ^{-1}\left(1-\{x\}^2\right) \sin ^{-1}(1-\{x\})}{\{x\}-\{x\}^3}, & x \neq 0 \\ \alpha, & x=0\end{cases} $$ is...
JEE Main Mathematics Medium
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Q JEE MAIN 2021
If $a+\alpha=1, b+\beta=2$ and $a f(x)+\alpha f\left(\frac{1}{x}\right)=b x+\frac{\beta}{x}, x \neq 0$, then the value of expression $\frac{f(x)+f\left(\frac{1}{x}\right)}{x+\frac{1}{x}}$ is $\_\_\_\_$ .
JEE Main Mathematics Medium
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Q JEE MAIN 2021
If $\quad f(x)=\left\{\begin{array}{cl}\frac{1}{|x|} ; & |x| \geq 1 \\ a x^2+b ; & |x|<1\end{array}\right.$ is differentiable at every point of the domain, then the values...
JEE Main Mathematics Easy
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Q JEE MAIN 2021
Let the functions $f: \mathbb{R} \rightarrow \mathbb{R}$ and $g: \mathbb{R} \rightarrow \mathbb{R}$ be defined as
JEE Main Mathematics Easy
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