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Limits and Derivatives

Get chapter-wise JEE Main & Advanced questions with solutions

Q JEE MAIN 2026
The value of $\lim _{x \rightarrow 0} \frac{\log _e\left(\sec (e x) \cdot \sec \left(e^2 x\right) \cdot \ldots \cdot \sec \left(e^{10} x\right)\right)}{e^2-e^{2 \cos x}}$ is equal...
JEE Main Mathematics Easy
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Q JEE MAIN 2026
The value of $\sum_{k=1}^{\infty}(-1)^{k+1}\left(\frac{k(k+1)}{k!}\right)$ is
JEE Main Physics Medium
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Q JEE MAIN 2026
If $\lim _{x \rightarrow 0} \frac{\mathrm{e}^{(\mathrm{a}-1) x}+2 \cos \mathrm{~b} x+(\mathrm{c}-2) \mathrm{e}^{-x}}{x \cos x-\log _{\mathrm{e}}(1+x)}=2$, then $\mathrm{a}^2+\mathrm{b}^2+\mathrm{c}^2$ is equal to:
JEE Main Mathematics Medium
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Q JEE MAIN_2019
If $\lim _{x \rightarrow 1} \frac{x^4-1}{x-1}=\lim _{x \rightarrow *} \frac{x^3-k^3}{x^2-k^2}$, then $k$ is
JEE Main Mathematics Medium
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Q JEE Advanced 2025
Let $x_0$ be the real number such that $e^{x_0}+x_0=0$. For a given real number $\alpha$, define
$...
JEE Advance Mathematics Easy
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Q JEE MAIN 2019
$\lim _{x \rightarrow 0} \frac{x+2 \sin x}{\sqrt{x^2+2 \sin x+1}-\sqrt{\sin ^2 x-x+1}}$ is :
JEE Main Mathematics Hard
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Q JEE Main 2020
If $\lim _{x \rightarrow 1} \frac{x+x^2+x^3+\ldots .+x^n-n}{x-1}=820,(n \in N)$ then the value of $n$ is equal to $\_\_\_\_$
JEE Main Mathematics Medium
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Q JEE MAIN 2020
$\lim _{x \rightarrow 0}\left(\tan \left(\frac{\pi}{4}+x\right)\right)^{\frac{1}{x}}$ is equal to :
JEE Main Mathematics Easy
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Q JEE MAIN 2019
For each $x \in R$, let $[x]$ be the greatest integer less than or equal to $x$. Then $\lim _{x \rightarrow 0^{-}} \frac{x([x]+|x|) \sin [x]}{|x|}$...
JEE Main Mathematics Medium
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Q JEE MAIN 2020
If $\alpha$ is the positive root of the equation, $p(x)=x^2-x -2=0$, then $\lim _{x \rightarrow \alpha^{+}} \frac{\sqrt{1-\cos (p(x))}}{x+\alpha-4}$ is equal to :
JEE Main Mathematics Medium
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