1
JEE Main 2025 (Online) 4th April Morning Shift
Numerical
+4
-1
Change Language

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 differentiable and not continuous, respectively. Then $m+n$ is equal to _________.

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2
JEE Main 2025 (Online) 3rd April Evening Shift
Numerical
+4
-1
Change Language
$$If\,\,\mathop {\lim }\limits_{x \to 0} \left(\frac{\tan x}{x}\right)^{\frac{1}{x^2}}=p \text {, then } 96 \log _{\mathrm{e}} p \text { is equal to____________ }$$
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3
JEE Main 2025 (Online) 29th January Morning Shift
Numerical
+4
-1
Change Language

Let [t] be the greatest integer less than or equal to t. Then the least value of p ∈ N for which

$ \lim\limits_{x \to 0^+} \left( x (\left[ \frac{1}{x} \right] + \left[ \frac{2}{x} \right] + \ldots + \left[ \frac{p}{x} \right] \right) - x^2 \left( \left[ \frac{1}{x^2} \right] + \left[ \frac{2^2}{x^2} \right] + \ldots + \left[ \frac{9^2}{x^2} \right] \right) \geq 1 $ is equal to _______.

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4
JEE Main 2025 (Online) 28th January Evening Shift
Numerical
+4
-1
Change Language

Let $f(x)=\lim \limits_{n \rightarrow \infty} \sum\limits_{r=0}^n\left(\frac{\tan \left(x / 2^{r+1}\right)+\tan ^3\left(x / 2^{r+1}\right)}{1-\tan ^2\left(x / 2^{r+1}\right)}\right)$ Then $\lim\limits_{x \rightarrow 0} \frac{e^x-e^{f(x)}}{(x-f(x))}$ is equal to ___________.

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