1
JEE Main 2025 (Online) 3rd April Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

Let $f: \mathrm{R} \rightarrow \mathrm{R}$ be a function defined by $f(x)=||x+2|-2| x \|$. If $m$ is the number of points of local minima and $n$ is the number of points of local maxima of $f$, then $m+n$ is

A
3
B
4
C
2
D
5
2
JEE Main 2025 (Online) 3rd April Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language
The sum $1+\frac{1+3}{2!}+\frac{1+3+5}{3!}+\frac{1+3+5+7}{4!}+\ldots$ upto $\infty$ terms, is equal to
A
$3 e$
B
$2 e$
C
$4 e$
D
$6 e$
3
JEE Main 2025 (Online) 3rd April Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language
If the four distinct points $(4,6),(-1,5),(0,0)$ and $(k, 3 k)$ lie on a circle of radius $r$, then $10 k+r^2$ is equal to
A
34
B
32
C
35
D
33
4
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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