1
JEE Main 2025 (Online) 3rd April Morning Shift
MCQ (Single Correct Answer)
+4
-1
Change Language
The radius of the smallest circle which touches the parabolas $y=x^2+2$ and $x=y^2+2$ is
A
$\frac{7 \sqrt{2}}{16}$
B
$\frac{7 \sqrt{2}}{8}$
C
$\frac{7 \sqrt{2}}{2}$
D
$\frac{7 \sqrt{2}}{4}$
2
JEE Main 2025 (Online) 3rd April Morning Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

$$ \text { Let } f(x)=\int x^3 \sqrt{3-x^2} d x \text {. If } 5 f(\sqrt{2})=-4 \text {, then } f(1) \text { is equal to } $$

A
$-\frac{6 \sqrt{2}}{5}$
B
$-\frac{8 \sqrt{2}}{5}$
C
$-\frac{2 \sqrt{2}}{5}$
D
$-\frac{4 \sqrt{2}}{5}$
3
JEE Main 2025 (Online) 3rd April Morning Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

Let the domain of the function $f(x)=\log _2 \log _4 \log _6\left(3+4 x-x^2\right)$ be $(a, b)$. If $\int_0^{b-a}\left[x^2\right] d x=p-\sqrt{q}-\sqrt{r}, p, q, r \in \mathbb{N}, \operatorname{gcd}(p, q, r)=1$, where $[\cdot]$ is the greatest integer function, then $p+q+r$ is equal to

A
10
B
11
C
9
D
8
4
JEE Main 2025 (Online) 3rd April Morning Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

Let $\alpha$ and $\beta$ be the roots of $x^2+\sqrt{3} x-16=0$, and $\gamma$ and $\delta$ be the roots of $x^2+3 x-1=0$. If $P_n=$ $\alpha^n+\beta^n$ and $Q_n=\gamma^n+\hat{o}^n$, then $\frac{P_{25}+\sqrt{3} P_{24}}{2 P_{23}}+\frac{Q_{25}-Q_{23}}{Q_{24}}$ is equal to

A
4
B
3
C
5
D
7
JEE Main Papers
2023
2021
EXAM MAP