1
JEE Main 2025 (Online) 22nd January Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

If $\int \mathrm{e}^x\left(\frac{x \sin ^{-1} x}{\sqrt{1-x^2}}+\frac{\sin ^{-1} x}{\left(1-x^2\right)^{3 / 2}}+\frac{x}{1-x^2}\right) \mathrm{d} x=\mathrm{g}(x)+\mathrm{C}$, where C is the constant of integration, then $g\left(\frac{1}{2}\right)$ equals :

A
$\frac{\pi}{6} \sqrt{\frac{\mathrm{e}}{3}}$
B
$\frac{\pi}{6} \sqrt{\frac{\mathrm{e}}{2}}$
C
$\frac{\pi}{4} \sqrt{\frac{\mathrm{e}}{3}}$
D
$\frac{\pi}{4} \sqrt{\frac{\mathrm{e}}{2}}$
2
JEE Main 2025 (Online) 22nd January Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

Let $\vec{a}$ and $\vec{b}$ be two unit vectors such that the angle between them is $\frac{\pi}{3}$. If $\lambda \vec{a}+2 \vec{b}$ and $3 \vec{a}-\lambda \vec{b}$ are perpendicular to each other, then the number of values of $\lambda$ in $[-1,3]$ is :

A
1
B
3
C
2
D
0
3
JEE Main 2025 (Online) 22nd January Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

The area of the region enclosed by the curves $y=x^2-4 x+4$ and $y^2=16-8 x$ is :

A
$\frac{8}{3}$
B
$5$
C
$8$
D
$\frac{4}{3}$
4
JEE Main 2025 (Online) 22nd January Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

In a group of 3 girls and 4 boys, there are two boys $B_1$ and $B_2$. The number of ways, in which these girls and boys can stand in a queue such that all the girls stand together, all the boys stand together, but $B_1$ and $B_2$ are not adjacent to each other, is :

A
120
B
96
C
72
D
144
JEE Main Papers
2023
2021
EXAM MAP