1
JEE Main 2025 (Online) 23rd January Morning Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

Let a curve $y=f(x)$ pass through the points $(0,5)$ and $\left(\log _e 2, k\right)$. If the curve satisfies the differential equation $2(3+y) e^{2 x} d x-\left(7+e^{2 x}\right) d y=0$, then $k$ is equal to

A
32
B
8
C
4
D
16
2
JEE Main 2025 (Online) 23rd January Morning Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

Let P be the foot of the perpendicular from the point $\mathrm{Q}(10,-3,-1)$ on the line $\frac{x-3}{7}=\frac{y-2}{-1}=\frac{z+1}{-2}$. Then the area of the right angled triangle $P Q R$, where $R$ is the point $(3,-2,1)$, is

A
 $\sqrt{30}$
B
$9 \sqrt{15}$
C
$3 \sqrt{30}$
D
$8 \sqrt{15}$
3
JEE Main 2025 (Online) 23rd January Morning Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

The number of words, which can be formed using all the letters of the word "DAUGHTER", so that all the vowels never come together, is :

A
34000
B
37000
C
35000
D
36000
4
JEE Main 2025 (Online) 23rd January Morning Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

Let $f(x)=\log _{\mathrm{e}} x$ and $g(x)=\frac{x^4-2 x^3+3 x^2-2 x+2}{2 x^2-2 x+1}$. Then the domain of $f \circ g$ is

A
$(0, \infty)$
B
$[1, \infty)$
C
$\mathbb{R}$
D
$[0, \infty)$
JEE Main Papers
2023
2021
EXAM MAP