1
JEE Main 2023 (Online) 15th April Morning Shift
MCQ (Single Correct Answer)
+4
-1
Change Language
If the domain of the function

$f(x)=\log _{e}\left(4 x^{2}+11 x+6\right)+\sin ^{-1}(4 x+3)+\cos ^{-1}\left(\frac{10 x+6}{3}\right)$ is $(\alpha, \beta]$, then

$36|\alpha+\beta|$ is equal to :
A
72
B
54
C
45
D
63
2
JEE Main 2023 (Online) 15th April Morning Shift
MCQ (Single Correct Answer)
+4
-1
Out of Syllabus
Change Language
Let the foot of perpendicular of the point $P(3,-2,-9)$ on the plane passing through the points $(-1,-2,-3),(9,3,4),(9,-2,1)$ be $Q(\alpha, \beta, \gamma)$. Then the distance of $Q$ from the origin is :
A
$\sqrt{38}$
B
$\sqrt{29}$
C
$\sqrt{42}$
D
$\sqrt{35}$
3
JEE Main 2023 (Online) 15th April Morning Shift
MCQ (Single Correct Answer)
+4
-1
Out of Syllabus
Change Language
The number of common tangents, to the circles

$x^{2}+y^{2}-18 x-15 y+131=0$

and $x^{2}+y^{2}-6 x-6 y-7=0$, is :
A
4
B
2
C
3
D
1
4
JEE Main 2023 (Online) 15th April Morning Shift
MCQ (Single Correct Answer)
+4
-1
Change Language
Let $[x]$ denote the greatest integer function and

$f(x)=\max \{1+x+[x], 2+x, x+2[x]\}, 0 \leq x \leq 2$. Let $m$ be the number of

points in $[0,2]$, where $f$ is not continuous and $n$ be the number of points in

$(0,2)$, where $f$ is not differentiable. Then $(m+n)^{2}+2$ is equal to :
A
3
B
6
C
2
D
11
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