1
JEE Main 2023 (Online) 31st January Evening Shift
MCQ (Single Correct Answer)
+4
-1
Out of Syllabus
Change Language
The foot of perpendicular from the origin $\mathrm{O}$ to a plane $\mathrm{P}$ which meets the co-ordinate axes at the points $\mathrm{A}, \mathrm{B}, \mathrm{C}$ is $(2, \mathrm{a}, 4), \mathrm{a} \in \mathrm{N}$. If the volume of the tetrahedron $\mathrm{OABC}$ is 144 unit$^{3}$, then which of the following points is NOT on P ?
A
$(3,0,4)$
B
$(0,6,3)$
C
$(0,4,4)$
D
$(2,2,4)$
2
JEE Main 2023 (Online) 31st January Evening Shift
MCQ (Single Correct Answer)
+4
-1
Out of Syllabus
Change Language
Let $P$ be the plane, passing through the point $(1,-1,-5)$ and perpendicular to the line joining the points $(4,1,-3)$ and $(2,4,3)$. Then the distance of $P$ from the point $(3,-2,2)$ is :
A
5
B
4
C
6
D
7
3
JEE Main 2023 (Online) 31st January Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language
The absolute minimum value, of the function

$f(x)=\left|x^{2}-x+1\right|+\left[x^{2}-x+1\right]$,

where $[t]$ denotes the greatest integer function, in the interval $[-1,2]$, is :
A
$\frac{3}{4}$
B
$\frac{3}{2}$
C
$\frac{1}{4}$
D
$\frac{5}{4}$
4
JEE Main 2023 (Online) 31st January Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language
If $\phi(x)=\frac{1}{\sqrt{x}} \int\limits_{\frac{\pi}{4}}^x\left(4 \sqrt{2} \sin t-3 \phi^{\prime}(t)\right) d t, x>0$,

then $\emptyset^{\prime}\left(\frac{\pi}{4}\right)$ is equal to :
A
$\frac{4}{6+\sqrt{\pi}}$
B
$\frac{4}{6-\sqrt{\pi}}$
C
$\frac{8}{\sqrt{\pi}}$
D
$\frac{8}{6+\sqrt{\pi}}$
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