1
JEE Main 2023 (Online) 31st January Evening Shift
+4
-1
Out of Syllabus
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
+4
-1
Out of Syllabus
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
+4
-1
Out of Syllabus
If a point $\mathrm{P}(\alpha, \beta, \gamma)$ satisfying

$$\left( {\matrix{ \alpha & \beta & \gamma \cr } } \right)\left( {\matrix{ 2 & {10} & 8 \cr 9 & 3 & 8 \cr 8 & 4 & 8 \cr } } \right) = \left( {\matrix{ 0 & 0 & 0 \cr } } \right)$$

lies on the plane $2 x+4 y+3 z=5$, then $6 \alpha+9 \beta+7 \gamma$ is equal to :
A
$\frac{11}{5}$
B
11
C
$-1$
D
$\frac{5}{4}$
4
JEE Main 2023 (Online) 31st January Morning Shift
+4
-1

Let the shortest distance between the lines

$$L: \frac{x-5}{-2}=\frac{y-\lambda}{0}=\frac{z+\lambda}{1}, \lambda \geq 0$$ and

$$L_{1}: x+1=y-1=4-z$$ be $$2 \sqrt{6}$$. If $$(\alpha, \beta, \gamma)$$ lies on $$L$$,

then which of the following is NOT possible?

A
$$\alpha+2 \gamma=24$$
B
$$2 \alpha+\gamma=7$$
C
$$\alpha-2 \gamma=19$$
D
$$2 \alpha-\gamma=9$$
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