1
MHT CET 2024 9th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

A line with positive direction cosines passes through the point $\mathrm{P}(2,1,2)$ and makes equal angles with the coordinate axes. The line meets the plane $2 x+y+\mathrm{z}=9$ at point Q . The length of the line segment PQ equals $\qquad$ units.

A
$\frac{5}{\sqrt{3}}$
B
$2 \sqrt{3}$
C
$\frac{4}{\sqrt{3}}$
D
$4 \sqrt{3}$
2
MHT CET 2024 9th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

Let L be the line of intersection of the planes $2 x+3 y+z=1$ and $x+3 y+2 z=2$. If L makes an angle $\alpha$ with the positive X -axis, then $\cos \alpha$ equals

A
1
B
$\frac{1}{\sqrt{2}}$
C
$\frac{1}{\sqrt{3}}$
D
$\frac{1}{2}$
3
MHT CET 2024 9th May Morning Shift
MCQ (Single Correct Answer)
+2
-0

The equation of the plane, passing through the point $(1,1,1)$ and perpendicular to the planes $2 x+y-2 z=5$ and $3 x-6 y-2 z=7$, is

A
$14 x+2 y-15 z=1$
B
$14 x-2 y+15 z=27$
C
$14 x+2 y+15 z=31$
D
$-14 x+2 y+15 z=3$
4
MHT CET 2024 9th May Morning Shift
MCQ (Single Correct Answer)
+2
-0

The distance of the point $(1,3,-7)$ from the plane passing through the point $(1,-1,-1)$ having normal perpendicular to both the lines $\frac{x-1}{1}=\frac{y+2}{-2}=\frac{z-4}{3}$ and $\frac{x-2}{2}=\frac{y+1}{-1}=\frac{z+7}{-1}$ is

A
$\frac{10}{\sqrt{83}}$ units.
B
$\frac{5}{\sqrt{83}}$ units.
C
$\frac{10}{\sqrt{74}}$ units.
D
$\frac{20}{\sqrt{74}}$ units.
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