1
MHT CET 2024 10th May Morning Shift
MCQ (Single Correct Answer)
+2
-0

If the line $\frac{x-2}{3}=\frac{y-1}{-5}=\frac{z+2}{2}$ lies in the plane $x+3 y-\alpha z+\beta=0$, then $(\alpha, \beta)=$

A
$(6,-7)$
B
$(-6,7)$
C
$(5,-15)$
D
$(-5,15)$
2
MHT CET 2024 9th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

A plane which is perpendicular to two planes $2 x-2 y+z=0$ and $x-y+2 z=4$, passes through $(1,2,1)$. The distance of the plane from the point $(2,3,4)$ is

A
$\sqrt{\frac{2}{5}}$ units
B
$\frac{2 \sqrt{2}}{5}$ units
C
$\frac{2}{\sqrt{5}}$ units
D
$\frac{1}{\sqrt{5}}$ units
3
MHT CET 2024 9th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

The value of m such that $\frac{x-4}{1}=\frac{y-2}{1}=\frac{z+m}{2}$ lies in the plane $2 x-4 y+z=7$ is

A
7
B
$-$7
C
no real value
D
4
4
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
$4 \sqrt{3}$
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