1
MHT CET 2024 16th May Morning 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 co-ordinate axes. The line meets the plane $2 x+y+z=9$ at point Q. Then the length of the line segment PQ equals

A
1 units
B
$\sqrt{2}$ units
C
$\sqrt{3}$ units
D
2 units
2
MHT CET 2024 16th May Morning Shift
MCQ (Single Correct Answer)
+2
-0

If the distance between the plane Ax-2y+z $=\mathrm{d}$ and the plane containing the lines $\frac{x-1}{2}=\frac{y-2}{3}=\frac{z-3}{4}$ and $\frac{x-2}{3}=\frac{y-3}{4}=\frac{z-4}{5}$ is $\sqrt{6}$ units, then $|d|$ is

A
1
B
$\sqrt{6}$
C
2
D
6
3
MHT CET 2024 16th May Morning Shift
MCQ (Single Correct Answer)
+2
-0

The length of the projection of the line segment joining the points $(5,-1,4)$ and $(4,-1,3)$ on the plane $x+y+z=7$ is

A
$\sqrt{\frac{2}{3}}$ units
B
$\frac{2}{\sqrt{3}}$ units
C
$\frac{2}{3}$ units
D
$\frac{\sqrt{2}}{3}$ units
4
MHT CET 2024 15th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

A line makes $45^{\circ}$ angle with positive X -axis and makes equal angles with positive Y -axis ad Z-axis respectively, then the sum of the three angles which the line makes with positive X -axis, Y -axis and Z -axis is

A
$135^{\circ}$
B
$150^{\circ}$
C
$165^{\circ}$
D
$180^{\circ}$
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