1
MHT CET 2023 14th May Morning Shift
+2
-0

If $$\triangle \mathrm{ABC}$$ is right angled at $$\mathrm{A}$$, where $$A \equiv(4,2, x), \mathrm{B} \equiv(3,1,8)$$ and $$C \equiv(2,-1,2)$$, then the value of $$x$$ is

A
4
B
2
C
3
D
1
2
MHT CET 2023 14th May Morning Shift
+2
-0

The angle between the lines, whose direction cosines $$l, \mathrm{~m}, \mathrm{n}$$ satisfy the equations $$l+\mathrm{m}+\mathrm{n}=0$$ and $$2 l^2+2 \mathrm{~m}^2-\mathrm{n}^2=0$$, is

A
$$60^{\circ}$$
B
$$180^{\circ}$$
C
$$90^{\circ}$$
D
$$30^{\circ}$$
3
MHT CET 2023 14th May Morning Shift
+2
-0

Equation of the plane passing through $$(1,-1,2)$$ and perpendicular to the planes $$x+2 y-2 z=4$$ and $$3 x+2 y+z=6$$ is

A
$$6 x-7 y-4 z-5=0$$
B
$$6 x+7 y-4 z+5=0$$
C
$$6 x-7 y+4 z+5=0$$
D
$$6 x+7 y+4 z-5=0$$
4
MHT CET 2023 14th May Morning Shift
+2
-0

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

A
3
B
$$\sqrt{2}$$
C
$$\sqrt{3}$$
D
2
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