1
MHT CET 2023 12th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

The length (in units) 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
$$\frac{2}{\sqrt{3}}$$
B
$$\frac{2}{3}$$
C
$$\frac{\sqrt{2}}{3}$$
D
$$\sqrt{\frac{2}{3}}$$
2
MHT CET 2023 12th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

If the volume of tetrahedron, whose vertices are $$\mathrm{A}(1,2,3), \mathrm{B}(-3,-1,1), \mathrm{C}(2,1,3)$$ and $$D(-1,2, x)$$ is $$\frac{11}{6}$$ cubic units, then the value of $$x$$ is

A
3
B
$$-$$2
C
4
D
$$-$$1
3
MHT CET 2023 12th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

Equation of plane containing the line $$\frac{x}{2}=\frac{y}{3}=\frac{z}{4}$$ and perpendicular to the plane containing the lines $$\frac{x}{3}=\frac{y}{4}=\frac{z}{2}$$ and $$\frac{x}{4}=\frac{y}{2}=\frac{z}{3}$$ is

A
$$x+2 y+z=0$$
B
$$x+2 y-z=0$$
C
$$x-2 y+z=0$$
D
$$x-2 y-z=0$$
4
MHT CET 2023 12th May Morning Shift
MCQ (Single Correct Answer)
+2
-0

The centroid of tetrahedron with vertices at $$\mathrm{A}(-1,2,3), \mathrm{B}(3,-2,1), \mathrm{C}(2,1,3)$$ and $$\mathrm{D}(-1,-2,4)$$ is

A
$$\left(\frac{3}{4}, \frac{-1}{4}, \frac{11}{4}\right)$$
B
$$\left(\frac{5}{4}, \frac{-3}{4}, \frac{7}{4}\right)$$
C
$$\left(\frac{-3}{4}, \frac{-1}{4}, \frac{11}{4}\right)$$
D
$$\left(\frac{-5}{4}, \frac{-3}{4}, \frac{-7}{4}\right)$$
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