1
MHT CET 2023 13th May Morning Shift
MCQ (Single Correct Answer)
+2
-0

If $$A(1,4,2)$$ and $$C(5,-7,1)$$ are two vertices of triangle $$A B C$$ and $$G\left(\frac{4}{3}, 0, \frac{-2}{3}\right)$$ is centroid of the triangle $$A B C$$, then the mid point of side $$B C$$ is

A
$$\left(-2,-2, \frac{3}{2}\right)$$
B
$$\left(2,2, \frac{3}{2}\right)$$
C
$$\left(\frac{3}{2}, 2,-2\right)$$
D
$$\left(\frac{3}{2},-2,-2\right)$$
2
MHT CET 2023 13th May Morning Shift
MCQ (Single Correct Answer)
+2
-0

The base of an equilateral triangle is represented by the equation $$2 x-y-1=0$$ and its vertex is $$(1,2)$$, then the length (in units) of the side of the triangle is

A
$$\sqrt{\frac{20}{3}}$$
B
$$\frac{2}{\sqrt{15}}$$
C
$$\sqrt{\frac{8}{15}}$$
D
$$\sqrt{\frac{15}{2}}$$
3
MHT CET 2023 13th May Morning Shift
MCQ (Single Correct Answer)
+2
-0

Five persons $$\mathrm{A}, \mathrm{B}, \mathrm{C}, \mathrm{D}$$ and $$\mathrm{E}$$ are seated in a circular arrangement. If each of them is given a cap of one of the three colours red, blue and green, then the number of ways of distributing the caps such that the persons seated in adjacent seats get different coloured caps, is

A
30
B
15
C
60
D
40
4
MHT CET 2023 13th May Morning Shift
MCQ (Single Correct Answer)
+2
-0

The distance of the point $$(-1,-5,-10)$$ from the point of intersection of the line $$\frac{x-2}{3}=\frac{y+1}{4}=\frac{z-2}{12}$$ and the plane $$x-y+z=5$$ is

A
13 units.
B
12 units.
C
5 units.
D
16 units.
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