1
MHT CET 2023 10th May Morning Shift
+2
-0

$$\mathrm{ABC}$$ is a triangle in a plane with vertices $$\mathrm{A}(2,3,5), \mathrm{B}(-1,3,2)$$ and $$\mathrm{C}(\lambda, 5, \mu)$$. If median through $$\mathrm{A}$$ is equally inclined to the co-ordinate axes, then value of $$\lambda+\mu$$ is

A
17
B
10
C
7
D
3
2
MHT CET 2023 9th May Evening Shift
+2
-0

If a line $$\mathrm{L}$$ is the line of intersection of the planes $$2 x+3 y+z=1$$ and $$x+3 y+2 z=2$$. If line $$\mathrm{L}$$ makes an angle $$\alpha$$ with the positive $$\mathrm{X}$$-axis, then the value of $$\sec \alpha$$ is

A
$$\sqrt{3}$$
B
2
C
1
D
$$\sqrt{2}$$
3
MHT CET 2023 9th May Evening Shift
+2
-0

The shortest distance between the lines $$\frac{x-1}{2}=\frac{y-2}{3}=\frac{z-3}{4}$$ and $$\frac{x-2}{3}=\frac{y-4}{4}=\frac{z-5}{5}$$ is

A
$$\frac{1}{\sqrt{14}}$$ units.
B
$$\frac{1}{\sqrt{5}}$$ units.
C
$$\frac{1}{\sqrt{11}}$$ units.
D
$$\frac{1}{\sqrt{6}}$$ units.
4
MHT CET 2023 9th May Evening Shift
+2
-0

The co-ordinates of the point, where the line $$\frac{x-1}{2}=\frac{y-2}{-3}=\frac{z+5}{4}$$ meets the plane $$2 x+4 y-\mathrm{z}=3$$, are

A
$$(3,-1,-1)$$
B
$$(3,1,-1)$$
C
$$(3,-1,1)$$
D
$$(-3,-1,-1)$$
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