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

The plane through the intersection of planes $$x+y+z=1$$ and $$2 x+3 y-z+4=0$$ and parallel to $$\mathrm{Y}$$-axis also passes through the point

A
$$(3,3,-1)$$
B
$$(-3,0,1)$$
C
$$(3,2,1)$$
D
$$(-3,0,-1)$$
2
MHT CET 2023 10th May Evening Shift
+2
-0

The perpendicular distance of the origin from the plane $$x-3 y+4 z-6=0$$ is

A
6
B
$$\frac{6}{\sqrt{26}}$$
C
$$\frac{1}{\sqrt{26}}$$
D
$$\frac{3}{\sqrt{26}}$$
3
MHT CET 2023 10th May Evening Shift
+2
-0

Two lines $$\frac{x-3}{1}=\frac{y+1}{3}=\frac{z-6}{-1}$$ and $$\frac{x+5}{7}=\frac{y-2}{-6}=\frac{z-3}{4} \quad$$ intersect at the point R. Then reflection of $$\mathrm{R}$$ in the $$x y$$-plane has co-ordinates

A
$$(2,-4,-7)$$
B
$$(2,-4,7)$$
C
$$(-2,4,7)$$
D
$$(2,4,7)$$
4
MHT CET 2023 10th May Morning Shift
+2
-0

The line $$\frac{x-2}{3}=\frac{y-1}{-5}=\frac{z+2}{2}$$ lies in the plane $$x+3 y-\alpha z+\beta=0$$, then the value of $$\alpha^2+\alpha \beta+\beta^2$$ is

A
127
B
43
C
109
D
61
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