1
MHT CET 2023 10th May Evening Shift
MCQ (Single Correct Answer)
+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
$$(2,4,7)$$
2
MHT CET 2023 10th May Morning Shift
MCQ (Single Correct Answer)
+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
3
MHT CET 2023 10th May Morning Shift
MCQ (Single Correct Answer)
+2
-0

Let $$\mathrm{P}$$ be a plane passing through the points $$(2,1,0),(4,1,1)$$ and $$(5,0,1)$$ and $$R$$ be the point $$(2,1,6)$$. Then image of $$R$$ in the plane $$P$$ is

A
$$(6,5,2)$$
B
$$(4,3,2)$$
C
$$(6,5,-2)$$
D
$$(3,4,-2)$$
4
MHT CET 2023 10th May Morning Shift
MCQ (Single Correct Answer)
+2
-0

The co-ordinates of the point, where the line through $$A(3,4,1)$$ and $$B(5,1,6)$$ crosses the $$\mathrm{XZ}$$-plane, are

A
$$\left(\frac{11}{3}, 0, \frac{21}{3}\right)$$
B
$$\left(\frac{17}{3}, 0, \frac{23}{3}\right)$$
C
$$\left(\frac{-11}{3}, 0, \frac{21}{3}\right)$$
D
$$\left(\frac{17}{3}, 0, \frac{-23}{3}\right)$$
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