1
MHT CET 2023 11th May Morning Shift
MCQ (Single Correct Answer)
+2
-0

If the direction cosines $$l, \mathrm{~m}, \mathrm{n}$$ of two lines are connected by relations $$l-5 \mathrm{~m}+3 \mathrm{n}=0$$ and $$7 l^2+5 \mathrm{~m}^2-3 \mathrm{n}^2=0$$, then value of $$l+\mathrm{m}+\mathrm{n}$$ is

A
$$\frac{2}{\sqrt{6}}$$ or $$\frac{6}{\sqrt{14}}$$
B
$$\frac{1}{\sqrt{6}}$$ or $$\frac{5}{\sqrt{14}}$$
C
$$\frac{2}{\sqrt{6}}$$ or $$\frac{5}{\sqrt{14}}$$
D
$$\frac{1}{\sqrt{6}}$$ or $$\frac{6}{\sqrt{14}}$$
2
MHT CET 2023 11th May Morning Shift
MCQ (Single Correct Answer)
+2
-0

The mirror image of the point $$(1,2,3)$$ in a plane is $$\left(-\frac{7}{3},-\frac{4}{3},-\frac{1}{3}\right)$$. Thus, the point _________ lies on this plane.

A
$$(1,-1,1)$$
B
$$(-1,-1,1)$$
C
$$(1,1,1)$$
D
$$(-1,-1,-1)$$
3
MHT CET 2023 11th May Morning Shift
MCQ (Single Correct Answer)
+2
-0

A plane is parallel to two lines, whose direction ratios are $$1,0,-1$$ and $$-1,1,0$$ and it contains the point $$(1,1,1)$$. If it cuts co-ordinate axes $$(\mathrm{X}, \mathrm{Y}, \mathrm{Z}$$ - axes resp.) at $$\mathrm{A}, \mathrm{B}, \mathrm{C}$$, then the volume of the tetrahedron $$\mathrm{OABC}$$ is _________ cu. units.

A
9
B
$$\frac{9}{4}$$
C
$$\frac{9}{2}$$
D
27
4
MHT CET 2023 11th May Morning Shift
MCQ (Single Correct Answer)
+2
-0

The lines $$\frac{x-1}{3}=\frac{y+1}{2}=\frac{z-1}{5} \quad$$ and $$\frac{x+2}{4}=\frac{y-1}{3}=\frac{z+1}{2}$$

A
intersect each other and point of intersection is $$(2,1,3)$$
B
intersect each other and point of intersection is $$(3,2,4)$$
C
intersect each other and point of intersection is $$(-2,3,3)$$
D
do not intersect.
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