1
MHT CET 2023 12th May Morning Shift
+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 the co-ordinate axes at $$\mathrm{A}, \mathrm{B}, \mathrm{C}$$, then the volume of the tetrahedron $$\mathrm{OABC}$$ (in cubic units) is

A
$$\frac{9}{4}$$
B
$$\frac{9}{2}$$
C
9
D
27
2
MHT CET 2023 12th May Morning Shift
+2
-0

The equation of the plane through $$(-1,1,2)$$ whose normal makes equal acute angles with co-ordinate axes is

A
$$x+y+z-3=0$$
B
$$x+y+z-2=0$$
C
$$x+y-z-2=0$$
D
$$x-y+z-3=0$$
3
MHT CET 2023 12th May Morning Shift
+2
-0

The distance of the point $$\mathrm{P}(-2,4,-5)$$ from the line $$\frac{x+3}{3}=\frac{y-4}{5}=\frac{z+8}{6}$$ is

A
$$\frac{\sqrt{37}}{10}$$
B
$$\sqrt{\frac{37}{10}}$$
C
$$\frac{37}{\sqrt{10}}$$
D
$$\frac{37}{10}$$
4
MHT CET 2023 12th May Morning Shift
+2
-0

If the line $$\frac{1-x}{3}=\frac{7 y-14}{2 p}=\frac{z-3}{2}$$ and $$\frac{7-7 x}{3 \mathrm{p}}=\frac{y-5}{1}=\frac{6-\mathrm{z}}{5}$$ are at right angles, then $$\mathrm{p}=$$

A
$$\frac{70}{11}$$
B
$$\frac{11}{70}$$
C
$$\frac{-70}{11}$$
D
$$\frac{-11}{70}$$
EXAM MAP
Medical
NEETAIIMS