1
MHT CET 2021 23th September Morning Shift
MCQ (Single Correct Answer)
+2
-0

The vector equation of the line passing through $$\mathrm{P}(1,2,3)$$ and $$\mathrm{Q}(2,3,4)$$ is

A
$$(\hat{i}+2 \hat{j}+3 \hat{k})+\lambda(\hat{i}+\hat{j}+\hat{k})$$
B
$$(\hat{i}+2 \hat{j}+3 \hat{k})+\lambda(\hat{i}-\hat{j}-\hat{k})$$
C
$$(\hat{\mathrm{i}}+2 \hat{\mathrm{j}}+3 \hat{\mathrm{k}})+\lambda(2 \hat{\mathrm{i}}+3 \hat{\mathrm{j}}+4 \hat{\mathrm{k}})$$
D
$$(\hat{i}+2 \hat{j}+3 \hat{k})+\lambda(2 \hat{i}+6 \hat{j}+12 \hat{k})$$
2
MHT CET 2021 23th September Morning Shift
MCQ (Single Correct Answer)
+2
-0

Equation of planes parallel to the plane $$x-2y+2z+4=0$$ which are at a distance of one unit from the point (1, 2, 3) are

A
$$x+2 y+2 z=6, x+2 y+2 z=0$$
B
$$x-2 y+2 z=0, x-2 y+2 z-6=0$$
C
$$x-2 y-6=0, x-2 y+z=6$$
D
$$x+2 y+2 z=-6, x+2 y+2 z=5$$
3
MHT CET 2021 22th September Evening Shift
MCQ (Single Correct Answer)
+2
-0

The area of triangle with vertices $$(1,2,0),(1,0, a)$$ and $$(0,3,1)$$ is $$\sqrt{6}$$ sq. units, then the values of '$$a$$' are

A
$$-8,1$$
B
$$2,-4$$
C
$$-2,4$$
D
$$8,-1$$
4
MHT CET 2021 22th September Evening Shift
MCQ (Single Correct Answer)
+2
-0

If $$\mathrm{G}(4,3,3)$$ is the centroid of the triangle $$\mathrm{ABC}$$ whose vertices are $$\mathrm{A}(\mathrm{a}, 3,1), \mathrm{B}(4,5, \mathrm{~b})$$ and $$C(6, c, 5)$$, then the values of $$a, b, c$$ are

A
$$\mathrm{a}=1, \mathrm{~b}=2, \mathrm{c}=3$$
B
$$\mathrm{a=3, b=2, c=1}$$
C
$$\mathrm{a=2, b=1, c=3}$$
D
$$\mathrm{a}=2, \mathrm{~b}=3, \mathrm{c}=1$$
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