1
MHT CET 2024 11th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

Let $P(3,2,6)$ be a point in space and $Q$ be a point on the line $\bar{r}=\hat{i}-\hat{j}+2 \hat{k}+\mu(-3 \hat{i}+\hat{j}+5 \hat{k})$. Then the value of $\mu$ for which the vector $\overline{\mathrm{PQ}}$ is parallel to the plane $x-4 y+3 z=1$ is

A
$\frac{1}{4}$
B
$-\frac{1}{4}$
C
$\frac{1}{8}$
D
$-\frac{1}{8}$
2
MHT CET 2024 11th May Morning Shift
MCQ (Single Correct Answer)
+2
-0

The perpendicular distance of the origin from the plane $2 x+y-2 z-18=0$ is

A
18 units
B
9 units
C
6 units
D
4 units
3
MHT CET 2024 11th May Morning Shift
MCQ (Single Correct Answer)
+2
-0

The plane $2 x+3 y+4 z=1$ meets $X$-axis in $A$, Y -axis in B and Z -axis in C . Then the centroid of $\triangle A B C$ is

A
$(2,3,4)$
B
$\left(\frac{1}{2}, \frac{1}{3}, \frac{1}{4}\right)$
C
$\left(\frac{1}{6}, \frac{1}{9}, \frac{1}{12}\right)$
D
$\left(\frac{3}{2}, \frac{3}{3}, \frac{3}{4}\right)$
4
MHT CET 2024 11th May Morning Shift
MCQ (Single Correct Answer)
+2
-0

If the lines $\frac{x+1}{-10}=\frac{y+k}{-1}=\frac{z-4}{1} \quad$ and $\frac{x+10}{-1}=\frac{y+1}{-3}=\frac{z-1}{4}$ intersect each other, then the value of $k$ is

A
$-$3
B
3
C
4
D
2
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