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

If for some $\alpha \in \mathbb{R}$, the lines $\mathrm{L}_1: \frac{x+1}{2}=\frac{y-2}{-1}=\frac{z-1}{1}$ and $\mathrm{L}_2: \frac{x+2}{\alpha}=\frac{y+1}{5-\alpha}=\frac{z+1}{1}$ are coplanar, then the line $L_2$ passes through the point

A
$(10,2,2)$
B
$(2,-10,-2)$
C
$(10,-2,-2)$
D
$(-2,10,2)$
2
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
$-\frac{1}{8}$
3
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
4
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
$\left(\frac{3}{2}, \frac{3}{3}, \frac{3}{4}\right)$
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