1
MHT CET 2024 3rd May Morning Shift
MCQ (Single Correct Answer)
+2
-0

The image of the line $\frac{x-1}{3}=\frac{y-3}{1}=\frac{z-4}{-5}$ in the plane $2 x-y+z+3=0$ is the line

A
$\frac{x+3}{-3}=\frac{y-5}{-1}=\frac{z+2}{5}$
B
$\frac{x-3}{3}=\frac{y+5}{1}=\frac{z-2}{-5}$
C
$\frac{x-3}{-3}=\frac{y+5}{-1}=\frac{z-2}{5}$
D
$\frac{x+3}{3}=\frac{y-5}{1}=\frac{z-2}{-5}$
2
MHT CET 2024 3rd May Morning Shift
MCQ (Single Correct Answer)
+2
-0

Let $\mathrm{P}(2,3,6)$ 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 vector $\overline{\mathrm{PQ}}$ is parallel to the plane $x-4 y+4 z=1$ is

A
$\frac{13}{6}$
B
$-\frac{6}{13}$
C
$\frac{6}{13}$
D
$-\frac{13}{6}$
3
MHT CET 2024 2nd May Evening Shift
MCQ (Single Correct Answer)
+2
-0

Distance between the parallel lines $\frac{x}{3}=\frac{y-1}{-2}=\frac{z}{1}$ and $\frac{x+4}{3}=\frac{y-3}{-2}=\frac{z+2}{1}$ is

A
$\sqrt{\frac{6}{7}}$ units
B
$\sqrt{\frac{3}{7}}$ units
C
$\sqrt{\frac{3}{14}}$ units
D
$\sqrt{\frac{5}{14}}$ units
4
MHT CET 2024 2nd May Evening Shift
MCQ (Single Correct Answer)
+2
-0

The equation of the plane, passing through the mid point of the line segment of join of the points $\mathrm{P}(1,2,5)$ and $\mathrm{Q}(3,4,3)$ and perpendicular to it, is

A
$x+y-z+1=0$
B
$x+y-z-1=0$
C
$x+y+z+1=0$
D
$x-y-z+1=0$
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