1
MHT CET 2024 10th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

If the line $\frac{x-1}{2}=\frac{y+1}{3}=\frac{z-1}{4}$ and $\frac{x-3}{1}=\frac{y-\mathrm{k}}{2}=\frac{\mathrm{z}}{1}$ intersect, then the value of k is

A
$\frac{3}{2}$
B
$\frac{9}{2}$
C
$-\frac{2}{9}$
D
$-\frac{3}{2}$
2
MHT CET 2024 10th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

The projection of $\overline{\mathrm{AB}}$ on $\overline{\mathrm{CD}}$, where $A \equiv(2,-3,0), B \equiv(1,-4,-2), C \equiv(4,6,8)$ and $\mathrm{D} \equiv(7,0,10)$ is

A
$\frac{1}{\sqrt{6}}$
B
$\frac{1}{7}$
C
$\frac{4}{\sqrt{6}}$
D
$\frac{4}{7}$
3
MHT CET 2024 10th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

The equation of the plane through the point $(2,-1,-3)$ and parallel to the lines $\frac{x-1}{3}=\frac{y+2}{2}=\frac{z}{-4}$ and $\frac{x}{2}=\frac{y-1}{-3}=\frac{z-2}{2}$ is

A
$8 x+y-13 z+27=0$
B
$2 x+y+z=0$
C
$3 x-y-z-10=0$
D
$8 x+14 y+13 z+37=0$
4
MHT CET 2024 10th May Morning Shift
MCQ (Single Correct Answer)
+2
-0

Equation of the plane, through the points $(-1,2,-2)$ and $(-1,3,2)$ and perpendicular to $y \mathrm{z}$ - plane, is

A
$4 y+z=10$
B
$4 y-z+10=0$
C
$4 y-z=10$
D
$4 y+z+10=0$
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