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

The equation of the line passing through the point $(3,1,2)$ and perpendicular to the lines $\frac{x-1}{1}=\frac{y-2}{2}=\frac{z-3}{3}$ and $\frac{x}{-3}=\frac{y}{2}=\frac{z}{5}$ is

A
$\frac{x+3}{2}=\frac{y+1}{7}=\frac{z+2}{4}$
B
$\frac{x-3}{-2}=\frac{y-1}{7}=\frac{z-2}{4}$
C
$\frac{x-3}{2}=\frac{y-1}{-7}=\frac{z-2}{4}$
D
$\frac{x-3}{2}=\frac{y-1}{5}=\frac{z-2}{4}$
2
MHT CET 2024 11th May Morning Shift
MCQ (Single Correct Answer)
+2
-0

The area of the triangle with vertices $(1,2,0)$, $(1,0,2)$ and $(0,3,1)$ is

A
$\sqrt{3}$ sq. units
B
$\sqrt{6}$ sq. units
C
$\sqrt{5}$ sq. units
D
$\sqrt{7}$ sq. units
3
MHT CET 2024 11th May Morning Shift
MCQ (Single Correct Answer)
+2
-0

If the volume of tetrahedron whose vertices are $A \equiv(1,-6,10), B \equiv(-1,-3,7), C \equiv(5,-1, k)$ and $D \equiv(7,-4,7)$ is 11 cu . units, then the value of $k$ is

A
7
B
5
C
3
D
1
4
MHT CET 2024 10th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

The vector equation of the plane passing through the point $\mathrm{A}(1,2,-1)$ and parallel to the vectors $2 \hat{i}+\hat{j}-\hat{k}$ and $\hat{i}-\hat{j}+3 \hat{k}$ is

A
$\overline{\mathrm{r}} \cdot(2 \hat{\mathrm{i}}+7 \hat{\mathrm{j}}+3 \hat{\mathrm{k}})=-9$
B
$\overline{\mathrm{r}} \cdot(\hat{\mathrm{i}}+2 \hat{\mathrm{j}}+2 \hat{\mathrm{k}})=9$
C
$\overline{\mathrm{r}} \cdot(3 \hat{\mathrm{i}}+2 \hat{\mathrm{j}}-2 \hat{\mathrm{k}})=9$
D
$\overline{\mathrm{r}} \cdot(2 \hat{\mathrm{i}}-7 \hat{\mathrm{j}}-3 \hat{\mathrm{k}})=-9$
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