1
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
2
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
3
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
$\overline{\mathrm{r}} \cdot(2 \hat{\mathrm{i}}-7 \hat{\mathrm{j}}-3 \hat{\mathrm{k}})=-9$
4
MHT CET 2024 10th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

The shortest distance between lines $\bar{r}=(\hat{i}+2 \hat{j}-\hat{k})+\lambda(2 \hat{i}+\hat{j}-3 \hat{k})$ and $\bar{r}=(2 \hat{i}-\hat{j}+2 \hat{k})+\mu(\hat{i}-\hat{j}+\hat{k})$ is

A
$\frac{4 \sqrt{2}}{19}$ units
B
$\frac{3 \sqrt{2}}{\sqrt{19}}$ units
C
$\frac{5 \sqrt{2}}{\sqrt{19}}$ units
D
$\frac{2 \sqrt{2}}{\sqrt{19}}$ units
MHT CET Subjects
EXAM MAP