1
MHT CET 2024 15th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

If the vector $\overline{\mathrm{c}}$ lies in the plane of $\overline{\mathrm{a}}$ and $\overline{\mathrm{b}}$, where $\overline{\mathrm{a}}=\hat{\mathrm{i}}-\hat{\mathrm{j}}+2 \hat{\mathrm{k}}, \overline{\mathrm{b}}=\hat{\mathrm{i}}+\hat{\mathrm{j}}+\hat{\mathrm{k}}$ and $\overline{\mathrm{c}}=x \hat{\mathrm{i}}-(2-x) \hat{\mathrm{j}}-\hat{\mathrm{k}}$, then the value of $x$ is

A
4
B
$-$4
C
2
D
$-$2
2
MHT CET 2024 15th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

The equation of a line passing through the point $(2,-1,1)$ and parallel to the line joining the points $\hat{i}+2 \hat{j}+2 \hat{k}$ and $-\hat{i}+4 \hat{j}+\hat{k}$ is

A
$\bar{r}=(2 \hat{i}-\hat{j}+\hat{k})+\lambda(-2 \hat{i}+2 \hat{j}-\hat{k})$
B
$\bar{r}=(2 \hat{i}-\hat{j}+\hat{k})+\lambda(2 \hat{i}+6 \hat{j}+3 \hat{k})$
C
$\bar{r}=(2 \hat{i}-\hat{j}+\hat{k})+\lambda(2 \hat{i}-2 \hat{j}-\hat{k})$
D
$\overline{\mathrm{r}}=(2 \hat{\mathrm{i}}-\hat{\mathrm{j}}+\hat{\mathrm{k}})+\lambda(2 \hat{\mathrm{i}}-6 \hat{\mathrm{j}}-3 \hat{\mathrm{k}})$
3
MHT CET 2024 15th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

The foot of the perpendicular drawn from origin to a plane is $\mathrm{M}(2,1,-2)$, then vector equation of the plane is

A
$\overline{\mathrm{r}} \cdot(2 \hat{\mathrm{i}}+\hat{\mathrm{j}}-2 \hat{\mathrm{k}})=9$
B
$\overline{\mathrm{r}} \cdot(-2 \hat{\mathrm{i}}-\hat{\mathrm{j}}-2 \hat{\mathrm{k}})=7$
C
$\bar{r} \cdot(2 \hat{i}-\hat{j}-2 \hat{k})=9$
D
$\overline{\mathrm{r}} \cdot(2 \hat{\mathrm{i}}-\hat{\mathrm{j}}-\hat{\mathrm{k}})=7$
4
MHT CET 2024 15th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

If $f(1)=1, f^{\prime}(1)=3$, then the derivative of $\mathrm{f}(\mathrm{f}(\mathrm{f}(x)))+(\mathrm{f}(x))^2$ at $x=1$ is

A
12
B
30
C
15
D
33
MHT CET Papers
EXAM MAP