1
MHT CET 2024 4th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

The incenter of the triangle ABC , whose vertices are $\mathrm{A}(0,2,1), \mathrm{B}(-2,0,0)$ and $\mathrm{C}(-2,0,2)$ is

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

Let $\overline{\mathrm{a}}=2 \hat{\mathrm{i}}+\hat{\mathrm{j}}-2 \hat{\mathrm{k}}$ and $\overline{\mathrm{b}}=\hat{\mathrm{i}}+\hat{\mathrm{j}}$. Let $\overline{\mathrm{c}}$ be a vector such that $|\overline{\mathrm{c}}-\overline{\mathrm{a}}|=3$ and $|(\overline{\mathrm{a}} \times \overline{\mathrm{b}}) \times \overline{\mathrm{c}}|=3$ and the angle between $\bar{c}$ and $\bar{a} \times \bar{b}$ is $30^{\circ}$, then $\bar{a} \cdot \bar{c}$ is equal to

A
$\frac{2 \sqrt{2}}{3}$
B
5
C
$-\frac{1}{8}$
D
2
3
MHT CET 2024 4th May Morning Shift
MCQ (Single Correct Answer)
+2
-0

Let $\quad \overline{\mathrm{a}}=\alpha \hat{\mathrm{i}}+3 \hat{\mathrm{j}}-\hat{\mathrm{k}}, \overline{\mathrm{b}}=3 \hat{\mathrm{i}}-\beta \hat{j}+4 \hat{\mathrm{k}} \quad$ and $\overline{\mathrm{c}}=\hat{\mathrm{i}}+2 \hat{\mathrm{j}}-2 \hat{\mathrm{k}}$, where $\alpha, \beta \in \mathbb{R}$, be three vectors. If the projection of $\overline{\mathrm{a}}$ on $\overline{\mathrm{c}}$ is $\frac{10}{3}$ and $\overline{\mathrm{b}} \times \overline{\mathrm{c}}=-6 \hat{\mathrm{i}}+10 \hat{\mathrm{j}}+7 \hat{\mathrm{k}}$, then the value of $2 \alpha+\beta$ is

A
3
B
4
C
5
D
6
4
MHT CET 2024 4th May Morning Shift
MCQ (Single Correct Answer)
+2
-0

Let $\bar{p}$ and $\bar{q}$ be the position vectors of $P$ and $Q$ respectively, with respect to $O$ and $|\vec{p}|=p,|\vec{q}|=q$. The points $R$ and $S$ divide PQ internally and externally in the ratio $2: 3$ respectively. If OR and $O S$ are perpendiculars, then

A
$9 p^2=4 q^2$
B
$4 p^2=9 q^2$
C
$9 p=4 q$
D
$4 \mathrm{p}=9 \mathrm{q}$
MHT CET Subjects
EXAM MAP