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

What is the number of Lewis structures for $\mathrm{NO}_2^{-}$?

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

Let two non-collinear unit vectors $\hat{\mathrm{a}}$ and $\hat{\mathrm{b}}$ form an acute angle. A point P moves, so that at any time $t$ the position vector $\overline{O P}$, where $O$ is the origin, is given by $\hat{a} \cos t+\hat{b} \sin t$. When $P$ is farthest from origin O , let M be the length of $\overline{\mathrm{OP}}$ and $\hat{\mathrm{u}}$ be the unit vector along $\overline{\mathrm{OP}}$, then

A
$\hat{\mathrm{u}}=\frac{\hat{\mathrm{a}}+\hat{\mathrm{b}}}{|\hat{\mathrm{a}}+\hat{\mathrm{b}}|}$ and $M=(1+\hat{\mathrm{a}} \cdot \hat{\mathrm{b}})^{\frac{1}{2}}$
B
$\hat{\mathrm{u}}=\frac{\hat{\mathrm{a}}-\hat{\mathrm{b}}}{|\hat{\mathrm{a}}-\hat{\mathrm{b}}|}$ and $M=(1+\hat{a} \cdot \hat{b})^{\frac{1}{2}}$
C
$\hat{\mathrm{u}}=\frac{\hat{\mathrm{a}}+\hat{\mathrm{b}}}{|\hat{\mathrm{a}}+\hat{\mathrm{b}}|}$ and $\mathrm{M}=(1+2 \hat{\mathrm{a}} \cdot \hat{\mathrm{b}})^{\frac{1}{2}}$
D
$\hat{\mathrm{u}}=\frac{\hat{\mathrm{a}}-\hat{\mathrm{b}}}{|\hat{\mathrm{a}}-\hat{\mathrm{b}}|}$ and $\mathrm{M}=(1-2 \hat{\mathrm{a}} \cdot \hat{\mathrm{b}})^{\frac{1}{2}}$
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

In a triangle ABC , with usual notations, if $\mathrm{m} \angle \mathrm{A}=45^{\circ}, \mathrm{m} \angle B=75^{\circ}$, then $\mathrm{a}+\mathrm{c} \sqrt{2}$ has the

A
$b$
B
$\frac{b}{2}$
C
$2b$
D
$3b$
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