1
AP EAPCET 2024 - 19th May Evening Shift
MCQ (Single Correct Answer)
+1
-0
Let $A B C$ be an equilateral triangle of side a. $M$ and $N$ are two points on the sides $A B$ and $A C$, respectively such that $\mathbf{A N}={ }^{\prime} K \mathbf{A C}$ and $\mathbf{A B}=3 \mathbf{A M}$. If the vectors $\mathbf{B N}$ and $\mathbf{C M}$ are perpendicular, then $K=$
A
$\frac{1}{5}$
B
$\frac{2}{5}$
C
$-\frac{1}{5}$
D
$-\frac{2}{5}$
2
AP EAPCET 2024 - 19th May Evening Shift
MCQ (Single Correct Answer)
+1
-0
Let $\mathbf{a}$ and $\mathbf{b}$ be two non-collinear vector of unit modulus. If $\mathbf{u}=\mathbf{a}-(\mathbf{a} \cdot \mathbf{b}) \mathbf{b}$ and $\mathbf{v}=\mathbf{a} \times \mathbf{b}$, then $|\mathbf{v}|=$
A
$|\mathbf{u}|+|\mathbf{u} \cdot \mathbf{v}|$
B
$\frac{|\mathbf{u}|}{2}$
C
$|\mathbf{u}|+\frac{|\mathbf{u} \cdot \mathbf{b}|}{2}$
D
$\frac{|\mathbf{u}|}{5}$
3
AP EAPCET 2024 - 18th May Morning Shift
MCQ (Single Correct Answer)
+1
-0
In a regular hexagon $A B C D E F, \mathbf{A B}=\mathbf{a}$ and $\mathbf{B C}=\mathbf{b}$, then $F A=$
A
$\mathbf{a}-\mathbf{b}$
B
$a+b$
C
$\mathbf{b}-\mathbf{a}$
D
$2 \mathbf{b}-\mathbf{a}$
4
AP EAPCET 2024 - 18th May Morning Shift
MCQ (Single Correct Answer)
+1
-0
If $\mathbf{f}, \mathbf{g}, \mathbf{h}$ be mutually orthogonal vectors of equal magnitudes, then the angle between the vectors $\mathbf{f}+\mathbf{g}+\mathbf{h}$ and $\mathbf{h}$ is
A
$\cos ^{-1}\left(\frac{\sqrt{3}}{4}\right)$
B
$\cos ^{-1}\left(\frac{1}{\sqrt{3}}\right)$
C
$\pi-\cos ^{-1}\left(\frac{1}{\sqrt{3}}\right)$
D
$\pi-\cos ^{-1}\left(\frac{\sqrt{3}}{4}\right)$
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