1
AP EAPCET 2024 - 18th May Morning Shift
MCQ (Single Correct Answer)
+1
-0
If the angle between the asymptotes of the hyperbola $x^2-k y^2=3$ is $\frac{\pi}{3}$ and $e$ is its eccentricity, then the pole of the line $x+y-1=0$ with respect to this hyperbola is
A
$\left(k, \frac{\sqrt{30}}{2}\right)$
B
$\left(-k, \frac{\sqrt{3} e}{2}\right)$
C
$\left(-k,-\frac{\sqrt{3} e}{2}\right)$
D
$\left(k_1-\frac{\sqrt{3} e}{2}\right)$
2
AP EAPCET 2024 - 18th May Morning Shift
MCQ (Single Correct Answer)
+1
-0
Let $P(\alpha, 4,7)$ and $Q(\beta, \beta, 8)$ be two points. If $Y Z$-plane divides the join of the points $P$ and $Q$ in the ratio $2: 3$ and $Z X$-plane divides the join of $P$ and $Q$ in the ratio $4: 5$, then length of line segment $P Q$ is
A
$\sqrt{107}$
B
$\sqrt{27}$
C
$\sqrt{83}$
D
$\sqrt{97}$
3
AP EAPCET 2024 - 18th May Morning Shift
MCQ (Single Correct Answer)
+1
-0
If $(\alpha, \beta, \gamma)$ are the direction cosines of an angular bisector of two lines whose direction ratios are $(2,2,1)$ and $(2,-1,-2)$, then $(\alpha+\beta+\gamma)^2=$
A
3
B
2
C
4
D
5
4
AP EAPCET 2024 - 18th May Morning Shift
MCQ (Single Correct Answer)
+1
-0
If the distance between the planes $2 x+y+z+1=0$ and $2 x+y+z+\alpha=0$ is 3 units, then product of all possible values of $\alpha$ is
A
-43
B
43
C
53
D
-53
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