1
AP EAPCET 2024 - 18th May Morning Shift
MCQ (Single Correct Answer)
+1
-0
If the line $5 x-2 y-6=0$ is a tangent to the hyperbola $5 x^2-k y^2=12$, then the equation of the normal to this hyperbola at the point $(\sqrt{6}, p)(p<0)$ is
A
$\sqrt{6} x+2 y=0$
B
$2 \sqrt{6} x+3 y=3$
C
$\sqrt{6} x-5 y=21$
D
$3 \sqrt{6} x-y=21$
2
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
$\left(k_1-\frac{\sqrt{3} e}{2}\right)$
3
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
$\sqrt{97}$
4
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
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