1
AP EAPCET 2024 - 20th May Evening Shift
MCQ (Single Correct Answer)
+1
-0
If a directrix of a hyperbola centred at the origin and passing through the point $(4,-2 \sqrt{3})$ is $\sqrt{5} x=4$ and e is its eccentricity, then $e^2=$
A
$\frac{\sqrt{7}}{2}$
B
$\frac{7}{2}$
C
$\frac{35}{4}$
D
$2 \sqrt{3}$
2
AP EAPCET 2024 - 20th May Evening Shift
MCQ (Single Correct Answer)
+1
-0
If $l_1$ and $l_2$ are the lengths of the perpendiculars drawn from a point on the hyperbola $5 x^2-4 y^2-20=0$ to its asymptotes, then $\frac{l_1{ }^2 l_2{ }^2}{100}=$
A
$\frac{20}{9}$
B
$\frac{16}{81}$
C
$\frac{4}{81}$
D
$\frac{2}{9}$
3
AP EAPCET 2024 - 20th May Evening Shift
MCQ (Single Correct Answer)
+1
-0
If $O(0,0,0), A(3,0,0)$ and $B(0,4,0)$ form a triangle, then the incentre of $\triangle O A B$ is
A
$(0,1,0)$
B
$(0,1,1)$
C
$(1,0,1)$
D
$(1,1,0)$
4
AP EAPCET 2024 - 20th May Evening Shift
MCQ (Single Correct Answer)
+1
-0
The direction cosines of the line of intersection of the planes $x+2 y+z-4=0$ and $2 x-y+z-3=0$ are
A
$\left(\frac{3}{\sqrt{26}}, \frac{1}{\sqrt{26}}, \frac{-4}{\sqrt{26}}\right)$
B
$\left(\frac{3}{\sqrt{14}}, \frac{2}{\sqrt{14}}, \frac{-1}{\sqrt{14}}\right)$
C
$\left(\frac{3}{\sqrt{35}}, \frac{1}{\sqrt{35}}, \frac{-5}{\sqrt{35}}\right)$
D
$\left(\frac{3}{\sqrt{22}}, \frac{-2}{\sqrt{22}}, \frac{3}{\sqrt{22}}\right)$
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