1
COMEDK 2024 Evening Shift
MCQ (Single Correct Answer)
+1
-0

$$ \text { The area of the region enclosed by the curve }\left\{(x, y): 4 x^2+25 y^2=100\right\} \text { is } $$

A
$$ \frac{16 \pi}{3} \text { sq units } $$
B
$$9 \pi$$ sq units
C
$$10 \pi$$ sq units
D
$$ \frac{9 \pi}{5} \text { sq units } $$
2
COMEDK 2024 Afternoon Shift
MCQ (Single Correct Answer)
+1
-0

The points on the ellipse $$16 x^2+9 y^2=400$$ at which the ordinate decreases at the same rate at which the abscissa increases are

A
$$ \left(3, \frac{16}{3}\right) \text { and }\left(-3,-\frac{16}{3}\right) $$
B
$$ \left(-3,-\frac{16}{3}\right) \text { and }\left(-3, \frac{16}{3}\right) $$
C
$$ \left(-3, \frac{16}{3}\right) \text { and }\left(3,-\frac{16}{3}\right) $$
D
$$ \left(3, \frac{16}{3}\right) \text { and }\left(-3, \frac{16}{3}\right) $$
3
COMEDK 2024 Afternoon Shift
MCQ (Single Correct Answer)
+1
-0

If an ellipse has an equation in the standard form and it passes through the points $$\left(\frac{5}{2}, \frac{\sqrt{6}}{4}\right)$$ and $$\left(-2, \frac{\sqrt{15}}{5}\right)$$ then the length of its latus rectum is

A
$$\frac{1}{10}$$
B
$$\frac{1}{\sqrt{10}}$$
C
$$\sqrt{\frac{10}{5}}$$
D
$$\frac{\sqrt{10}}{5}$$
4
COMEDK 2024 Morning Shift
MCQ (Single Correct Answer)
+1
-0

The equation of an ellipse, whose focus is $$(1,0)$$, directrix is $$x=4$$ and whose eccentricity is a root of the quadratic equation $$2 x^2-3 x+1=0$$, is

A
$$\frac{x^2}{4}+\frac{y^2}{3}=1$$
B
$$\frac{x^2}{3}+\frac{y^2}{4}=1$$
C
$$\frac{x^2}{2}+\frac{y^2}{3}=1$$
D
$$\frac{x^2}{3}+\frac{y^2}{8}=1$$
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