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

The equation of the circle which touches the $$x$$-axis, passes through the point $$(1,1)$$ and whose centre lies on the line $$x+y=3$$ in the first quadrant is

A
$$x^2+y^2+4 x+2 y+4=0$$
B
$$x^2+y^2-4 x-2 y+4=0$$
C
$$x^2+y^2+4 x-2 y+4=0$$
D
$$x^2+y^2-4 x+2 y+4=0$$
2
COMEDK 2024 Morning Shift
MCQ (Single Correct Answer)
+1
-0

The equation of a circle passing through the origin is $$x^2+y^2-6 x+2 y=0$$. The equation of one of its diameter is

A
$$3 x-y=0$$
B
$$x+y=0$$
C
$$x-3 y=0$$
D
$$x+3 y=0$$
3
COMEDK 2024 Morning Shift
MCQ (Single Correct Answer)
+1
-0

The area (in sq units) of the minor segment bounded by the circle $$x^2+y^2=a^2$$ and the line $$x=\frac{a}{\sqrt{2}}$$ is

A
$$\frac{a^2}{4}(\pi-2)$$
B
$$\frac{a^2}{4}(\pi+2)$$
C
$$\frac{\pi a^2}{4}$$
D
$$\frac{a^2}{4}(3 \pi-2)$$
4
COMEDK 2023 Morning Shift
MCQ (Single Correct Answer)
+1
-0

The points of intersection of circles $$(x+1)^2+y^2=4$$ and $$(x-1)^2+y^2=9$$ are $$(a, \pm b)$$, then $$(a, b)$$ equals to

A
$$\left(1.25, \frac{3}{4} \sqrt{7}\right)$$
B
$$\left(-1.25, \frac{3}{4} \sqrt{7}\right)$$
C
$$(-1,2)$$
D
$$(1,3)$$
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