1
JEE Main 2024 (Online) 31st January Morning Shift
+4
-1

If one of the diameters of the circle $$x^2+y^2-10 x+4 y+13=0$$ is a chord of another circle $$\mathrm{C}$$, whose center is the point of intersection of the lines $$2 x+3 y=12$$ and $$3 x-2 y=5$$, then the radius of the circle $$\mathrm{C}$$ is :

A
4
B
3$$\sqrt2$$
C
6
D
$$\sqrt{20}$$
2
JEE Main 2024 (Online) 30th January Morning Shift
+4
-1

If the circles $$(x+1)^2+(y+2)^2=r^2$$ and $$x^2+y^2-4 x-4 y+4=0$$ intersect at exactly two distinct points, then

A
$$\frac{1}{2}<\mathrm{r}<7$$
B
$$3<\mathrm{r}<7$$
C
$$5<\mathrm{r}<9$$
D
$$0<\mathrm{r}<7$$
3
JEE Main 2024 (Online) 27th January Morning Shift
+4
-1
Four distinct points $(2 k, 3 k),(1,0),(0,1)$ and $(0,0)$ lie on a circle for $k$ equal to :
A
$\frac{3}{13}$
B
$\frac{2}{13}$
C
$\frac{5}{13}$
D
$\frac{1}{13}$
4
JEE Main 2023 (Online) 15th April Morning Shift
+4
-1
Out of Syllabus
The number of common tangents, to the circles

$x^{2}+y^{2}-18 x-15 y+131=0$

and $x^{2}+y^{2}-6 x-6 y-7=0$, is :
A
4
B
2
C
3
D
1
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