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1
JEE Main 2024 (Online) 30th January Morning Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

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
$$0<\mathrm{r}<7$$
2
JEE Main 2024 (Online) 27th January Morning Shift
MCQ (Single Correct Answer)
+4
-1
Change Language
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
$\frac{1}{13}$
3
JEE Main 2023 (Online) 15th April Morning Shift
MCQ (Single Correct Answer)
+4
-1
Out of Syllabus
Change Language
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
4
JEE Main 2023 (Online) 13th April Evening Shift
MCQ (Single Correct Answer)
+4
-1
Out of Syllabus
Change Language

Let the centre of a circle C be $$(\alpha, \beta)$$ and its radius $$r < 8$$. Let $$3 x+4 y=24$$ and $$3 x-4 y=32$$ be two tangents and $$4 x+3 y=1$$ be a normal to C. Then $$(\alpha-\beta+r)$$ is equal to :

A
7
B
9
C
5
D
6
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