1
JEE Main 2024 (Online) 1st February Morning Shift
+4
-1
Let $C: x^2+y^2=4$ and $C^{\prime}: x^2+y^2-4 \lambda x+9=0$ be two circles. If the set of all values of $\lambda$ so that the circles $\mathrm{C}$ and $\mathrm{C}$ intersect at two distinct points, is $\mathrm{R}-[\mathrm{a}, \mathrm{b}]$, then the point $(8 \mathrm{a}+12,16 \mathrm{~b}-20)$ lies on the curve :
A
$x^2+2 y^2-5 x+6 y=3$
B
$5 x^2-y=-11$
C
$x^2-4 y^2=7$
D
$6 x^2+y^2=42$
2
JEE Main 2024 (Online) 31st January Evening Shift
+4
-1

Let a variable line passing through the centre of the circle $$x^2+y^2-16 x-4 y=0$$, meet the positive co-ordinate axes at the points $$A$$ and $$B$$. Then the minimum value of $$O A+O B$$, where $$O$$ is the origin, is equal to

A
12
B
20
C
24
D
18
3
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
$$\sqrt{20}$$
4
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
$$0<\mathrm{r}<7$$
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