1
JEE Main 2022 (Online) 27th July Evening Shift
+4
-1 A circle $$C_{1}$$ passes through the origin $$\mathrm{O}$$ and has diameter 4 on the positive $$x$$-axis. The line $$y=2 x$$ gives a chord $$\mathrm{OA}$$ of circle $$\mathrm{C}_{1}$$. Let $$\mathrm{C}_{2}$$ be the circle with $$\mathrm{OA}$$ as a diameter. If the tangent to $$\mathrm{C}_{2}$$ at the point $$\mathrm{A}$$ meets the $$x$$-axis at $$\mathrm{P}$$ and $$y$$-axis at $$\mathrm{Q}$$, then $$\mathrm{QA}: \mathrm{AP}$$ is equal to :

A
1 : 4
B
1 : 5
C
2 : 5
D
1 : 3
2
JEE Main 2022 (Online) 27th July Morning Shift
+4
-1 If the circle $$x^{2}+y^{2}-2 g x+6 y-19 c=0, g, c \in \mathbb{R}$$ passes through the point $$(6,1)$$ and its centre lies on the line $$x-2 c y=8$$, then the length of intercept made by the circle on $$x$$-axis is

A
$$\sqrt{11}$$
B
4
C
3
D
$$2 \sqrt{23}$$
3
JEE Main 2022 (Online) 26th July Evening Shift
+4
-1 Let the abscissae of the two points $$P$$ and $$Q$$ on a circle be the roots of $$x^{2}-4 x-6=0$$ and the ordinates of $$\mathrm{P}$$ and $$\mathrm{Q}$$ be the roots of $$y^{2}+2 y-7=0$$. If $$\mathrm{PQ}$$ is a diameter of the circle $$x^{2}+y^{2}+2 a x+2 b y+c=0$$, then the value of $$(a+b-c)$$ is _____________.

A
12
B
13
C
14
D
16
4
JEE Main 2022 (Online) 30th June Morning Shift
+4
-1

Consider three circles:

$${C_1}:{x^2} + {y^2} = {r^2}$$

$${C_2}:{(x - 1)^2} + {(y - 1)^2} = {r^2}$$

$${C_3}:{(x - 2)^2} + {(y - 1)^2} = {r^2}$$

If a line L : y = mx + c be a common tangent to C1, C2 and C3 such that C1 and C3 lie on one side of line L while C2 lies on other side, then the value of $$20({r^2} + c)$$ is equal to :

A
23
B
15
C
12
D
6
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