1
JEE Main 2022 (Online) 30th June Morning Shift
+4
-1
Out of Syllabus

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
2
JEE Main 2022 (Online) 29th June Evening Shift
+4
-1

Let a triangle ABC be inscribed in the circle $${x^2} - \sqrt 2 (x + y) + {y^2} = 0$$ such that $$\angle BAC = {\pi \over 2}$$. If the length of side AB is $$\sqrt 2$$, then the area of the $$\Delta$$ABC is equal to :

A
1
B
$$\left( {\sqrt 6 + \sqrt 3 } \right)/2$$
C
$$\left( {3 + \sqrt 3 } \right)/4$$
D
$$\left( {\sqrt 6 + 2\sqrt 3 } \right)/4$$
3
JEE Main 2022 (Online) 29th June Morning Shift
+4
-1
Out of Syllabus

Let the tangent to the circle C1 : x2 + y2 = 2 at the point M($$-$$1, 1) intersect the circle C2 : (x $$-$$ 3)2 + (y $$-$$ 2)2 = 5, at two distinct points A and B. If the tangents to C2 at the points A and B intersect at N, then the area of the triangle ANB is equal to :

A
$${1 \over 2}$$
B
$${2 \over 3}$$
C
$${1 \over 6}$$
D
$${5 \over 3}$$
4
JEE Main 2022 (Online) 28th June Morning Shift
+4
-1
Out of Syllabus

If the tangents drawn at the points $$O(0,0)$$ and $$P\left( {1 + \sqrt 5 ,2} \right)$$ on the circle $${x^2} + {y^2} - 2x - 4y = 0$$ intersect at the point Q, then the area of the triangle OPQ is equal to :

A
$${{3 + \sqrt 5 } \over 2}$$
B
$${{4 + 2\sqrt 5 } \over 2}$$
C
$${{5 + 3\sqrt 5 } \over 2}$$
D
$${{7 + 3\sqrt 5 } \over 2}$$
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