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1
JEE Main 2022 (Online) 29th June Morning Shift
+4
-1
English
Hindi

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
$${5 \over 3}$$
2
JEE Main 2022 (Online) 28th June Morning Shift
+4
-1
English
Hindi

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
$${{7 + 3\sqrt 5 } \over 2}$$
3
JEE Main 2022 (Online) 27th June Evening Shift
+4
-1
English
Hindi

The set of values of k, for which the circle $$C:4{x^2} + 4{y^2} - 12x + 8y + k = 0$$ lies inside the fourth quadrant and the point $$\left( {1, - {1 \over 3}} \right)$$ lies on or inside the circle C, is

A
an empty set
B
$$\left( {6,{{65} \over 9}} \right]$$
C
$$\left[ {{{80} \over 9},10} \right)$$
D
$$\left( {9,{{92} \over 9}} \right]$$
4
JEE Main 2022 (Online) 26th June Morning Shift
+4
-1
English
Hindi
Bengali

Let C be a circle passing through the points A(2, $$-$$1) and B(3, 4). The line segment AB s not a diameter of C. If r is the radius of C and its centre lies on the circle $${(x - 5)^2} + {(y - 1)^2} = {{13} \over 2}$$, then r2 is equal to:

A
32
B
$${{65} \over 2}$$
C
$${{61} \over 2}$$
D
30
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