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1
JEE Main 2022 (Online) 29th June Evening Shift
MCQ (Single Correct Answer)  +4  -1 English
Hindi

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
$$\left( {\sqrt 6 + 2\sqrt 3 } \right)/4$$
2
JEE Main 2022 (Online) 29th June Morning Shift
MCQ (Single Correct Answer)  +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
$${5 \over 3}$$
3
JEE Main 2022 (Online) 28th June Morning Shift
MCQ (Single Correct Answer)  +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
$${{7 + 3\sqrt 5 } \over 2}$$
4
JEE Main 2022 (Online) 27th June Evening Shift
MCQ (Single Correct Answer)  +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
$$\left( {9,{{92} \over 9}} \right]$$
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