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1
JEE Main 2021 (Online) 17th March Evening Shift
+4
-1
Two tangents are drawn from a point P to the circle x2 + y2 $$-$$ 2x $$-$$ 4y + 4 = 0, such that the angle between these tangents is $${\tan ^{ - 1}}\left( {{{12} \over 5}} \right)$$, where $${\tan ^{ - 1}}\left( {{{12} \over 5}} \right)$$ $$\in$$(0, $$\pi$$). If the centre of the circle is denoted by C and these tangents touch the circle at points A and B, then the ratio of the areas of $$\Delta$$PAB and $$\Delta$$CAB is :
A
3 : 1
B
9 : 4
C
2 : 1
D
11 : 4
2
JEE Main 2021 (Online) 17th March Morning Shift
+4
-1
The line 2x $$-$$ y + 1 = 0 is a tangent to the circle at the point (2, 5) and the centre of the circle lies on x $$-$$ 2y = 4. Then, the radius of the circle is :
A
5$$\sqrt 3$$
B
4$$\sqrt 5$$
C
3$$\sqrt 5$$
D
5$$\sqrt 4$$
3
JEE Main 2021 (Online) 17th March Morning Shift
+4
-1
Choose the incorrect statement about the two circles whose equations are given below :

x2 + y2 $$-$$ 10x $$-$$ 10y + 41 = 0 and

x2 + y2 $$-$$ 16x $$-$$ 10y + 80 = 0
A
Distance between two centres is the average of radii of both the circles.
B
Both circles pass through the centre of each other.
C
Circles have two intersection points.
D
Both circle's centers lie inside region of one another.
4
JEE Main 2021 (Online) 16th March Evening Shift
+4
-1
Let the lengths of intercepts on x-axis and y-axis made by the circle
x2 + y2 + ax + 2ay + c = 0, (a < 0) be 2$${\sqrt 2 }$$ and 2$${\sqrt 5 }$$, respectively. Then the shortest distance from origin to a tangent to this circle which is perpendicular to the line x + 2y = 0, is equal to :
A
$${\sqrt {10} }$$
B
$${\sqrt {6} }$$
C
$${\sqrt {11} }$$
D
$${\sqrt {7} }$$
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