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1
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$$\sqrt 4$$
2
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.
3
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
$${\sqrt {7} }$$
4
JEE Main 2021 (Online) 26th February Evening Shift
+4
-1
Let A(1, 4) and B(1, $$-$$5) be two points. Let P be a point on the circle
(x $$-$$ 1)2 + (y $$-$$ 1)2 = 1 such that (PA)2 + (PB)2 have maximum value, then the points, P, A and B lie on :
A
a straight line
B
an ellipse
C
a parabola
D
a hyperbola
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