1
JEE Main 2021 (Online) 18th March Evening Shift
+4
-1
Out of Syllabus
Let S1 : x2 + y2 = 9 and S2 : (x $$-$$ 2)2 + y2 = 1. Then the locus of center of a variable circle S which touches S1 internally and S2 externally always passes through the points :
A
$$\left( {{1 \over 2}, \pm {{\sqrt 5 } \over 2}} \right)$$
B
(1, $$\pm$$ 2)
C
$$\left( {2, \pm {3 \over 2}} \right)$$
D
(0, $$\pm$$ $$\sqrt 3$$)
2
JEE Main 2021 (Online) 18th March Morning Shift
+4
-1
Out of Syllabus
Choose the correct statement about two circles whose equations are given below :

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

x2 + y2 $$-$$ 22x $$-$$ 10y + 137 = 0
A
circles have same centre
B
circles have no meeting point
C
circles have only one meeting point
D
circles have two meeting points
3
JEE Main 2021 (Online) 18th March Morning Shift
+4
-1
For the four circles M, N, O and P, following four equations are given :

Circle M : x2 + y2 = 1

Circle N : x2 + y2 $$-$$ 2x = 0

Circle O : x2 + y2 $$-$$ 2x $$-$$ 2y + 1 = 0

Circle P : x2 + y2 $$-$$ 2y = 0

If the centre of circle M is joined with centre of the circle N, further center of circle N is joined with centre of the circle O, centre of circle O is joined with the centre of circle P and lastly, centre of circle P is joined with centre of circle M, then these lines form the sides of a :
A
Rhombus
B
Square
C
Rectangle
D
Parallelogram
4
JEE Main 2021 (Online) 17th March Evening Shift
+4
-1
Out of Syllabus
Let the tangent to the circle x2 + y2 = 25 at the point R(3, 4) meet x-axis and y-axis at points P and Q, respectively. If r is the radius of the circle passing through the origin O and having centre at the incentre of the triangle OPQ, then r2 is equal to :
A
$${{585} \over {66}}$$
B
$${{625} \over {72}}$$
C
$${{529} \over {64}}$$
D
$${{125} \over {72}}$$
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