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1
JEE Main 2021 (Online) 18th March Morning Shift
MCQ (Single Correct Answer)
+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
2
JEE Main 2021 (Online) 17th March Evening Shift
MCQ (Single Correct Answer)
+4
-1
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
$${{125} \over {72}}$$
3
JEE Main 2021 (Online) 17th March Evening Shift
MCQ (Single Correct Answer)
+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
4
JEE Main 2021 (Online) 17th March Morning Shift
MCQ (Single Correct Answer)
+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$$\sqrt 4 $$
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