1
JEE Main 2021 (Online) 27th August Evening Shift
Numerical
+4
-1
Out of Syllabus
Two circles each of radius 5 units touch each other at the point (1, 2). If the equation of their common tangent is 4x + 3y = 10, and C1($$\alpha$$, $$\beta$$) and C2($$\gamma$$, $$\delta$$), C1 $$\ne$$ C2 are their centres, then |($$\alpha$$ + $$\beta$$) ($$\gamma$$ + $$\delta$$)| is equal to ___________.
2
JEE Main 2021 (Online) 27th August Morning Shift
Numerical
+4
-1
Out of Syllabus
Let the equation x2 + y2 + px + (1 $$-$$ p)y + 5 = 0 represent circles of varying radius r $$\in$$ (0, 5]. Then the number of elements in the set S = {q : q = p2 and q is an integer} is __________.
3
JEE Main 2021 (Online) 26th August Morning Shift
Numerical
+4
-1
The locus of a point, which moves such that the sum of squares of its distances from the points (0, 0), (1, 0), (0, 1), (1, 1) is 18 units, is a circle of diameter d. Then d2 is equal to _____________.
4
JEE Main 2021 (Online) 17th March Morning Shift
Numerical
+4
-1
Out of Syllabus
The minimum distance between any two points P1 and P2 while considering point P1 on one circle and point P2 on the other circle for the given circles' equations

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

x2 + y2 $$-$$ 24x $$-$$ 10y + 160 = 0 is ___________.