1
JEE Main 2021 (Online) 27th August Evening Shift
Numerical
+4
-1
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
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
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 ___________.
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