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1
JEE Main 2021 (Online) 22th July Evening Shift
+4
-1
Let the circle S : 36x2 + 36y2 $$-$$ 108x + 120y + C = 0 be such that it neither intersects nor touches the co-ordinate axes. If the point of intersection of the lines, x $$-$$ 2y = 4 and 2x $$-$$ y = 5 lies inside the circle S, then :
A
$${{25} \over 9} < C < {{13} \over 3}$$
B
100 < C < 165
C
81 < C < 156
D
100 < C < 156
2
JEE Main 2021 (Online) 20th July Evening Shift
+4
-1
Let r1 and r2 be the radii of the largest and smallest circles, respectively, which pass through the point ($$-$$4, 1) and having their centres on the circumference of the circle x2 + y2 + 2x + 4y $$-$$ 4 = 0. If $${{{r_1}} \over {{r_2}}} = a + b\sqrt 2$$, then a + b is equal to :
A
3
B
11
C
5
D
7
3
JEE Main 2021 (Online) 18th March Evening Shift
+4
-1
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, $$\pm$$ $$\sqrt 3$$)
4
JEE Main 2021 (Online) 18th March Morning Shift
+4
-1
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
Policy