1
JEE Main 2021 (Online) 27th July Morning Shift
+4
-1
Two tangents are drawn from the point P($$-$$1, 1) to the circle x2 + y2 $$-$$ 2x $$-$$ 6y + 6 = 0. If these tangents touch the circle at points A and B, and if D is a point on the circle such that length of the segments AB and AD are equal, then the area of the triangle ABD is equal to :
A
2
B
$$(3\sqrt 2 + 2)$$
C
4
D
$$3(\sqrt 2 - 1)$$
2
JEE Main 2021 (Online) 27th July Morning Shift
+4
-1
Let $$A = \{ (x,y) \in R \times R|2{x^2} + 2{y^2} - 2x - 2y = 1\}$$, $$B = \{ (x,y) \in R \times R|4{x^2} + 4{y^2} - 16y + 7 = 0\}$$ and $$C = \{ (x,y) \in R \times R|{x^2} + {y^2} - 4x - 2y + 5 \le {r^2}\}$$.

Then the minimum value of |r| such that $$A \cup B \subseteq C$$ is equal to
A
$${{3 + \sqrt {10} } \over 2}$$
B
$${{2 + \sqrt {10} } \over 2}$$
C
$${{3 + 2\sqrt 5 } \over 2}$$
D
$$1 + \sqrt 5$$
3
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
4
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
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