1
JEE Main 2021 (Online) 26th August Morning Shift
+4
-1
If a line along a chord of the circle 4x2 + 4y2 + 120x + 675 = 0, passes through the point ($$-$$30, 0) and is tangent to the parabola y2 = 30x, then the length of this chord is :
A
5
B
7
C
5$${\sqrt 3 }$$
D
3$${\sqrt 5 }$$
2
JEE Main 2021 (Online) 27th July Evening Shift
+4
-1
Consider a circle C which touches the y-axis at (0, 6) and cuts off an intercept $$6\sqrt 5$$ on the x-axis. Then the radius of the circle C is equal to :
A
$$\sqrt {53}$$
B
9
C
8
D
$$\sqrt {82}$$
3
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
$$3(\sqrt 2 - 1)$$
4
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
$$1 + \sqrt 5$$
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