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1
JEE Main 2021 (Online) 25th July Morning Shift
+4
-1
Let a parabola b be such that its vertex and focus lie on the positive x-axis at a distance 2 and 4 units from the origin, respectively. If tangents are drawn from O(0, 0) to the parabola P which meet P at S and R, then the area (in sq. units) of $$\Delta$$SOR is equal to :
A
$$16\sqrt 2$$
B
16
C
32
D
$$8\sqrt 2$$
2
JEE Main 2021 (Online) 25th July Morning Shift
+4
-1
Let an ellipse $$E:{{{x^2}} \over {{a^2}}} + {{{y^2}} \over {{b^2}}} = 1$$, $${a^2} > {b^2}$$, passes through $$\left( {\sqrt {{3 \over 2}} ,1} \right)$$ and has eccentricity $${1 \over {\sqrt 3 }}$$. If a circle, centered at focus F($$\alpha$$, 0), $$\alpha$$ > 0, of E and radius $${2 \over {\sqrt 3 }}$$, intersects E at two points P and Q, then PQ2 is equal to :
A
$${8 \over 3}$$
B
$${4 \over 3}$$
C
$${{16} \over 3}$$
D
3
3
JEE Main 2021 (Online) 22th July Evening Shift
+4
-1
Let a line L : 2x + y = k, k > 0 be a tangent to the hyperbola x2 $$-$$ y2 = 3. If L is also a tangent to the parabola y2 = $$\alpha$$x, then $$\alpha$$ is equal to :
A
12
B
$$-$$12
C
24
D
$$-$$24
4
JEE Main 2021 (Online) 22th July Evening Shift
Let $${E_1}:{{{x^2}} \over {{a^2}}} + {{{y^2}} \over {{b^2}}} = 1,a > b$$. Let E2 be another ellipse such that it touches the end points of major axis of E1 and the foci of E2 are the end points of minor axis of E1. If E1 and E2 have same eccentricities, then its value is :
$${{ - 1 + \sqrt 5 } \over 2}$$
$${{ - 1 + \sqrt 8 } \over 2}$$
$${{ - 1 + \sqrt 3 } \over 2}$$
$${{ - 1 + \sqrt 6 } \over 2}$$