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1
JEE Main 2021 (Online) 18th March Evening Shift
+4
-1
Consider a hyperbola H : x2 $$-$$ 2y2 = 4. Let the tangent at a
point P(4, $${\sqrt 6 }$$) meet the x-axis at Q and latus rectum at R(x1, y1), x1 > 0. If F is a focus of H which is nearer to the point P, then the area of $$\Delta$$QFR is equal to :
A
$${\sqrt 6 }$$ $$-$$ 1
B
$${7 \over {\sqrt 6 }}$$ $$-$$ 2
C
$${4\sqrt 6 }$$ $$-$$ 1
D
$${4\sqrt 6 }$$
2
JEE Main 2021 (Online) 18th March Evening Shift
+4
-1
Let a tangent be drawn to the ellipse $${{{x^2}} \over {27}} + {y^2} = 1$$ at $$(3\sqrt 3 \cos \theta ,\sin \theta )$$ where $$0 \in \left( {0,{\pi \over 2}} \right)$$. Then the value of $$\theta$$ such that the sum of intercepts on axes made by this tangent is minimum is equal to :
A
$${{\pi \over 6}}$$
B
$${{\pi \over 3}}$$
C
$${{\pi \over 8}}$$
D
$${{\pi \over 4}}$$
3
JEE Main 2021 (Online) 17th March Evening Shift
+4
-1
Let L be a tangent line to the parabola y2 = 4x $$-$$ 20 at (6, 2). If L is also a tangent to the ellipse $${{{x^2}} \over 2} + {{{y^2}} \over b} = 1$$, then the value of b is equal to:
A
20
B
14
C
16
D
11
4
JEE Main 2021 (Online) 16th March Evening Shift
+4
-1
If the points of intersections of the ellipse $${{{x^2}} \over {16}} + {{{y^2}} \over {{b^2}}} = 1$$ and the
circle x2 + y2 = 4b, b > 4 lie on the curve y2 = 3x2, then b is equal to :
A
12
B
10
C
6
D
5
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