1
JEE Main 2021 (Online) 18th March Evening Shift
+4
-1
Out of Syllabus
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
$${{\pi \over 4}}$$
2
JEE Main 2021 (Online) 16th March Evening Shift
+4
-1
Out of Syllabus
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
3
JEE Main 2021 (Online) 25th February Evening Shift
+4
-1
If the curve x2 + 2y2 = 2 intersects the line x + y = 1 at two points P and Q, then the angle subtended by the line segment PQ at the origin is :
A
$${\pi \over 2} - {\tan ^{ - 1}}\left( {{1 \over 4}} \right)$$
B
$${\pi \over 2} + {\tan ^{ - 1}}\left( {{1 \over 3}} \right)$$
C
$${\pi \over 2} - {\tan ^{ - 1}}\left( {{1 \over 3}} \right)$$
D
$${\pi \over 2} + {\tan ^{ - 1}}\left( {{1 \over 4}} \right)$$
4
JEE Main 2020 (Online) 6th September Evening Slot
+4
-1
Out of Syllabus
If the normal at an end of a latus rectum of an ellipse passes through an extremity of the minor axis, then the eccentricity e of the ellipse satisfies :
A
e4 + 2e2 – 1 = 0
B
e4 + e2 – 1 = 0
C
e2 + 2e – 1 = 0
D
e2 + e – 1 = 0
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