1

JEE Main 2021 (Online) 25th July Evening Shift

MCQ (Single Correct Answer)

+4

-1

Out of Syllabus

If a tangent to the ellipse x

^{2}+ 4y^{2}= 4 meets the tangents at the extremities of it major axis at B and C, then the circle with BC as diameter passes through the point :2

JEE Main 2021 (Online) 25th July Morning Shift

MCQ (Single Correct Answer)

+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 PQ

^{2}is equal to :3

JEE Main 2021 (Online) 22th July Evening Shift

MCQ (Single Correct Answer)

+4

-1

Let $${E_1}:{{{x^2}} \over {{a^2}}} + {{{y^2}} \over {{b^2}}} = 1,a > b$$. Let E

_{2}be another ellipse such that it touches the end points of major axis of E_{1}and the foci of E_{2}are the end points of minor axis of E_{1}. If E_{1}and E_{2}have same eccentricities, then its value is :4

JEE Main 2021 (Online) 18th March Evening Shift

MCQ (Single Correct Answer)

+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 :

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