JEE Maths PYQ Practice, chapter-wise

JEE Main 2021 (Online) 26th August Morning ShiftQuestion 1

On the ellipse $\frac{x^{2}}{8}+\frac{y^{2}}{4}=1$ let $P$ be a point in the second quadrant such that the tangent at $P$ to the ellipse is perpendicular to the line $x+2y=0$. Let $S$ and $S'$ be the foci of the ellipse and $e$ be its eccentricity. If $A$ is the area of the triangle $SPS'$ then, the value of $(5-e^{2})\cdot A$ is :

Ellipse

$24$$14$$12$$6$

JEE Main 2021 (Online) 3rd August Evening ShiftQuestion 2

If an ellipse passes through the point $(4,1)$ and has foci at $(\pm3,0)$, then its eccentricity is

Ellipse

$\frac{2\sqrt{2}}{3}$$\frac{\sqrt{2}}{3}$$\frac{1}{\sqrt{2}}$$\frac{1}{2}$

JEE Main 2021 (Online) 31st August Evening ShiftQuestion 3

An angle of intersection of the curves, $\frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1$ and $x^{2}+y^{2}=ab$, $a>b$, is :

Ellipse

$\tan^{-1}\left(\frac{a-b}{\sqrt{ab}}\right)$$\tan^{-1}\left(\frac{a+b}{\sqrt{ab}}\right)$$\tan^{-1}\left(\frac{a-b}{2\sqrt{ab}}\right)$$\tan^{-1}\left(2\sqrt{ab}\right)$

JEE Main 2021 (Online) 25th July Evening ShiftQuestion 4

If a tangent to the ellipse $x^{2}+4y^{2}=4$ meets the tangents at the extremities of its major axis at $B$ and $C$, then the circle with $BC$ as diameter passes through the point :

Ellipse

$(\sqrt{3},0)$$(1,1)$$(-1,1)$$(\sqrt{2},0)$

JEE Main 2023 (Online) 10th April Morning ShiftQuestion 5

Let the ellipse $E:x^{2}+9y^{2}=9$ intersect the positive $x$- and $y$-axes at the points $A$ and $B$ respectively. Let the major axis of $E$ be a diameter of the circle $C$. Let the line passing through $A$ and $B$ meet the circle $C$ at the point $P$. If the area of the triangle with vertices $A$, $P$ and the origin $O$ is $\frac{m}{n}$, where $m$ and $n$ are coprime, then $m-n$ is equal to

Ellipse

$15$$16$$17$$18$