JEE Maths PYQ Practice, chapter-wise

JEE Main 2024 (Online) 9th April Evening ShiftQuestion 1

Let the foci of a hyperbola $H$ coincide with the foci of the ellipse $E:\frac{(x-1)^{2}}{100}+\frac{(y-1)^{2}}{75}=1$ and the eccentricity of the hyperbola $H$ be the reciprocal of the eccentricity of the ellipse $E$. If the length of the transverse axis of $H$ is $\alpha$ and the length of its conjugate axis is $\beta$, then $3\alpha^{2}+2\beta^{2}$ is equal to

Hyperbola

$205$$242$$237$$225$

JEE Main 2022 (Online) 25th July Evening ShiftQuestion 2

Let the foci of the ellipse $\frac{x^2}{16}+\frac{y^2}{7}=1$ and the hyperbola $\frac{x^2}{144}-\frac{y^2}{\alpha}=\frac{1}{25}$ coincide. Then the length of the latus rectum of the hyperbola is :

Hyperbola

$\frac{32}{9}$$\frac{18}{5}$$\frac{27}{4}$$\frac{27}{10}$

JEE Main 2022 (Online) 26th June Evening ShiftQuestion 3

The normal to the hyperbola $\frac{x^{2}}{a^{2}}-\frac{y^{2}}{9}=1$ at the point $(8,3\sqrt{3})$ on it passes through the point :

Hyperbola

$\left(15,-2\sqrt{3}\right)$$\left(9,2\sqrt{3}\right)$$\left(-1,9\sqrt{3}\right)$$\left(-1,6\sqrt{3}\right)$

JEE Main 2026 (Online) 5th April Evening ShiftQuestion 4

Let the eccentricity $e$ of a hyperbola satisfy the equation $6e^{2}-11e+3=0$. If the foci of the hyperbola are $(3,5)$ and $(3,-4)$, then the length of its latus rectum is :

Hyperbola

$\frac{11}{3}$$\frac{17}{3}$$\frac{15}{2}$$\frac{17}{2}$

JEE Main 2024 (Online) 30th January Evening ShiftQuestion 5

Let $P$ be a point on the hyperbola $H:\frac{x^{2}}{9}-\frac{y^{2}}{4}=1$, in the first quadrant such that the area of triangle formed by $P$ and the two foci of $H$ is $2\sqrt{13}$. Then, the square of the distance of $P$ from the origin is

Hyperbola

$18$$20$$22$$26$