Let $E:\ \dfrac{x^{2}}{a^{2}}+\dfrac{y^{2}}{b^{2}}=1,\ a>b$ and $H:\ \dfrac{x^{2}}{A^{2}}-\dfrac{y^{2}}{B^{2}}=1$. Let the distance between the foci of $E$ and the foci of $H$ be $2\sqrt{3}$. If $a-A=2$, and the ratio of the eccentricities of $E$ and $H$ is $\dfrac{1}{3}$, then the sum of the lengths of their latus recta is equal to:
Previous 10 Questions — JEE Main 2025 (22 January Evening Shift)
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Let $P(4,4\sqrt{3})$ be a point on the parabola $y^{2}=4ax$ and $PQ$ be a focal chord of the parabola. If $M$ and $N$ a…
Topic: JEE Main 2025 (22 January Evening Shift)
Suppose that the number of terms in an A.P. is $2k$, $k\in\mathbb{N}$. If the sum of all odd terms of the A.P. is $40$,…
Topic: JEE Main 2025 (22 January Evening Shift)
Let the curve $z(1+i)+\overline{z}(1-i)=4,\ z\in\mathbb{C}$, divide the region $|z-3|\le 1$ into two parts of areas $\a…
Topic: JEE Main 2025 (22 January Evening Shift)
Let $A=\{1,2,3,4\}$ and $B=\{1,4,9,16\}$. Then the number of many-one functions $f:A\to B$ such that $1\in f(A)$ is equ…
Topic: JEE Main 2025 (22 January Evening Shift)
Let $f(x)=\displaystyle \int_{0}^{e^{x^{2}}}\frac{t^{2}-8t+15}{e^{t}}\,dt,\ x\in\mathbb{R}$.
Then the numbers of loca…
Topic: JEE Main 2025 (22 January Evening Shift)
If $\displaystyle \lim_{x\to\infty}\left(\frac{e}{1-e}\left(\frac{1}{e}-\frac{x}{1+x}\right)\right)^{x}=\alpha$, then t…
Topic: JEE Main 2025 (22 January Evening Shift)
In a group of 3 girls and 4 boys, there are two boys $B_1$ and $B_2$. The number of ways in which these girls and boys …
Topic: JEE Main 2025 (22 January Evening Shift)
The area of the region enclosed by the curves $y=x^2-4 x+4$ and $y^2=16-8 x$ is :
Topic: JEE Main 2025 (22 January Evening Shift)
Let $\vec{a}$ and $\vec{b}$ be two unit vectors such that the angle between them is $\frac{\pi}{3}$. If $\lambda \vec{a…
Topic: JEE Main 2025 (22 January Evening Shift)
If $\displaystyle \int e^{x}\!\left(\frac{x\sin^{-1}x}{\sqrt{1-x^{2}}}+\frac{\sin^{-1}x}{(1-x^{2})^{3/2}}+\frac{x}{1-x^…
Topic: JEE Main 2025 (22 January Evening Shift)
