In a group of 100 persons, 75 speak English and 40 speak Hindi. Each person speaks at least one of the two languages. If the number of persons who speak only English is $\alpha$ and the number of persons who speak only Hindi is $\beta$, then the eccentricity of the ellipse \[ 25\big(\beta^2 x^2 + \alpha^2 y^2\big)=\alpha^2\beta^2 \] is:
Previous 10 Questions — JEE Main 2023 (6 April Evening Shift)
Nearest first
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\[
\lim_{n\to\infty} \left\{ \left(2^{\tfrac12}-2^{\tfrac13}\right)\left(2^{\tfrac12}-2^{\tfrac15}\right)\cdots\left(2^…
Topic: JEE Main 2023 (6 April Evening Shift)
Let \(f(x)\) be a function satisfying \(f(x)+f(\pi-x)=\pi^{2}\), \(\forall x\in\mathbb{R}\).
Then \(\displaystyle \int_…
Topic: JEE Main 2023 (6 April Evening Shift)
If the solution curve $f(x,y)=0$ of the differential equation
$(1+\log_e x)\frac{dx}{dy}-x\log_e x=e^y,\; x>0,$
pas…
Topic: JEE Main 2023 (6 April Evening Shift)
Among the statements:
(S1): $2023^{2022}-1999^{2022}$ is divisible by $8$.
(S2): $13(13)^n-12n-13$ is divisible by $1…
Topic: JEE Main 2023 (6 April Evening Shift)
Let $P$ be a square matrix such that $P^{2}=I-P$.
For $\alpha,\beta,\gamma,\delta\in\mathbb{N}$, if
$P^{\alpha}+P^{…
Topic: JEE Main 2023 (6 April Evening Shift)
Let $a\ne b$ be two non-zero real numbers. Then the number of elements in the set
$X=\{\, z\in\mathbb{C} : \operatorn…
Topic: JEE Main 2023 (6 April Evening Shift)
The area bounded by the curves $y=\lvert x-1\rvert+\lvert x-2\rvert$ and $y=3$ is equal to:
Topic: JEE Main 2023 (6 April Evening Shift)
If the coefficient of $x^{7}$ in $\left(a x^{2}+\dfrac{1}{2 b x}\right)^{11}$ and $x^{-7}$ in $\left(a x-\dfrac{1}{3 b …
Topic: JEE Main 2023 (6 April Evening Shift)
All the letters of the word PUBLIC are written in all possible orders and these words are written as in a dictionary wi…
Topic: JEE Main 2023 (6 April Evening Shift)
Next 10 Questions — JEE Main 2023 (6 April Evening Shift)
Ascending by ID
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Three dice are rolled. If the probability of getting different numbers on the three dice is $\frac{p}{q}$, where $p$ an…
Topic: JEE Main 2023 (6 April Evening Shift)
For the system of equations
\[
\begin{cases}
x+y+z=6,\\
x+2y+\alpha z=10,\\
x+3y+5z=\beta,
\end{cases}
\]
which one of …
Topic: JEE Main 2023 (6 April Evening Shift)
Let the sets A and B denote the domain and range respectively of the function $f(x)=\frac{1}{\sqrt{\lceil x\rceil-x}}$,…
Topic: JEE Main 2023 (6 April Evening Shift)
