Let the sets A and B denote the domain and range respectively of the function $f(x)=\frac{1}{\sqrt{\lceil x\rceil-x}}$, where $\lceil x\rceil$ denotes the smallest integer greater than or equal to $x$. Then among the statements
(S1) : $A \cap B=(1, \infty)-\mathbb{N}$ and
(S2) : $A \cup B=(1, \infty)$
Previous 10 Questions — JEE Main 2023 (6 April Evening Shift)
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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)
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)
In a group of 100 persons, 75 speak English and 40 speak Hindi. Each person speaks at least one of the two
languages. I…
Topic: JEE Main 2023 (6 April Evening Shift)
\[
\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)
