Let A=\xinmathbbR:[x+3]+[x+4]le3\ , B= \xinmathbbR:3^x (sum_r=1^inftyfrac310^r )^x-3<3^-3x \ , where [t] denotes greatest integer function. Then,

Sets, Relations and Function: Let A=\xinmathbbR:[x+3]+[x+4]le3\ , B= \xinmathbbR:3^x… | JEE Main 2023

JEE Main 2023 (Online) 6th April Morning ShiftQuestion 1

Let $A=\{x\in\mathbb{R}:[x+3]+[x+4]\le3\}$, $B=\left\{x\in\mathbb{R}:3^{x}\left(\sum_{r=1}^{\infty}\frac{3}{10^{r}}\right)^{x-3}<3^{-3x}\right\}$, where $[t]$ denotes greatest integer function. Then,

Sets, Relations and Function

$A=B$✓ Correct answer$A\subset B,\ A\neq B$$B\subset C,\ A\neq B$$A\cap B=\phi$

Solution

$[x+3]+[x+4]=2[x]+7\le3\Rightarrow[x]\le-2\Rightarrow x<-1$. $\sum 3/10^r=1/3$, so $3^x\cdot3^{-(x-3)}=27<3^{-3x}\Rightarrow -3x>3\Rightarrow x<-1$. $A=B$. Option (A).

Sets, Relations and Function - JEE Mathematics question (JEE Main 2023 (Online) 6th April Morning Shift)

More from Sets, Relations and Function