JEE Main · 2023 · 31 Jan 2023 · Shift 1 · Permutations and Combinations

Count the four-digit numbers from $1000$ to $2800$. Those divisible by $3$ run from $1002$ to $2799$, giving $\frac{2799-1002}{3}+1=600$. Those divisible by $11$ run from $1001$ to $2794$, giving $254-91+1=164$. Those divisible by $33$ run from $1023$ to $2772$, giving $84-31+1=54$. By inclusion and exclusion, the count divisible by $3$ or by $11$ is $600+164-54=710$.