JEE Main 2023 (Online) 29th January Evening ShiftQuestion 1
The total number of $4$-digit numbers whose greatest common divisor with $54$ is $2$, is
Permutation and Combination
Answer$3000$
Solution
$\gcd(n,54)=2$ iff $n$ is even and $3\nmid n$: $4500$ even four-digit numbers minus $1500$ multiples of $6$ gives $3000$.