JEE Main 2024 (Online) 8th April Morning ShiftQuestion 1
Let $[t]$ be the greatest integer less than or equal to $t$. Let $A$ be the set of all prime factors of $2310$ and $f:A\to\mathbb{Z}$ be the function $f(x)=\left[\log_2\left(x^{2}+\left[\frac{x^{3}}{5}\right]\right)\right]$. The number of one-to-one functions from $A$ to the range of $f$ is
Sets, Relations and Function
Solution
$2310=2\cdot3\cdot5\cdot7\cdot11$. $f(2)=[\log_2 5]=2$, $f(3)=[\log_2 14]=3$, $f(5)=[\log_2 50]=5$, $f(7)=[\log_2 117]=6$, $f(11)=[\log_2 387]=8$. Range has 5 elements; one-one functions $A\to$ range: $5!=120$. Option (C).